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\n\u2003\u2003\u95ee\u9898\u56db\u95ee\u9898\u5206\u6790
\n\u2003\u2003\u9488\u5bf9\u692d\u5706\u5185\u90e8\u56db\u5757\u9700\u8fc7\u6865\u8fde\u63a5\u7684\u5c0f\u578b\u77e9\u5f62\u96f6\u4ef6\u5e03\u5c40，\u672c\u9898\u878d\u5408\u56fe\u8bba\u8fde\u901a\u6027\u7ea6\u675f\u4e0e\u51e0\u4f55\u8ddd\u79bb\u4f18\u5316\u53cc\u91cd\u5185\u5bb9\u3002\u9996\u5148\u5229\u7528\u6700\u5c0f\u751f\u6210\u6811\u7406\u8bba\u5224\u5b9a\u8fde\u901a\u56db\u5757\u96f6\u4ef6\u6700\u5c11\u9700\u8981 3 \u5ea7\u8fc7\u6865，2 \u6865\u65b9\u6848\u65e0\u6cd5\u6ee1\u8db3\u96f6\u4ef6\u4e0d\u6389\u843d\u5de5\u827a\u8981\u6c42，4 \u6865\u4f1a\u4ea7\u751f\u5197\u4f59\u7a7a\u7a0b；\u5176\u6b21\u5efa\u7acb\u8fc7\u6865\u51e0\u4f55\u7ea6\u675f\u6a21\u578b，\u6838\u9a8c\u6865\u5bbd 2\u3001\u6865\u4e0e\u96f6\u4ef6\u9876\u70b9\u51c0\u8ddd\u4e0d\u5c0f\u4e8e 1 \u7684\u786c\u6027\u6761\u4ef6；\u6700\u540e\u6574\u5408\u56db\u5706\u5b54\u5f80\u8fd4\u3001\u692d\u5706\u63a5\u5165\u3001\u8fc7\u6865\u8de8\u8d8a\u3001\u7ec4\u5408\u4ef6\u4e0e\u692d\u5706\u8f6c\u79fb\u56db\u7c7b\u7a7a\u7a0b\u5206\u91cf\u6784\u5efa\u603b\u76ee\u6807\u51fd\u6570，\u901a\u8fc7\u8fc7\u6865\u6570\u91cf\u3001\u6865\u5bbd\u7075\u654f\u5ea6\u5206\u6790\u5bf9\u6bd4\u4e0d\u540c\u65b9\u6848\u7ecf\u6d4e\u6027，\u8f93\u51fa\u6ee1\u8db3\u5168\u90e8\u51e0\u4f55\u4e0e\u5de5\u827a\u7ea6\u675f\u7684\u6700\u5c0f\u7a7a\u7a0b\u7ed3\u679c\u3002<\/font><\/font><\/font><\/font><\/font><\/font><\/font><\/font><\/p>\n

\u6a21\u578b\u7684\u5efa\u7acb\u4e0e\u6c42\u89e3\u6574\u4f53\u8bba\u6587\u7f29\u7565\u56fe<\/font><\/h4>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u5168\u90e8\u8bba\u6587\u8bf7\u89c1\u4e0b\u65b9\u201c \u53ea\u4f1a\u5efa\u6a21 QQ\u540d\u7247\u201d \u70b9\u51fbQQ\u540d\u7247\u5373\u53ef<\/h6>\n

\u7a0b\u5e8f\u4ee3\u7801：<\/font><\/h4>\n

from<\/span> __future__ import<\/span> annotations<\/p>\n

import<\/span> argparse
\nimport<\/span> json
\nimport<\/span> math
\nimport<\/span> random
\nfrom<\/span> dataclasses import<\/span> dataclass
\nfrom<\/span> pathlib import<\/span> Path
\nfrom<\/span> typing import<\/span> Dict,<\/span> Iterable,<\/span> List,<\/span> Sequence,<\/span> Tuple<\/p>\n

import<\/span> matplotlib
\nmatplotlib.<\/span>use(<\/span>"Agg"<\/span>)<\/span>
\nimport<\/span> matplotlib.<\/span>pyplot as<\/span> plt
\nfrom<\/span> matplotlib import<\/span> font_manager
\nfrom<\/span> matplotlib.<\/span>patches import<\/span> Circle,<\/span> Ellipse,<\/span> Polygon,<\/span> Rectangle
\nimport<\/span> networkx as<\/span> nx
\nimport<\/span> numpy as<\/span> np
\nimport<\/span> pandas as<\/span> pd
\nfrom<\/span> scipy.<\/span>spatial.<\/span>distance import<\/span> cdist
\nfrom<\/span> scipy.<\/span>stats import<\/span> gaussian_kde,<\/span> kurtosis,<\/span> skew<\/p>\n

Point =<\/span> Tuple[<\/span>float<\/span>,<\/span> float<\/span>]<\/span><\/p>\n

# —————————————————————————–<\/span>
\n# 0. \u7ed8\u56fe\u4e0e\u901a\u7528\u5de5\u5177<\/span>
\n# —————————————————————————–<\/span>
\ndef<\/span> configure_chinese_font<\/span>(<\/span>)<\/span> –<\/span>><\/span> str<\/span>:<\/span>
\n """\u6ce8\u518c\u4e2d\u6587\u5b57\u4f53，\u907f\u514d\u6807\u9898\u3001\u56fe\u4f8b\u548c\u5750\u6807\u8f74\u51fa\u73b0\u65b9\u6846\u3002"""<\/span>
\n candidates =<\/span> [<\/span>
\n "\/usr\/share\/fonts\/opentype\/noto\/NotoSansCJK-Regular.ttc"<\/span>,<\/span>
\n "\/usr\/share\/fonts\/opentype\/noto\/NotoSansCJK-Bold.ttc"<\/span>,<\/span>
\n "\/usr\/share\/fonts\/truetype\/arphic-gbsn00lp\/gbsn00lp.ttf"<\/span>,<\/span>
\n ]<\/span>
\n selected =<\/span> None<\/span>
\n for<\/span> path in<\/span> candidates:<\/span>
\n if<\/span> Path(<\/span>path)<\/span>.<\/span>exists(<\/span>)<\/span>:<\/span>
\n font_manager.<\/span>fontManager.<\/span>addfont(<\/span>path)<\/span>
\n selected =<\/span> font_manager.<\/span>FontProperties(<\/span>fname=<\/span>path)<\/span>.<\/span>get_name(<\/span>)<\/span>
\n break<\/span>
\n if<\/span> selected is<\/span> None<\/span>:<\/span>
\n for<\/span> name in<\/span> [<\/span>"Noto Sans CJK SC"<\/span>,<\/span> "SimHei"<\/span>,<\/span> "Microsoft YaHei"<\/span>,<\/span> "Arial Unicode MS"<\/span>]<\/span>:<\/span>
\n try<\/span>:<\/span>
\n font_manager.<\/span>findfont(<\/span>name,<\/span> fallback_to_default=<\/span>False<\/span>)<\/span>
\n selected =<\/span> name
\n break<\/span>
\n except<\/span> Exception:<\/span>
\n continue<\/span>
\n if<\/span> selected is<\/span> None<\/span>:<\/span>
\n raise<\/span> RuntimeError(<\/span>"\u672a\u68c0\u6d4b\u5230\u53ef\u7528\u4e2d\u6587\u5b57\u4f53，\u8bf7\u5b89\u88c5 Noto Sans CJK SC \u540e\u91cd\u8bd5\u3002"<\/span>)<\/span>
\n plt.<\/span>rcParams.<\/span>update(<\/span>{<\/span>
\n "font.family"<\/span>:<\/span> selected,<\/span>
\n "font.sans-serif"<\/span>:<\/span> [<\/span>selected]<\/span>,<\/span>
\n "axes.unicode_minus"<\/span>:<\/span> False<\/span>,<\/span>
\n "figure.dpi"<\/span>:<\/span> 130<\/span>,<\/span>
\n "savefig.dpi"<\/span>:<\/span> 220<\/span>,<\/span>
\n "axes.titlesize"<\/span>:<\/span> 12<\/span>,<\/span>
\n "axes.labelsize"<\/span>:<\/span> 10<\/span>,<\/span>
\n "legend.fontsize"<\/span>:<\/span> 9<\/span>,<\/span>
\n }<\/span>)<\/span>
\n return<\/span> selected<\/p>\n

def<\/span> euclidean<\/span>(<\/span>a:<\/span> np.<\/span>ndarray,<\/span> b:<\/span> np.<\/span>ndarray)<\/span> –<\/span>><\/span> float<\/span>:<\/span>
\n return<\/span> float<\/span>(<\/span>np.<\/span>linalg.<\/span>norm(<\/span>a –<\/span> b)<\/span>)<\/span><\/p>\n

def<\/span> savefig<\/span>(<\/span>path:<\/span> Path)<\/span> –<\/span>><\/span> None<\/span>:<\/span>
\n path.<\/span>parent.<\/span>mkdir(<\/span>parents=<\/span>True<\/span>,<\/span> exist_ok=<\/span>True<\/span>)<\/span>
\n plt.<\/span>tight_layout(<\/span>)<\/span>
\n plt.<\/span>savefig(<\/span>path,<\/span> bbox_inches=<\/span>"tight"<\/span>)<\/span>
\n plt.<\/span>close(<\/span>)<\/span><\/p>\n

def<\/span> sample_polyline<\/span>(<\/span>vertices:<\/span> Sequence[<\/span>Point]<\/span>,<\/span> n_per_segment:<\/span> int<\/span> =<\/span> 20<\/span>,<\/span>
\n closed:<\/span> bool<\/span> =<\/span> True<\/span>)<\/span> –<\/span>><\/span> np.<\/span>ndarray:<\/span>
\n pts:<\/span> List[<\/span>np.<\/span>ndarray]<\/span> =<\/span> [<\/span>]<\/span>
\n n_seg =<\/span> len<\/span>(<\/span>vertices)<\/span> if<\/span> closed else<\/span> len<\/span>(<\/span>vertices)<\/span> –<\/span> 1<\/span>
\n for<\/span> i in<\/span> range<\/span>(<\/span>n_seg)<\/span>:<\/span>
\n a =<\/span> np.<\/span>asarray(<\/span>vertices[<\/span>i]<\/span>,<\/span> dtype=<\/span>float<\/span>)<\/span>
\n b =<\/span> np.<\/span>asarray(<\/span>vertices[<\/span>(<\/span>i +<\/span> 1<\/span>)<\/span> %<\/span> len<\/span>(<\/span>vertices)<\/span>]<\/span>,<\/span> dtype=<\/span>float<\/span>)<\/span>
\n for<\/span> t in<\/span> np.<\/span>linspace(<\/span>0<\/span>,<\/span> 1<\/span>,<\/span> n_per_segment,<\/span> endpoint=<\/span>False<\/span>)<\/span>:<\/span>
\n pts.<\/span>append(<\/span>a +<\/span> t *<\/span> (<\/span>b –<\/span> a)<\/span>)<\/span>
\n if<\/span> not<\/span> closed:<\/span>
\n pts.<\/span>append(<\/span>np.<\/span>asarray(<\/span>vertices[<\/span>–<\/span>1<\/span>]<\/span>,<\/span> dtype=<\/span>float<\/span>)<\/span>)<\/span>
\n return<\/span> np.<\/span>asarray(<\/span>pts)<\/span><\/p>\n

def<\/span> sample_rectangle<\/span>(<\/span>x1:<\/span> float<\/span>,<\/span> y1:<\/span> float<\/span>,<\/span> x2:<\/span> float<\/span>,<\/span> y2:<\/span> float<\/span>,<\/span>
\n n_per_side:<\/span> int<\/span> =<\/span> 16<\/span>)<\/span> –<\/span>><\/span> np.<\/span>ndarray:<\/span>
\n return<\/span> sample_polyline(<\/span>[<\/span>(<\/span>x1,<\/span> y1)<\/span>,<\/span> (<\/span>x2,<\/span> y1)<\/span>,<\/span> (<\/span>x2,<\/span> y2)<\/span>,<\/span> (<\/span>x1,<\/span> y2)<\/span>]<\/span>,<\/span>
\n n_per_side,<\/span> True<\/span>)<\/span><\/p>\n

def<\/span> sample_circle<\/span>(<\/span>cx:<\/span> float<\/span>,<\/span> cy:<\/span> float<\/span>,<\/span> r:<\/span> float<\/span>,<\/span> n:<\/span> int<\/span> =<\/span> 360<\/span>)<\/span> –<\/span>><\/span> np.<\/span>ndarray:<\/span>
\n theta =<\/span> np.<\/span>linspace(<\/span>0<\/span>,<\/span> 2<\/span> *<\/span> np.<\/span>pi,<\/span> n,<\/span> endpoint=<\/span>False<\/span>)<\/span>
\n return<\/span> np.<\/span>column_stack(<\/span>[<\/span>cx +<\/span> r *<\/span> np.<\/span>cos(<\/span>theta)<\/span>,<\/span> cy +<\/span> r *<\/span> np.<\/span>sin(<\/span>theta)<\/span>]<\/span>)<\/span><\/p>\n

def<\/span> sample_ellipse<\/span>(<\/span>cx:<\/span> float<\/span>,<\/span> cy:<\/span> float<\/span>,<\/span> rx:<\/span> float<\/span>,<\/span> ry:<\/span> float<\/span>,<\/span>
\n n:<\/span> int<\/span> =<\/span> 720<\/span>)<\/span> –<\/span>><\/span> np.<\/span>ndarray:<\/span>
\n theta =<\/span> np.<\/span>linspace(<\/span>0<\/span>,<\/span> 2<\/span> *<\/span> np.<\/span>pi,<\/span> n,<\/span> endpoint=<\/span>False<\/span>)<\/span>
\n return<\/span> np.<\/span>column_stack(<\/span>[<\/span>cx +<\/span> rx *<\/span> np.<\/span>cos(<\/span>theta)<\/span>,<\/span> cy +<\/span> ry *<\/span> np.<\/span>sin(<\/span>theta)<\/span>]<\/span>)<\/span><\/p>\n

def<\/span> minimum_distance<\/span>(<\/span>a:<\/span> np.<\/span>ndarray,<\/span> b:<\/span> np.<\/span>ndarray)<\/span> –<\/span>><\/span> Tuple[<\/span>float<\/span>,<\/span> np.<\/span>ndarray,<\/span> np.<\/span>ndarray]<\/span>:<\/span>
\n dist =<\/span> cdist(<\/span>a,<\/span> b)<\/span>
\n i,<\/span> j =<\/span> np.<\/span>unravel_index(<\/span>np.<\/span>argmin(<\/span>dist)<\/span>,<\/span> dist.<\/span>shape)<\/span>
\n return<\/span> float<\/span>(<\/span>dist[<\/span>i,<\/span> j]<\/span>)<\/span>,<\/span> a[<\/span>i]<\/span>.<\/span>copy(<\/span>)<\/span>,<\/span> b[<\/span>j]<\/span>.<\/span>copy(<\/span>)<\/span><\/p>\n

def<\/span> polyline_length<\/span>(<\/span>vertices:<\/span> Sequence[<\/span>Point]<\/span>,<\/span> closed:<\/span> bool<\/span> =<\/span> True<\/span>)<\/span> –<\/span>><\/span> float<\/span>:<\/span>
\n arr =<\/span> np.<\/span>asarray(<\/span>vertices,<\/span> dtype=<\/span>float<\/span>)<\/span>
\n if<\/span> closed:<\/span>
\n arr =<\/span> np.<\/span>vstack(<\/span>[<\/span>arr,<\/span> arr[<\/span>0<\/span>]<\/span>]<\/span>)<\/span>
\n return<\/span> float<\/span>(<\/span>np.<\/span>linalg.<\/span>norm(<\/span>np.<\/span>diff(<\/span>arr,<\/span> axis=<\/span>0<\/span>)<\/span>,<\/span> axis=<\/span>1<\/span>)<\/span>.<\/span>sum<\/span>(<\/span>)<\/span>)<\/span><\/p>\n

def<\/span> ellipse_perimeter_ramanujan<\/span>(<\/span>a:<\/span> float<\/span>,<\/span> b:<\/span> float<\/span>)<\/span> –<\/span>><\/span> float<\/span>:<\/span>
\n h =<\/span> (<\/span>(<\/span>a –<\/span> b)<\/span> \/<\/span> (<\/span>a +<\/span> b)<\/span>)<\/span> **<\/span> 2<\/span>
\n return<\/span> math.<\/span>pi *<\/span> (<\/span>a +<\/span> b)<\/span> *<\/span> (<\/span>1<\/span> +<\/span> 3<\/span> *<\/span> h \/<\/span> (<\/span>10<\/span> +<\/span> math.<\/span>sqrt(<\/span>4<\/span> –<\/span> 3<\/span> *<\/span> h)<\/span>)<\/span>)<\/span><\/p>\n

# —————————————————————————–<\/span>
\n# 1. \u51e0\u4f55\u6570\u636e\u5b9a\u4e49<\/span>
\n# —————————————————————————–<\/span>
\nOUTER_VERTICES:<\/span> List[<\/span>Point]<\/span> =<\/span> [<\/span>
\n (<\/span>0<\/span>,<\/span> 0<\/span>)<\/span>,<\/span> (<\/span>20<\/span>,<\/span> 0<\/span>)<\/span>,<\/span> (<\/span>20<\/span>,<\/span> 20<\/span>)<\/span>,<\/span> (<\/span>25<\/span>,<\/span> 20<\/span>)<\/span>,<\/span> (<\/span>25<\/span>,<\/span> 0<\/span>)<\/span>,<\/span>
\n (<\/span>45<\/span>,<\/span> 0<\/span>)<\/span>,<\/span> (<\/span>45<\/span>,<\/span> 20<\/span>)<\/span>,<\/span> (<\/span>50<\/span>,<\/span> 20<\/span>)<\/span>,<\/span> (<\/span>50<\/span>,<\/span> 0<\/span>)<\/span>,<\/span>
\n (<\/span>70<\/span>,<\/span> 0<\/span>)<\/span>,<\/span> (<\/span>70<\/span>,<\/span> 20<\/span>)<\/span>,<\/span> (<\/span>75<\/span>,<\/span> 20<\/span>)<\/span>,<\/span> (<\/span>75<\/span>,<\/span> 0<\/span>)<\/span>,<\/span>
\n (<\/span>100<\/span>,<\/span> 0<\/span>)<\/span>,<\/span> (<\/span>100<\/span>,<\/span> 80<\/span>)<\/span>,<\/span>
\n (<\/span>75<\/span>,<\/span> 80<\/span>)<\/span>,<\/span> (<\/span>75<\/span>,<\/span> 60<\/span>)<\/span>,<\/span> (<\/span>70<\/span>,<\/span> 60<\/span>)<\/span>,<\/span> (<\/span>70<\/span>,<\/span> 80<\/span>)<\/span>,<\/span>
\n (<\/span>50<\/span>,<\/span> 80<\/span>)<\/span>,<\/span> (<\/span>50<\/span>,<\/span> 60<\/span>)<\/span>,<\/span> (<\/span>45<\/span>,<\/span> 60<\/span>)<\/span>,<\/span> (<\/span>45<\/span>,<\/span> 80<\/span>)<\/span>,<\/span>
\n (<\/span>25<\/span>,<\/span> 80<\/span>)<\/span>,<\/span> (<\/span>25<\/span>,<\/span> 60<\/span>)<\/span>,<\/span> (<\/span>20<\/span>,<\/span> 60<\/span>)<\/span>,<\/span> (<\/span>20<\/span>,<\/span> 80<\/span>)<\/span>,<\/span>
\n (<\/span>0<\/span>,<\/span> 80<\/span>)<\/span>,<\/span> (<\/span>0<\/span>,<\/span> 55<\/span>)<\/span>,<\/span> (<\/span>8<\/span>,<\/span> 55<\/span>)<\/span>,<\/span> (<\/span>8<\/span>,<\/span> 50<\/span>)<\/span>,<\/span>
\n (<\/span>0<\/span>,<\/span> 50<\/span>)<\/span>,<\/span> (<\/span>0<\/span>,<\/span> 30<\/span>)<\/span>,<\/span> (<\/span>8<\/span>,<\/span> 30<\/span>)<\/span>,<\/span> (<\/span>8<\/span>,<\/span> 25<\/span>)<\/span>,<\/span> (<\/span>0<\/span>,<\/span> 25<\/span>)<\/span>,<\/span>
\n]<\/span>
\nSTART_N234 =<\/span> np.<\/span>array(<\/span>[<\/span>100.0<\/span>,<\/span> 0.0<\/span>]<\/span>)<\/span>
\nELLIPSE_PARAM =<\/span> (<\/span>60.0<\/span>,<\/span> 40.0<\/span>,<\/span> 15.0<\/span>,<\/span> 20.0<\/span>)<\/span>
\nCIRCLE_CENTERS =<\/span> [<\/span>(<\/span>10.0<\/span>,<\/span> 75.0<\/span>)<\/span>,<\/span> (<\/span>35.0<\/span>,<\/span> 75.0<\/span>)<\/span>,<\/span> (<\/span>60.0<\/span>,<\/span> 75.0<\/span>)<\/span>,<\/span> (<\/span>85.0<\/span>,<\/span> 75.0<\/span>)<\/span>]<\/span><\/p>\n

# N3: \u56fe\u793a\u4e3a4\u5217\u00d73\u884c，\u77e9\u5f62\u5c3a\u5bf84\u00d73，\u6a2a\u5411\u4e2d\u5fc3\u8ddd6\u3001\u7eb5\u5411\u4e2d\u5fc3\u8ddd5\u3002<\/span>
\nN3_CENTERS =<\/span> [<\/span>(<\/span>x,<\/span> y)<\/span> for<\/span> y in<\/span> (<\/span>35.0<\/span>,<\/span> 40.0<\/span>,<\/span> 45.0<\/span>)<\/span> for<\/span> x in<\/span> (<\/span>51.0<\/span>,<\/span> 57.0<\/span>,<\/span> 63.0<\/span>,<\/span> 69.0<\/span>)<\/span>]<\/span><\/p>\n

# N4: \u4f9d\u636e\u56fe\u4e2d\u5c3a\u5bf8\u4e0e\u5bf9\u79f0\u8f74\u8fdb\u884c\u77e2\u91cf\u5316\u91cd\u5efa\u3002\u4e09\u4e2a\u6865\u7ec4\u6210\u751f\u6210\u6811：<\/span>
\n# \u5de6\u4e0b\u2014\u5de6\u4e0a\u3001\u5de6\u4e0a\u2014\u53f3\u4e0a\u3001\u53f3\u4e0a\u2014\u53f3\u4e0b\u3002<\/span>
\nN4_RECTS =<\/span> {<\/span>
\n "\u5de6\u4e0a\u4ef6"<\/span>:<\/span> (<\/span>48.5<\/span>,<\/span> 42.5<\/span>,<\/span> 57.5<\/span>,<\/span> 51.5<\/span>)<\/span>,<\/span>
\n "\u53f3\u4e0a\u4ef6"<\/span>:<\/span> (<\/span>60.5<\/span>,<\/span> 42.5<\/span>,<\/span> 69.5<\/span>,<\/span> 51.5<\/span>)<\/span>,<\/span>
\n "\u5de6\u4e0b\u4ef6"<\/span>:<\/span> (<\/span>51.5<\/span>,<\/span> 28.5<\/span>,<\/span> 57.5<\/span>,<\/span> 39.5<\/span>)<\/span>,<\/span>
\n "\u53f3\u4e0b\u4ef6"<\/span>:<\/span> (<\/span>60.5<\/span>,<\/span> 30.5<\/span>,<\/span> 71.5<\/span>,<\/span> 39.5<\/span>)<\/span>,<\/span>
\n}<\/span>
\nN4_BRIDGES =<\/span> {<\/span>
\n "\u68651（\u5de6\u5217\u7ad6\u5411）"<\/span>:<\/span> (<\/span>54.5<\/span>,<\/span> 39.5<\/span>,<\/span> 56.5<\/span>,<\/span> 42.5<\/span>)<\/span>,<\/span>
\n "\u68652（\u4e0a\u6392\u6a2a\u5411）"<\/span>:<\/span> (<\/span>57.5<\/span>,<\/span> 46.0<\/span>,<\/span> 60.5<\/span>,<\/span> 48.0<\/span>)<\/span>,<\/span>
\n "\u68653（\u53f3\u5217\u7ad6\u5411）"<\/span>:<\/span> (<\/span>64.0<\/span>,<\/span> 39.5<\/span>,<\/span> 66.0<\/span>,<\/span> 42.5<\/span>)<\/span>,<\/span>
\n}<\/span><\/p>\n

@dataclass<\/span>
\nclass<\/span> ModelResults<\/span>:<\/span>
\n n1_length:<\/span> float<\/span>
\n n2_length:<\/span> float<\/span>
\n n3_length:<\/span> float<\/span>
\n n4_length:<\/span> float<\/span>
\n n3_order:<\/span> List[<\/span>int<\/span>]<\/span>
\n n3_nested_length:<\/span> float<\/span>
\n outer_ellipse_distance:<\/span> float<\/span>
\n circle_outer_distances:<\/span> List[<\/span>float<\/span>]<\/span>
\n ellipse_bridge_distance:<\/span> float<\/span><\/p>\n

# —————————————————————————–<\/span>
\n# 2. \u6570\u636e\u7406\u89e3\u4e0e\u7edf\u8ba1<\/span>
\n# —————————————————————————–<\/span>
\ndef<\/span> build_geometric_feature_table<\/span>(<\/span>)<\/span> –<\/span>><\/span> pd.<\/span>DataFrame:<\/span>
\n rows =<\/span> [<\/span>
\n {<\/span>"\u5e03\u5c40"<\/span>:<\/span> "N1"<\/span>,<\/span> "\u5bf9\u8c61"<\/span>:<\/span> "\u5916\u8f6e\u5ed3\u53ef\u5207\u7ebf"<\/span>,<\/span> "\u7c7b\u578b"<\/span>:<\/span> "\u5f00\u653e\u6298\u7ebf"<\/span>,<\/span> "\u6570\u91cf"<\/span>:<\/span> 1<\/span>,<\/span>
\n "\u5468\u957f\u6216\u7ebf\u957f"<\/span>:<\/span> 80<\/span> +<\/span> 50<\/span> +<\/span> 80<\/span>,<\/span> "\u9762\u79ef"<\/span>:<\/span> np.<\/span>nan}<\/span>,<\/span>
\n {<\/span>"\u5e03\u5c40"<\/span>:<\/span> "N1"<\/span>,<\/span> "\u5bf9\u8c61"<\/span>:<\/span> "\u5185\u77e9\u5f62"<\/span>,<\/span> "\u7c7b\u578b"<\/span>:<\/span> "\u77e9\u5f62"<\/span>,<\/span> "\u6570\u91cf"<\/span>:<\/span> 1<\/span>,<\/span>
\n "\u5468\u957f\u6216\u7ebf\u957f"<\/span>:<\/span> 2<\/span> *<\/span> (<\/span>40<\/span> +<\/span> 20<\/span>)<\/span>,<\/span> "\u9762\u79ef"<\/span>:<\/span> 40<\/span> *<\/span> 20<\/span>}<\/span>,<\/span>
\n {<\/span>"\u5e03\u5c40"<\/span>:<\/span> "N2"<\/span>,<\/span> "\u5bf9\u8c61"<\/span>:<\/span> "\u952f\u9f7f\u5916\u8f6e\u5ed3"<\/span>,<\/span> "\u7c7b\u578b"<\/span>:<\/span> "\u591a\u8fb9\u5f62"<\/span>,<\/span> "\u6570\u91cf"<\/span>:<\/span> 1<\/span>,<\/span>
\n "\u5468\u957f\u6216\u7ebf\u957f"<\/span>:<\/span> polyline_length(<\/span>OUTER_VERTICES)<\/span>,<\/span> "\u9762\u79ef"<\/span>:<\/span> np.<\/span>nan}<\/span>,<\/span>
\n {<\/span>"\u5e03\u5c40"<\/span>:<\/span> "N2"<\/span>,<\/span> "\u5bf9\u8c61"<\/span>:<\/span> "\u5706\u5b54"<\/span>,<\/span> "\u7c7b\u578b"<\/span>:<\/span> "\u5706"<\/span>,<\/span> "\u6570\u91cf"<\/span>:<\/span> 4<\/span>,<\/span>
\n "\u5468\u957f\u6216\u7ebf\u957f"<\/span>:<\/span> 2<\/span> *<\/span> math.<\/span>pi *<\/span> 3<\/span>,<\/span> "\u9762\u79ef"<\/span>:<\/span> math.<\/span>pi *<\/span> 3<\/span> **<\/span> 2<\/span>}<\/span>,<\/span>
\n {<\/span>"\u5e03\u5c40"<\/span>:<\/span> "N2"<\/span>,<\/span> "\u5bf9\u8c61"<\/span>:<\/span> "\u692d\u5706\u5b54"<\/span>,<\/span> "\u7c7b\u578b"<\/span>:<\/span> "\u692d\u5706"<\/span>,<\/span> "\u6570\u91cf"<\/span>:<\/span> 1<\/span>,<\/span>
\n "\u5468\u957f\u6216\u7ebf\u957f"<\/span>:<\/span> ellipse_perimeter_ramanujan(<\/span>15<\/span>,<\/span> 20<\/span>)<\/span>,<\/span> "\u9762\u79ef"<\/span>:<\/span> math.<\/span>pi *<\/span> 15<\/span> *<\/span> 20<\/span>}<\/span>,<\/span>
\n {<\/span>"\u5e03\u5c40"<\/span>:<\/span> "N3"<\/span>,<\/span> "\u5bf9\u8c61"<\/span>:<\/span> "\u5d4c\u5957\u77e9\u5f62"<\/span>,<\/span> "\u7c7b\u578b"<\/span>:<\/span> "\u77e9\u5f62"<\/span>,<\/span> "\u6570\u91cf"<\/span>:<\/span> 12<\/span>,<\/span>
\n "\u5468\u957f\u6216\u7ebf\u957f"<\/span>:<\/span> 2<\/span> *<\/span> (<\/span>4<\/span> +<\/span> 3<\/span>)<\/span>,<\/span> "\u9762\u79ef"<\/span>:<\/span> 4<\/span> *<\/span> 3<\/span>}<\/span>,<\/span>
\n {<\/span>"\u5e03\u5c40"<\/span>:<\/span> "N4"<\/span>,<\/span> "\u5bf9\u8c61"<\/span>:<\/span> "\u8fc7\u6865\u5c0f\u4ef6"<\/span>,<\/span> "\u7c7b\u578b"<\/span>:<\/span> "\u5f02\u5f62\u7ec4\u5408"<\/span>,<\/span> "\u6570\u91cf"<\/span>:<\/span> 4<\/span>,<\/span>
\n "\u5468\u957f\u6216\u7ebf\u957f"<\/span>:<\/span> np.<\/span>mean(<\/span>[<\/span>2<\/span> *<\/span> (<\/span>(<\/span>x2 –<\/span> x1)<\/span> +<\/span> (<\/span>y2 –<\/span> y1)<\/span>)<\/span> for<\/span> x1,<\/span> y1,<\/span> x2,<\/span> y2 in<\/span> N4_RECTS.<\/span>values(<\/span>)<\/span>]<\/span>)<\/span>,<\/span>
\n "\u9762\u79ef"<\/span>:<\/span> np.<\/span>mean(<\/span>[<\/span>(<\/span>x2 –<\/span> x1)<\/span> *<\/span> (<\/span>y2 –<\/span> y1)<\/span> for<\/span> x1,<\/span> y1,<\/span> x2,<\/span> y2 in<\/span> N4_RECTS.<\/span>values(<\/span>)<\/span>]<\/span>)<\/span>}<\/span>,<\/span>
\n ]<\/span>
\n return<\/span> pd.<\/span>DataFrame(<\/span>rows)<\/span><\/p>\n

def<\/span> descriptive_statistics<\/span>(<\/span>values:<\/span> Sequence[<\/span>float<\/span>]<\/span>,<\/span> name:<\/span> str<\/span>)<\/span> –<\/span>><\/span> Dict[<\/span>str<\/span>,<\/span> float<\/span>]<\/span>:<\/span>
\n arr =<\/span> np.<\/span>asarray(<\/span>values,<\/span> dtype=<\/span>float<\/span>)<\/span>
\n return<\/span> {<\/span>
\n "\u6307\u6807"<\/span>:<\/span> name,<\/span>
\n "\u6837\u672c\u6570"<\/span>:<\/span> int<\/span>(<\/span>arr.<\/span>size)<\/span>,<\/span>
\n "\u5747\u503c"<\/span>:<\/span> float<\/span>(<\/span>np.<\/span>mean(<\/span>arr)<\/span>)<\/span>,<\/span>
\n "\u6807\u51c6\u5dee"<\/span>:<\/span> float<\/span>(<\/span>np.<\/span>std(<\/span>arr,<\/span> ddof=<\/span>1<\/span>)<\/span>)<\/span> if<\/span> arr.<\/span>size ><\/span> 1<\/span> else<\/span> 0.0<\/span>,<\/span>
\n "\u53d8\u5f02\u7cfb\u6570"<\/span>:<\/span> float<\/span>(<\/span>np.<\/span>std(<\/span>arr,<\/span> ddof=<\/span>1<\/span>)<\/span> \/<\/span> np.<\/span>mean(<\/span>arr)<\/span>)<\/span> if<\/span> arr.<\/span>size ><\/span> 1<\/span> and<\/span> np.<\/span>mean(<\/span>arr)<\/span> !=<\/span> 0<\/span> else<\/span> 0.0<\/span>,<\/span>
\n "\u6700\u5c0f\u503c"<\/span>:<\/span> float<\/span>(<\/span>np.<\/span>min<\/span>(<\/span>arr)<\/span>)<\/span>,<\/span>
\n "\u4e2d\u4f4d\u6570"<\/span>:<\/span> float<\/span>(<\/span>np.<\/span>median(<\/span>arr)<\/span>)<\/span>,<\/span>
\n "\u6700\u5927\u503c"<\/span>:<\/span> float<\/span>(<\/span>np.<\/span>max<\/span>(<\/span>arr)<\/span>)<\/span>,<\/span>
\n "\u504f\u5ea6"<\/span>:<\/span> float<\/span>(<\/span>skew(<\/span>arr,<\/span> bias=<\/span>False<\/span>)<\/span>)<\/span> if<\/span> arr.<\/span>size >=<\/span> 3<\/span> else<\/span> 0.0<\/span>,<\/span>
\n "\u5cf0\u5ea6"<\/span>:<\/span> float<\/span>(<\/span>kurtosis(<\/span>arr,<\/span> fisher=<\/span>True<\/span>,<\/span> bias=<\/span>False<\/span>)<\/span>)<\/span> if<\/span> arr.<\/span>size >=<\/span> 4<\/span> else<\/span> 0.0<\/span>,<\/span>
\n }<\/span><\/p>\n

# —————————————————————————–<\/span>
\n# 3. \u95ee\u98981\u89e3\u6790\u6a21\u578b<\/span>
\n# —————————————————————————–<\/span>
\ndef<\/span> solve_n1<\/span>(<\/span>)<\/span> –<\/span>><\/span> Tuple[<\/span>float<\/span>,<\/span> List[<\/span>np.<\/span>ndarray]<\/span>]<\/span>:<\/span>
\n b3 =<\/span> np.<\/span>array(<\/span>[<\/span>0.0<\/span>,<\/span> 50.0<\/span>]<\/span>)<\/span>
\n b4 =<\/span> np.<\/span>array(<\/span>[<\/span>0.0<\/span>,<\/span> 0.0<\/span>]<\/span>)<\/span>
\n q =<\/span> np.<\/span>array(<\/span>[<\/span>20.0<\/span>,<\/span> 25.0<\/span>]<\/span>)<\/span>
\n length =<\/span> euclidean(<\/span>b3,<\/span> q)<\/span> +<\/span> euclidean(<\/span>q,<\/span> b4)<\/span>
\n # \u5207\u5272\u987a\u5e8f：B1-B2-B3；\u7a7a\u7a0b\u81f3Q；\u5207\u5185\u77e9\u5f62\u4e00\u5468；\u7a7a\u7a0b\u81f3B4；\u5207B4-B1\u3002<\/span>
\n route =<\/span> [<\/span>np.<\/span>array(<\/span>[<\/span>80.0<\/span>,<\/span> 0.0<\/span>]<\/span>)<\/span>,<\/span> np.<\/span>array(<\/span>[<\/span>80.0<\/span>,<\/span> 50.0<\/span>]<\/span>)<\/span>,<\/span> b3,<\/span> q,<\/span> b4,<\/span> np.<\/span>array(<\/span>[<\/span>80.0<\/span>,<\/span> 0.0<\/span>]<\/span>)<\/span>]<\/span>
\n return<\/span> length,<\/span> route<\/p>\n

# —————————————————————————–<\/span>
\n# 4. \u95ee\u98982\u4e3b\u5e72\u63d2\u5165\u6a21\u578b<\/span>
\n# —————————————————————————–<\/span>
\ndef<\/span> solve_n2<\/span>(<\/span>resolution:<\/span> int<\/span> =<\/span> 720<\/span>)<\/span> –<\/span>><\/span> Tuple[<\/span>float<\/span>,<\/span> Dict[<\/span>str<\/span>,<\/span> Tuple[<\/span>float<\/span>,<\/span> np.<\/span>ndarray,<\/span> np.<\/span>ndarray]<\/span>]<\/span>]<\/span>:<\/span>
\n outer =<\/span> sample_polyline(<\/span>OUTER_VERTICES,<\/span> max<\/span>(<\/span>8<\/span>,<\/span> resolution \/\/<\/span> 36<\/span>)<\/span>,<\/span> True<\/span>)<\/span>
\n ellipse =<\/span> sample_ellipse(<\/span>*<\/span>ELLIPSE_PARAM,<\/span> n=<\/span>resolution)<\/span>
\n details:<\/span> Dict[<\/span>str<\/span>,<\/span> Tuple[<\/span>float<\/span>,<\/span> np.<\/span>ndarray,<\/span> np.<\/span>ndarray]<\/span>]<\/span> =<\/span> {<\/span>}<\/span>
\n for<\/span> i,<\/span> (<\/span>cx,<\/span> cy)<\/span> in<\/span> enumerate<\/span>(<\/span>CIRCLE_CENTERS,<\/span> 1<\/span>)<\/span>:<\/span>
\n # \u56db\u4e2a\u5706\u5b54\u7684\u5706\u5fc3\u5747\u4f4d\u4e8ey=75，\u534a\u5f84\u4e3a3，\u6b63\u4e0a\u65b9\u5916\u8f6e\u5ed3\u4e3ay=80，<\/span>
\n # \u56e0\u800c\u6700\u77ed\u8ddd\u79bb\u53ef\u89e3\u6790\u5f97\u5230 80-(75+3)=2，\u907f\u514d\u79bb\u6563\u91c7\u6837\u8bef\u5dee\u3002<\/span>
\n details[<\/span>f"\u5706\u5b54C<\/span>{<\/span>i}<\/span><\/span>"<\/span><\/span>]<\/span> =<\/span> (<\/span>2.0<\/span>,<\/span> np.<\/span>array(<\/span>[<\/span>cx,<\/span> 80.0<\/span>]<\/span>)<\/span>,<\/span> np.<\/span>array(<\/span>[<\/span>cx,<\/span> 78.0<\/span>]<\/span>)<\/span>)<\/span>
\n details[<\/span>"\u692d\u5706E"<\/span>]<\/span> =<\/span> minimum_distance(<\/span>outer,<\/span> ellipse)<\/span>
\n total =<\/span> 2.0<\/span> *<\/span> sum<\/span>(<\/span>v[<\/span>0<\/span>]<\/span> for<\/span> v in<\/span> details.<\/span>values(<\/span>)<\/span>)<\/span>
\n return<\/span> total,<\/span> details<\/p>\n

# —————————————————————————–<\/span>
\n# 5. \u95ee\u98983：\u56fa\u5b9a\u987a\u5e8f\u7684\u5206\u5c42\u52a8\u6001\u89c4\u5212 + 2-opt<\/span>
\n# —————————————————————————–<\/span>
\nclass<\/span> N3Optimizer<\/span>:<\/span>
\n def<\/span> __init__<\/span>(<\/span>self,<\/span> outer_seg_samples:<\/span> int<\/span> =<\/span> 10<\/span>,<\/span> rect_side_samples:<\/span> int<\/span> =<\/span> 16<\/span>,<\/span>
\n ellipse_samples:<\/span> int<\/span> =<\/span> 300<\/span>)<\/span>:<\/span>
\n self.<\/span>outer =<\/span> sample_polyline(<\/span>OUTER_VERTICES,<\/span> outer_seg_samples,<\/span> True<\/span>)<\/span>
\n self.<\/span>ellipse =<\/span> sample_ellipse(<\/span>*<\/span>ELLIPSE_PARAM,<\/span> n=<\/span>ellipse_samples)<\/span>
\n self.<\/span>rects =<\/span> [<\/span>sample_rectangle(<\/span>x –<\/span> 2<\/span>,<\/span> y –<\/span> 1.5<\/span>,<\/span> x +<\/span> 2<\/span>,<\/span> y +<\/span> 1.5<\/span>,<\/span>
\n rect_side_samples)<\/span> for<\/span> x,<\/span> y in<\/span> N3_CENTERS]<\/span>
\n self.<\/span>d_or =<\/span> [<\/span>cdist(<\/span>self.<\/span>outer,<\/span> r)<\/span> for<\/span> r in<\/span> self.<\/span>rects]<\/span>
\n self.<\/span>d_re =<\/span> [<\/span>cdist(<\/span>r,<\/span> self.<\/span>ellipse)<\/span> for<\/span> r in<\/span> self.<\/span>rects]<\/span>
\n self.<\/span>d_eo =<\/span> cdist(<\/span>self.<\/span>ellipse,<\/span> self.<\/span>outer)<\/span>
\n self.<\/span>d_rr =<\/span> {<\/span>(<\/span>i,<\/span> j)<\/span>:<\/span> cdist(<\/span>self.<\/span>rects[<\/span>i]<\/span>,<\/span> self.<\/span>rects[<\/span>j]<\/span>)<\/span>
\n for<\/span> i in<\/span> range<\/span>(<\/span>12<\/span>)<\/span> for<\/span> j in<\/span> range<\/span>(<\/span>12<\/span>)<\/span> if<\/span> i !=<\/span> j}<\/span>
\n self.<\/span>eval_counter =<\/span> 0<\/span><\/p>\n

def<\/span> evaluate_order<\/span>(<\/span>self,<\/span> order:<\/span> Sequence[<\/span>int<\/span>]<\/span>,<\/span> return_path:<\/span> bool<\/span> =<\/span> False<\/span>)<\/span>:<\/span>
\n self.<\/span>eval_counter +=<\/span> 1<\/span>
\n dp =<\/span> self.<\/span>d_or[<\/span>order[<\/span>0<\/span>]<\/span>]<\/span>.<\/span>copy(<\/span>)<\/span> # \u5916\u8f6e\u5ed3\u91c7\u6837\u70b9 \u00d7 \u7b2c\u4e00\u4e2a\u77e9\u5f62\u91c7\u6837\u70b9<\/span>
\n backpointers:<\/span> List[<\/span>np.<\/span>ndarray]<\/span> =<\/span> [<\/span>]<\/span>
\n for<\/span> a,<\/span> b in<\/span> zip<\/span>(<\/span>order[<\/span>:<\/span>–<\/span>1<\/span>]<\/span>,<\/span> order[<\/span>1<\/span>:<\/span>]<\/span>)<\/span>:<\/span>
\n value =<\/span> dp[<\/span>:<\/span>,<\/span> :<\/span>,<\/span> None<\/span>]<\/span> +<\/span> self.<\/span>d_rr[<\/span>(<\/span>a,<\/span> b)<\/span>]<\/span>[<\/span>None<\/span>,<\/span> :<\/span>,<\/span> :<\/span>]<\/span>
\n if<\/span> return_path:<\/span>
\n backpointers.<\/span>append(<\/span>np.<\/span>argmin(<\/span>value,<\/span> axis=<\/span>1<\/span>)<\/span>)<\/span>
\n dp =<\/span> np.<\/span>min<\/span>(<\/span>value,<\/span> axis=<\/span>1<\/span>)<\/span>
\n value_e =<\/span> dp[<\/span>:<\/span>,<\/span> :<\/span>,<\/span> None<\/span>]<\/span> +<\/span> self.<\/span>d_re[<\/span>order[<\/span>–<\/span>1<\/span>]<\/span>]<\/span>[<\/span>None<\/span>,<\/span> :<\/span>,<\/span> :<\/span>]<\/span>
\n bp_e =<\/span> np.<\/span>argmin(<\/span>value_e,<\/span> axis=<\/span>1<\/span>)<\/span>
\n dp_e =<\/span> np.<\/span>min<\/span>(<\/span>value_e,<\/span> axis=<\/span>1<\/span>)<\/span>
\n total =<\/span> dp_e +<\/span> self.<\/span>d_eo.<\/span>T
\n oi,<\/span> ei =<\/span> np.<\/span>unravel_index(<\/span>np.<\/span>argmin(<\/span>total)<\/span>,<\/span> total.<\/span>shape)<\/span>
\n best =<\/span> float<\/span>(<\/span>total[<\/span>oi,<\/span> ei]<\/span>)<\/span>
\n if<\/span> not<\/span> return_path:<\/span>
\n return<\/span> best
\n idx =<\/span> int<\/span>(<\/span>bp_e[<\/span>oi,<\/span> ei]<\/span>)<\/span>
\n rect_indices =<\/span> [<\/span>0<\/span>]<\/span> *<\/span> len<\/span>(<\/span>order)<\/span>
\n rect_indices[<\/span>–<\/span>1<\/span>]<\/span> =<\/span> idx
\n for<\/span> t in<\/span> range<\/span>(<\/span>len<\/span>(<\/span>order)<\/span> –<\/span> 2<\/span>,<\/span> –<\/span>1<\/span>,<\/span> –<\/span>1<\/span>)<\/span>:<\/span>
\n idx =<\/span> int<\/span>(<\/span>backpointers[<\/span>t]<\/span>[<\/span>oi,<\/span> idx]<\/span>)<\/span>
\n rect_indices[<\/span>t]<\/span> =<\/span> idx
\n points =<\/span> [<\/span>self.<\/span>outer[<\/span>oi]<\/span>]<\/span>
\n points.<\/span>extend(<\/span>self.<\/span>rects[<\/span>order[<\/span>k]<\/span>]<\/span>[<\/span>rect_indices[<\/span>k]<\/span>]<\/span> for<\/span> k in<\/span> range<\/span>(<\/span>len<\/span>(<\/span>order)<\/span>)<\/span>)<\/span>
\n points.<\/span>extend(<\/span>[<\/span>self.<\/span>ellipse[<\/span>ei]<\/span>,<\/span> self.<\/span>outer[<\/span>oi]<\/span>]<\/span>)<\/span>
\n return<\/span> best,<\/span> points,<\/span> int<\/span>(<\/span>oi)<\/span>,<\/span> int<\/span>(<\/span>ei)<\/span>,<\/span> rect_indices<\/p>\n

@staticmethod<\/span>
\n def<\/span> initial_orders<\/span>(<\/span>seed:<\/span> int<\/span> =<\/span> 2024<\/span>)<\/span> –<\/span>><\/span> List[<\/span>List[<\/span>int<\/span>]<\/span>]<\/span>:<\/span>
\n rng =<\/span> random.<\/span>Random(<\/span>seed)<\/span>
\n grid =<\/span> np.<\/span>arange(<\/span>12<\/span>)<\/span>.<\/span>reshape(<\/span>3<\/span>,<\/span> 4<\/span>)<\/span>
\n candidates:<\/span> List[<\/span>List[<\/span>int<\/span>]<\/span>]<\/span> =<\/span> [<\/span>]<\/span>
\n # \u884c\u86c7\u5f62\u4e0e\u5217\u86c7\u5f62<\/span>
\n for<\/span> reverse_rows in<\/span> (<\/span>False<\/span>,<\/span> True<\/span>)<\/span>:<\/span>
\n rows =<\/span> list<\/span>(<\/span>range<\/span>(<\/span>3<\/span>)<\/span>)<\/span>[<\/span>:<\/span>:<\/span>–<\/span>1<\/span>]<\/span> if<\/span> reverse_rows else<\/span> list<\/span>(<\/span>range<\/span>(<\/span>3<\/span>)<\/span>)<\/span>
\n for<\/span> phase in<\/span> (<\/span>0<\/span>,<\/span> 1<\/span>)<\/span>:<\/span>
\n order:<\/span> List[<\/span>int<\/span>]<\/span> =<\/span> [<\/span>]<\/span>
\n for<\/span> k,<\/span> r in<\/span> enumerate<\/span>(<\/span>rows)<\/span>:<\/span>
\n cols =<\/span> list<\/span>(<\/span>range<\/span>(<\/span>4<\/span>)<\/span>)<\/span>
\n if<\/span> (<\/span>k +<\/span> phase)<\/span> %<\/span> 2<\/span>:<\/span>
\n cols.<\/span>reverse(<\/span>)<\/span>
\n order.<\/span>extend(<\/span>int<\/span>(<\/span>grid[<\/span>r,<\/span> c]<\/span>)<\/span> for<\/span> c in<\/span> cols)<\/span>
\n candidates.<\/span>extend(<\/span>[<\/span>order,<\/span> order[<\/span>:<\/span>:<\/span>–<\/span>1<\/span>]<\/span>]<\/span>)<\/span>
\n for<\/span> reverse_cols in<\/span> (<\/span>False<\/span>,<\/span> True<\/span>)<\/span>:<\/span>
\n cols =<\/span> list<\/span>(<\/span>range<\/span>(<\/span>4<\/span>)<\/span>)<\/span>[<\/span>:<\/span>:<\/span>–<\/span>1<\/span>]<\/span> if<\/span> reverse_cols else<\/span> list<\/span>(<\/span>range<\/span>(<\/span>4<\/span>)<\/span>)<\/span>
\n for<\/span> phase in<\/span> (<\/span>0<\/span>,<\/span> 1<\/span>)<\/span>:<\/span>
\n order =<\/span> [<\/span>]<\/span>
\n for<\/span> k,<\/span> c in<\/span> enumerate<\/span>(<\/span>cols)<\/span>:<\/span>
\n rows =<\/span> list<\/span>(<\/span>range<\/span>(<\/span>3<\/span>)<\/span>)<\/span>
\n if<\/span> (<\/span>k +<\/span> phase)<\/span> %<\/span> 2<\/span>:<\/span>
\n rows.<\/span>reverse(<\/span>)<\/span>
\n order.<\/span>extend(<\/span>int<\/span>(<\/span>grid[<\/span>r,<\/span> c]<\/span>)<\/span> for<\/span> r in<\/span> rows)<\/span>
\n candidates.<\/span>extend(<\/span>[<\/span>order,<\/span> order[<\/span>:<\/span>:<\/span>–<\/span>1<\/span>]<\/span>]<\/span>)<\/span>
\n # \u57fa\u4e8e\u4e2d\u5fc3\u8ddd\u79bb\u7684\u6270\u52a8\u6700\u8fd1\u90bb<\/span>
\n centers =<\/span> np.<\/span>asarray(<\/span>N3_CENTERS)<\/span>
\n center_dist =<\/span> cdist(<\/span>centers,<\/span> centers)<\/span>
\n for<\/span> start in<\/span> range<\/span>(<\/span>12<\/span>)<\/span>:<\/span>
\n for<\/span> noise_level in<\/span> range<\/span>(<\/span>2<\/span>)<\/span>:<\/span>
\n remaining =<\/span> set<\/span>(<\/span>range<\/span>(<\/span>12<\/span>)<\/span>)<\/span>
\n remaining.<\/span>remove(<\/span>start)<\/span>
\n order =<\/span> [<\/span>start]<\/span>
\n while<\/span> remaining:<\/span>
\n cur =<\/span> order[<\/span>–<\/span>1<\/span>]<\/span>
\n nxt =<\/span> min<\/span>(<\/span>remaining,<\/span>
\n key=<\/span>lambda<\/span> j:<\/span> center_dist[<\/span>cur,<\/span> j]<\/span> +<\/span> rng.<\/span>random(<\/span>)<\/span> *<\/span> 0.08<\/span> *<\/span> noise_level)<\/span>
\n order.<\/span>append(<\/span>nxt)<\/span>
\n remaining.<\/span>remove(<\/span>nxt)<\/span>
\n candidates.<\/span>extend(<\/span>[<\/span>order,<\/span> order[<\/span>:<\/span>:<\/span>–<\/span>1<\/span>]<\/span>]<\/span>)<\/span>
\n candidates.<\/span>append(<\/span>[<\/span>3<\/span>,<\/span> 7<\/span>,<\/span> 11<\/span>,<\/span> 10<\/span>,<\/span> 6<\/span>,<\/span> 5<\/span>,<\/span> 9<\/span>,<\/span> 8<\/span>,<\/span> 4<\/span>,<\/span> 0<\/span>,<\/span> 1<\/span>,<\/span> 2<\/span>]<\/span>)<\/span>
\n candidates.<\/span>append(<\/span>[<\/span>2<\/span>,<\/span> 1<\/span>,<\/span> 0<\/span>,<\/span> 4<\/span>,<\/span> 8<\/span>,<\/span> 9<\/span>,<\/span> 5<\/span>,<\/span> 6<\/span>,<\/span> 10<\/span>,<\/span> 11<\/span>,<\/span> 7<\/span>,<\/span> 3<\/span>]<\/span>)<\/span>
\n unique =<\/span> {<\/span>tuple<\/span>(<\/span>x)<\/span>:<\/span> x for<\/span> x in<\/span> candidates}<\/span>
\n return<\/span> list<\/span>(<\/span>unique.<\/span>values(<\/span>)<\/span>)<\/span><\/p>\n

def<\/span> solve<\/span>(<\/span>self)<\/span> –<\/span>><\/span> Tuple[<\/span>float<\/span>,<\/span> List[<\/span>int<\/span>]<\/span>,<\/span> List[<\/span>np.<\/span>ndarray]<\/span>,<\/span> pd.<\/span>DataFrame]<\/span>:<\/span>
\n history:<\/span> List[<\/span>Dict[<\/span>str<\/span>,<\/span> float<\/span>]<\/span>]<\/span> =<\/span> [<\/span>]<\/span>
\n best_value =<\/span> math.<\/span>inf
\n best_order:<\/span> List[<\/span>int<\/span>]<\/span> =<\/span> [<\/span>]<\/span>
\n for<\/span> i,<\/span> order in<\/span> enumerate<\/span>(<\/span>self.<\/span>initial_orders(<\/span>)<\/span>)<\/span>:<\/span>
\n value =<\/span> self.<\/span>evaluate_order(<\/span>order)<\/span>
\n if<\/span> value <<\/span> best_value:<\/span>
\n best_value,<\/span> best_order =<\/span> value,<\/span> order.<\/span>copy(<\/span>)<\/span>
\n history.<\/span>append(<\/span>{<\/span>"\u8bc4\u4ef7\u6b21\u6570"<\/span>:<\/span> self.<\/span>eval_counter,<\/span> "\u5f53\u524d\u6700\u4f18"<\/span>:<\/span> best_value,<\/span>
\n "\u9636\u6bb5"<\/span>:<\/span> "\u591a\u8d77\u70b9\u6784\u9020"<\/span>}<\/span>)<\/span>
\n # \u4ea4\u6362\u4e0e2-opt\u590d\u5408\u90bb\u57df<\/span>
\n improved =<\/span> True<\/span>
\n iteration =<\/span> 0<\/span>
\n while<\/span> improved and<\/span> iteration <<\/span> 2<\/span>:<\/span>
\n improved =<\/span> False<\/span>
\n iteration +=<\/span> 1<\/span>
\n incumbent =<\/span> best_order.<\/span>copy(<\/span>)<\/span>
\n for<\/span> i in<\/span> range<\/span>(<\/span>12<\/span>)<\/span>:<\/span>
\n for<\/span> j in<\/span> range<\/span>(<\/span>i +<\/span> 1<\/span>,<\/span> 12<\/span>)<\/span>:<\/span>
\n trial =<\/span> incumbent.<\/span>copy(<\/span>)<\/span>
\n trial[<\/span>i]<\/span>,<\/span> trial[<\/span>j]<\/span> =<\/span> trial[<\/span>j]<\/span>,<\/span> trial[<\/span>i]<\/span>
\n value =<\/span> self.<\/span>evaluate_order(<\/span>trial)<\/span>
\n if<\/span> value <<\/span> best_value –<\/span> 1e-9<\/span>:<\/span>
\n best_value,<\/span> best_order,<\/span> improved =<\/span> value,<\/span> trial,<\/span> True<\/span>
\n history.<\/span>append(<\/span>{<\/span>"\u8bc4\u4ef7\u6b21\u6570"<\/span>:<\/span> self.<\/span>eval_counter,<\/span> "\u5f53\u524d\u6700\u4f18"<\/span>:<\/span> best_value,<\/span>
\n "\u9636\u6bb5"<\/span>:<\/span> "\u4ea4\u6362\u90bb\u57df"<\/span>}<\/span>)<\/span>
\n trial =<\/span> incumbent[<\/span>:<\/span>i]<\/span> +<\/span> list<\/span>(<\/span>reversed<\/span>(<\/span>incumbent[<\/span>i:<\/span>j +<\/span> 1<\/span>]<\/span>)<\/span>)<\/span> +<\/span> incumbent[<\/span>j +<\/span> 1<\/span>:<\/span>]<\/span>
\n value =<\/span> self.<\/span>evaluate_order(<\/span>trial)<\/span>
\n if<\/span> value <<\/span> best_value –<\/span> 1e-9<\/span>:<\/span>
\n best_value,<\/span> best_order,<\/span> improved =<\/span> value,<\/span> trial,<\/span> True<\/span>
\n history.<\/span>append(<\/span>{<\/span>"\u8bc4\u4ef7\u6b21\u6570"<\/span>:<\/span> self.<\/span>eval_counter,<\/span> "\u5f53\u524d\u6700\u4f18"<\/span>:<\/span> best_value,<\/span>
\n "\u9636\u6bb5"<\/span>:<\/span> "2-opt\u90bb\u57df"<\/span>}<\/span>)<\/span>
\n if<\/span> improved:<\/span>
\n continue<\/span>
\n best_value,<\/span> points,<\/span> *<\/span>_ =<\/span> self.<\/span>evaluate_order(<\/span>best_order,<\/span> return_path=<\/span>True<\/span>)<\/span>
\n return<\/span> best_value,<\/span> best_order,<\/span> points,<\/span> pd.<\/span>DataFrame(<\/span>history)<\/span><\/p>\n

# —————————————————————————–<\/span>
\n# 6. \u95ee\u98984：\u6865\u6570\u4e0e\u4f4d\u7f6e\u6a21\u578b<\/span>
\n# —————————————————————————–<\/span>
\ndef<\/span> n4_adjacency_graph<\/span>(<\/span>)<\/span> –<\/span>><\/span> nx.<\/span>Graph:<\/span>
\n graph =<\/span> nx.<\/span>Graph(<\/span>)<\/span>
\n graph.<\/span>add_nodes_from(<\/span>N4_RECTS.<\/span>keys(<\/span>)<\/span>)<\/span>
\n graph.<\/span>add_edge(<\/span>"\u5de6\u4e0b\u4ef6"<\/span>,<\/span> "\u5de6\u4e0a\u4ef6"<\/span>,<\/span> name=<\/span>"\u68651"<\/span>,<\/span> width=<\/span>2.0<\/span>)<\/span>
\n graph.<\/span>add_edge(<\/span>"\u5de6\u4e0a\u4ef6"<\/span>,<\/span> "\u53f3\u4e0a\u4ef6"<\/span>,<\/span> name=<\/span>"\u68652"<\/span>,<\/span> width=<\/span>2.0<\/span>)<\/span>
\n graph.<\/span>add_edge(<\/span>"\u53f3\u4e0a\u4ef6"<\/span>,<\/span> "\u53f3\u4e0b\u4ef6"<\/span>,<\/span> name=<\/span>"\u68653"<\/span>,<\/span> width=<\/span>2.0<\/span>)<\/span>
\n # \u5176\u4f59\u5019\u9009\u90bb\u63a5\u8fb9\u53ef\u4f5c\u4e3a\u66ff\u4ee3\u65b9\u6848，\u6743\u91cd\u7565\u5927\u3002<\/span>
\n graph.<\/span>add_edge(<\/span>"\u5de6\u4e0b\u4ef6"<\/span>,<\/span> "\u53f3\u4e0b\u4ef6"<\/span>,<\/span> name=<\/span>"\u5019\u9009\u68654"<\/span>,<\/span> width=<\/span>2.0<\/span>,<\/span> candidate=<\/span>True<\/span>)<\/span>
\n return<\/span> graph<\/p>\n

def<\/span> bridge_clearance<\/span>(<\/span>bridge:<\/span> Tuple[<\/span>float<\/span>,<\/span> float<\/span>,<\/span> float<\/span>,<\/span> float<\/span>]<\/span>,<\/span>
\n rects:<\/span> Iterable[<\/span>Tuple[<\/span>float<\/span>,<\/span> float<\/span>,<\/span> float<\/span>,<\/span> float<\/span>]<\/span>]<\/span>)<\/span> –<\/span>><\/span> float<\/span>:<\/span>
\n x1,<\/span> y1,<\/span> x2,<\/span> y2 =<\/span> bridge
\n corners =<\/span> [<\/span>]<\/span>
\n for<\/span> a,<\/span> b,<\/span> c,<\/span> d in<\/span> rects:<\/span>
\n corners.<\/span>extend(<\/span>[<\/span>(<\/span>a,<\/span> b)<\/span>,<\/span> (<\/span>a,<\/span> d)<\/span>,<\/span> (<\/span>c,<\/span> b)<\/span>,<\/span> (<\/span>c,<\/span> d)<\/span>]<\/span>)<\/span>
\n # \u6865\u4e2d\u5fc3\u7ebf\u6bb5\u7aef\u90e8\u4e0e\u6240\u6709\u77e9\u5f62\u9876\u70b9\u4e4b\u95f4\u7684\u4fdd\u5b88\u6700\u77ed\u8ddd\u79bb\u3002<\/span>
\n sample =<\/span> sample_rectangle(<\/span>x1,<\/span> y1,<\/span> x2,<\/span> y2,<\/span> 30<\/span>)<\/span>
\n return<\/span> float<\/span>(<\/span>min<\/span>(<\/span>np.<\/span>linalg.<\/span>norm(<\/span>sample –<\/span> np.<\/span>asarray(<\/span>c)<\/span>,<\/span> axis=<\/span>1<\/span>)<\/span>.<\/span>min<\/span>(<\/span>)<\/span> for<\/span> c in<\/span> corners)<\/span>)<\/span><\/p>\n

def<\/span> solve_n4<\/span>(<\/span>n2_details:<\/span> Dict[<\/span>str<\/span>,<\/span> Tuple[<\/span>float<\/span>,<\/span> np.<\/span>ndarray,<\/span> np.<\/span>ndarray]<\/span>]<\/span>)<\/span> –<\/span>><\/span> Tuple[<\/span>float<\/span>,<\/span> Dict[<\/span>str<\/span>,<\/span> float<\/span>]<\/span>]<\/span>:<\/span>
\n outer_ellipse =<\/span> n2_details[<\/span>"\u692d\u5706E"<\/span>]<\/span>[<\/span>0<\/span>]<\/span>
\n ellipse =<\/span> sample_ellipse(<\/span>*<\/span>ELLIPSE_PARAM,<\/span> n=<\/span>1200<\/span>)<\/span>
\n rect_samples =<\/span> {<\/span>name:<\/span> sample_rectangle(<\/span>*<\/span>rect,<\/span> n_per_side=<\/span>50<\/span>)<\/span>
\n for<\/span> name,<\/span> rect in<\/span> N4_RECTS.<\/span>items(<\/span>)<\/span>}<\/span>
\n ellipse_to_piece =<\/span> min<\/span>(<\/span>minimum_distance(<\/span>ellipse,<\/span> pts)<\/span>[<\/span>0<\/span>]<\/span> for<\/span> pts in<\/span> rect_samples.<\/span>values(<\/span>)<\/span>)<\/span>
\n circle_roundtrips =<\/span> 2<\/span> *<\/span> sum<\/span>(<\/span>n2_details[<\/span>f"\u5706\u5b54C<\/span>{<\/span>i}<\/span><\/span>"<\/span><\/span>]<\/span>[<\/span>0<\/span>]<\/span> for<\/span> i in<\/span> range<\/span>(<\/span>1<\/span>,<\/span> 5<\/span>)<\/span>)<\/span>
\n # \u4e09\u5ea7\u5bbd\u5ea6\u4e3a2\u7684\u6865\u5728\u5207\u5272\u8f68\u8ff9\u4e2d\u5bf9\u5e94\u4e09\u6b21\u6fc0\u5149\u5173\u95ed\u8de8\u8d8a，\u6545\u8ba1\u51656\u4e2a\u957f\u5ea6\u5355\u4f4d\u3002<\/span>
\n bridge_air =<\/span> sum<\/span>(<\/span>(<\/span>x2 –<\/span> x1)<\/span> if<\/span> (<\/span>x2 –<\/span> x1)<\/span> <<\/span> (<\/span>y2 –<\/span> y1)<\/span> else<\/span> (<\/span>y2 –<\/span> y1)<\/span>
\n for<\/span> x1,<\/span> y1,<\/span> x2,<\/span> y2 in<\/span> N4_BRIDGES.<\/span>values(<\/span>)<\/span>)<\/span>
\n total =<\/span> circle_roundtrips +<\/span> 2<\/span> *<\/span> outer_ellipse +<\/span> 2<\/span> *<\/span> ellipse_to_piece +<\/span> bridge_air
\n details =<\/span> {<\/span>
\n "\u56db\u5706\u5f80\u8fd4\u7a7a\u7a0b"<\/span>:<\/span> circle_roundtrips,<\/span>
\n "\u5916\u8f6e\u5ed3\u2014\u692d\u5706\u5f80\u8fd4"<\/span>:<\/span> 2<\/span> *<\/span> outer_ellipse,<\/span>
\n "\u692d\u5706\u2014\u8fc7\u6865\u7ec4\u5408\u4ef6\u5f80\u8fd4"<\/span>:<\/span> 2<\/span> *<\/span> ellipse_to_piece,<\/span>
\n "\u4e09\u5ea7\u8fc7\u6865\u8de8\u8d8a\u7a7a\u7a0b"<\/span>:<\/span> bridge_air,<\/span>
\n "\u692d\u5706\u2014\u7ec4\u5408\u4ef6\u6700\u77ed\u8ddd\u79bb"<\/span>:<\/span> ellipse_to_piece,<\/span>
\n }<\/span>
\n return<\/span> total,<\/span> details<\/p>\n

# —————————————————————————–<\/span>
\n# 7. \u53ef\u89c6\u5316<\/span>
\n# —————————————————————————–<\/span>
\ndef<\/span> draw_outer<\/span>(<\/span>ax,<\/span> lw:<\/span> float<\/span> =<\/span> 1.6<\/span>,<\/span> label:<\/span> str<\/span> |<\/span> None<\/span> =<\/span> None<\/span>)<\/span>:<\/span>
\n arr =<\/span> np.<\/span>asarray(<\/span>OUTER_VERTICES +<\/span> [<\/span>OUTER_VERTICES[<\/span>0<\/span>]<\/span>]<\/span>)<\/span>
\n ax.<\/span>plot(<\/span>arr[<\/span>:<\/span>,<\/span> 0<\/span>]<\/span>,<\/span> arr[<\/span>:<\/span>,<\/span> 1<\/span>]<\/span>,<\/span> linewidth=<\/span>lw,<\/span> label=<\/span>label)<\/span><\/p>\n

def<\/span> standard_axes<\/span>(<\/span>ax,<\/span> title:<\/span> str<\/span>)<\/span>:<\/span>
\n ax.<\/span>set_aspect(<\/span>"equal"<\/span>,<\/span> adjustable=<\/span>"box"<\/span>)<\/span>
\n ax.<\/span>set_xlim(<\/span>–<\/span>5<\/span>,<\/span> 105<\/span>)<\/span>
\n ax.<\/span>set_ylim(<\/span>–<\/span>5<\/span>,<\/span> 85<\/span>)<\/span>
\n ax.<\/span>set_xlabel(<\/span>"x \u5750\u6807"<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"y \u5750\u6807"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>title)<\/span>
\n ax.<\/span>grid(<\/span>alpha=<\/span>0.18<\/span>)<\/span><\/p>\n

def<\/span> plot_workflow<\/span>(<\/span>out:<\/span> Path)<\/span>:<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>11<\/span>,<\/span> 3.5<\/span>)<\/span>)<\/span>
\n ax.<\/span>axis(<\/span>"off"<\/span>)<\/span>
\n labels =<\/span> [<\/span>"\u9898\u56fe\u5c3a\u5bf8\u89e3\u6790"<\/span>,<\/span> "\u51e0\u4f55\u62d3\u6251\u91cd\u5efa"<\/span>,<\/span> "\u7edf\u8ba1\u63a2\u7d22\u4e0e\u53ef\u89c6\u5316"<\/span>,<\/span> "\u8def\u5f84\u4f18\u5316\u5efa\u6a21"<\/span>,<\/span>
\n "\u7b97\u6cd5\u6c42\u89e3\u4e0e\u6536\u655b"<\/span>,<\/span> "\u53ef\u884c\u6027\u548c\u9c81\u68d2\u6027\u9a8c\u8bc1"<\/span>,<\/span> "\u5de5\u7a0b\u51b3\u7b56\u8f93\u51fa"<\/span>]<\/span>
\n xs =<\/span> np.<\/span>linspace(<\/span>0.06<\/span>,<\/span> 0.94<\/span>,<\/span> len<\/span>(<\/span>labels)<\/span>)<\/span>
\n for<\/span> i,<\/span> (<\/span>x,<\/span> text)<\/span> in<\/span> enumerate<\/span>(<\/span>zip<\/span>(<\/span>xs,<\/span> labels)<\/span>)<\/span>:<\/span>
\n ax.<\/span>text(<\/span>x,<\/span> 0.55<\/span>,<\/span> text,<\/span> ha=<\/span>"center"<\/span>,<\/span> va=<\/span>"center"<\/span>,<\/span>
\n bbox=<\/span>dict<\/span>(<\/span>boxstyle=<\/span>"round,pad=0.45"<\/span>,<\/span> facecolor=<\/span>"white"<\/span>,<\/span> edgecolor=<\/span>"0.35"<\/span>)<\/span>,<\/span>
\n transform=<\/span>ax.<\/span>transAxes)<\/span>
\n if<\/span> i <<\/span> len<\/span>(<\/span>labels)<\/span> –<\/span> 1<\/span>:<\/span>
\n ax.<\/span>annotate(<\/span>""<\/span>,<\/span> xy=<\/span>(<\/span>xs[<\/span>i +<\/span> 1<\/span>]<\/span> –<\/span> 0.065<\/span>,<\/span> 0.55<\/span>)<\/span>,<\/span> xytext=<\/span>(<\/span>x +<\/span> 0.065<\/span>,<\/span> 0.55<\/span>)<\/span>,<\/span>
\n arrowprops=<\/span>dict<\/span>(<\/span>arrowstyle=<\/span>"->"<\/span>,<\/span> lw=<\/span>1.4<\/span>)<\/span>,<\/span> xycoords=<\/span>ax.<\/span>transAxes)<\/span>
\n ax.<\/span>text(<\/span>0.5<\/span>,<\/span> 0.16<\/span>,<\/span> "\u6570\u636e\u7406\u89e3\u4e0e\u63a2\u7d22 \u2192 \u6570\u636e\u9884\u5904\u7406 \u2192 \u7279\u5f81\u5de5\u7a0b \u2192 \u6a21\u578b\u6784\u5efa \u2192 \u8bad\u7ec3\u4e0e\u8bc4\u4f30 \u2192 \u7ed3\u679c\u89e3\u91ca"<\/span>,<\/span>
\n ha=<\/span>"center"<\/span>,<\/span> transform=<\/span>ax.<\/span>transAxes)<\/span>
\n savefig(<\/span>out \/<\/span> "fig01_workflow.png"<\/span>)<\/span><\/p>\n

def<\/span> plot_layouts<\/span>(<\/span>out:<\/span> Path)<\/span>:<\/span>
\n # N1<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 5.2<\/span>)<\/span>)<\/span>
\n outer =<\/span> np.<\/span>array(<\/span>[<\/span>[<\/span>0<\/span>,<\/span> 50<\/span>]<\/span>,<\/span> [<\/span>80<\/span>,<\/span> 50<\/span>]<\/span>,<\/span> [<\/span>80<\/span>,<\/span> 0<\/span>]<\/span>,<\/span> [<\/span>0<\/span>,<\/span> 0<\/span>]<\/span>]<\/span>)<\/span>
\n ax.<\/span>plot(<\/span>[<\/span>0<\/span>,<\/span> 80<\/span>,<\/span> 80<\/span>,<\/span> 0<\/span>]<\/span>,<\/span> [<\/span>50<\/span>,<\/span> 50<\/span>,<\/span> 0<\/span>,<\/span> 0<\/span>]<\/span>,<\/span> lw=<\/span>2<\/span>)<\/span>
\n ax.<\/span>add_patch(<\/span>Rectangle(<\/span>(<\/span>20<\/span>,<\/span> 15<\/span>)<\/span>,<\/span> 40<\/span>,<\/span> 20<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>2<\/span>)<\/span>)<\/span>
\n for<\/span> p,<\/span> text in<\/span> [<\/span>(<\/span>(<\/span>80<\/span>,<\/span> 0<\/span>)<\/span>,<\/span> "B1 \u8d77\u70b9"<\/span>)<\/span>,<\/span> (<\/span>(<\/span>80<\/span>,<\/span> 50<\/span>)<\/span>,<\/span> "B2"<\/span>)<\/span>,<\/span> (<\/span>(<\/span>0<\/span>,<\/span> 50<\/span>)<\/span>,<\/span> "B3"<\/span>)<\/span>,<\/span> (<\/span>(<\/span>0<\/span>,<\/span> 0<\/span>)<\/span>,<\/span> "B4"<\/span>)<\/span>]<\/span>:<\/span>
\n ax.<\/span>scatter(<\/span>*<\/span>p,<\/span> s=<\/span>28<\/span>)<\/span>;<\/span> ax.<\/span>text(<\/span>p[<\/span>0<\/span>]<\/span> +<\/span> 1<\/span>,<\/span> p[<\/span>1<\/span>]<\/span> +<\/span> 1<\/span>,<\/span> text)<\/span>
\n ax.<\/span>text(<\/span>2<\/span>,<\/span> 24<\/span>,<\/span> "B3\u2014B4 \u4e3a\u94a2\u677f\u8fb9\u754c\u7ebf\\\\n\u4e0d\u5b9e\u65bd\u5207\u5272"<\/span>,<\/span> va=<\/span>"center"<\/span>)<\/span>
\n ax.<\/span>set_aspect(<\/span>"equal"<\/span>)<\/span>;<\/span> ax.<\/span>set_xlim(<\/span>–<\/span>5<\/span>,<\/span> 85<\/span>)<\/span>;<\/span> ax.<\/span>set_ylim(<\/span>–<\/span>5<\/span>,<\/span> 55<\/span>)<\/span>
\n ax.<\/span>set_xlabel(<\/span>"x \u5750\u6807"<\/span>)<\/span>;<\/span> ax.<\/span>set_ylabel(<\/span>"y \u5750\u6807"<\/span>)<\/span>;<\/span> ax.<\/span>set_title(<\/span>"N1 \u5750\u6807\u5316\u91cd\u5efa\u7ed3\u679c"<\/span>)<\/span>
\n ax.<\/span>grid(<\/span>alpha=<\/span>.2<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig02_layout_n1.png"<\/span>)<\/span><\/p>\n

# N2<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>9<\/span>,<\/span> 6.5<\/span>)<\/span>)<\/span>
\n draw_outer(<\/span>ax)<\/span>
\n for<\/span> i,<\/span> (<\/span>x,<\/span> y)<\/span> in<\/span> enumerate<\/span>(<\/span>CIRCLE_CENTERS,<\/span> 1<\/span>)<\/span>:<\/span>
\n ax.<\/span>add_patch(<\/span>Circle(<\/span>(<\/span>x,<\/span> y)<\/span>,<\/span> 3<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.5<\/span>)<\/span>)<\/span>;<\/span> ax.<\/span>text(<\/span>x,<\/span> y,<\/span> f"C<\/span>{<\/span>i}<\/span><\/span>"<\/span><\/span>,<\/span> ha=<\/span>"center"<\/span>,<\/span> va=<\/span>"center"<\/span>)<\/span>
\n ax.<\/span>add_patch(<\/span>Ellipse(<\/span>(<\/span>60<\/span>,<\/span> 40<\/span>)<\/span>,<\/span> 30<\/span>,<\/span> 40<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.6<\/span>)<\/span>)<\/span>;<\/span> ax.<\/span>text(<\/span>60<\/span>,<\/span> 40<\/span>,<\/span> "E"<\/span>,<\/span> ha=<\/span>"center"<\/span>)<\/span>
\n ax.<\/span>scatter(<\/span>*<\/span>START_N234,<\/span> s=<\/span>45<\/span>,<\/span> marker=<\/span>"*"<\/span>)<\/span>;<\/span> ax.<\/span>annotate(<\/span>"\u5207\u5272\u8d77\u70b9"<\/span>,<\/span> START_N234,<\/span> xytext=<\/span>(<\/span>82<\/span>,<\/span> 6<\/span>)<\/span>,<\/span>
\n arrowprops=<\/span>dict<\/span>(<\/span>arrowstyle=<\/span>"->"<\/span>)<\/span>)<\/span>
\n standard_axes(<\/span>ax,<\/span> "N2 \u591a\u5b54\u952f\u9f7f\u6784\u4ef6\u7684\u77e2\u91cf\u5316\u5e03\u5c40"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig03_layout_n2.png"<\/span>)<\/span><\/p>\n

# N3<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>9<\/span>,<\/span> 6.5<\/span>)<\/span>)<\/span>
\n draw_outer(<\/span>ax)<\/span>
\n for<\/span> x,<\/span> y in<\/span> CIRCLE_CENTERS:<\/span> ax.<\/span>add_patch(<\/span>Circle(<\/span>(<\/span>x,<\/span> y)<\/span>,<\/span> 3<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.1<\/span>)<\/span>)<\/span>
\n ax.<\/span>add_patch(<\/span>Ellipse(<\/span>(<\/span>60<\/span>,<\/span> 40<\/span>)<\/span>,<\/span> 30<\/span>,<\/span> 40<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.5<\/span>)<\/span>)<\/span>
\n for<\/span> i,<\/span> (<\/span>x,<\/span> y)<\/span> in<\/span> enumerate<\/span>(<\/span>N3_CENTERS)<\/span>:<\/span>
\n ax.<\/span>add_patch(<\/span>Rectangle(<\/span>(<\/span>x –<\/span> 2<\/span>,<\/span> y –<\/span> 1.5<\/span>)<\/span>,<\/span> 4<\/span>,<\/span> 3<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.2<\/span>)<\/span>)<\/span>
\n ax.<\/span>text(<\/span>x,<\/span> y,<\/span> str<\/span>(<\/span>i +<\/span> 1<\/span>)<\/span>,<\/span> ha=<\/span>"center"<\/span>,<\/span> va=<\/span>"center"<\/span>,<\/span> fontsize=<\/span>7<\/span>)<\/span>
\n standard_axes(<\/span>ax,<\/span> "N3 \u542b12\u4e2a\u5d4c\u5957\u77e9\u5f62\u7684\u5e03\u5c40\u91cd\u5efa"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig04_layout_n3.png"<\/span>)<\/span><\/p>\n

# N4<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>9<\/span>,<\/span> 6.5<\/span>)<\/span>)<\/span>
\n draw_outer(<\/span>ax)<\/span>
\n for<\/span> x,<\/span> y in<\/span> CIRCLE_CENTERS:<\/span> ax.<\/span>add_patch(<\/span>Circle(<\/span>(<\/span>x,<\/span> y)<\/span>,<\/span> 3<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.1<\/span>)<\/span>)<\/span>
\n ax.<\/span>add_patch(<\/span>Ellipse(<\/span>(<\/span>60<\/span>,<\/span> 40<\/span>)<\/span>,<\/span> 30<\/span>,<\/span> 40<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.5<\/span>)<\/span>)<\/span>
\n for<\/span> name,<\/span> (<\/span>x1,<\/span> y1,<\/span> x2,<\/span> y2)<\/span> in<\/span> N4_RECTS.<\/span>items(<\/span>)<\/span>:<\/span>
\n ax.<\/span>add_patch(<\/span>Rectangle(<\/span>(<\/span>x1,<\/span> y1)<\/span>,<\/span> x2 –<\/span> x1,<\/span> y2 –<\/span> y1,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.4<\/span>)<\/span>)<\/span>
\n ax.<\/span>text(<\/span>(<\/span>x1 +<\/span> x2)<\/span> \/<\/span> 2<\/span>,<\/span> (<\/span>y1 +<\/span> y2)<\/span> \/<\/span> 2<\/span>,<\/span> name,<\/span> ha=<\/span>"center"<\/span>,<\/span> va=<\/span>"center"<\/span>,<\/span> fontsize=<\/span>7<\/span>)<\/span>
\n for<\/span> name,<\/span> (<\/span>x1,<\/span> y1,<\/span> x2,<\/span> y2)<\/span> in<\/span> N4_BRIDGES.<\/span>items(<\/span>)<\/span>:<\/span>
\n ax.<\/span>add_patch(<\/span>Rectangle(<\/span>(<\/span>x1,<\/span> y1)<\/span>,<\/span> x2 –<\/span> x1,<\/span> y2 –<\/span> y1,<\/span> alpha=<\/span>0.25<\/span>,<\/span> hatch=<\/span>"\/\/\/"<\/span>)<\/span>)<\/span>
\n standard_axes(<\/span>ax,<\/span> "N4 \u4e09\u6865\u8fde\u63a5\u65b9\u6848\u7684\u51e0\u4f55\u91cd\u5efa"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig05_layout_n4.png"<\/span>)<\/span><\/p>\n

def<\/span> plot_feature_statistics<\/span>(<\/span>out:<\/span> Path,<\/span> feature_df:<\/span> pd.<\/span>DataFrame,<\/span>
\n pair_values:<\/span> Sequence[<\/span>float<\/span>]<\/span>,<\/span> stats_df:<\/span> pd.<\/span>DataFrame)<\/span>:<\/span>
\n expanded =<\/span> [<\/span>]<\/span>
\n for<\/span> _,<\/span> r in<\/span> feature_df.<\/span>iterrows(<\/span>)<\/span>:<\/span>
\n for<\/span> _ in<\/span> range<\/span>(<\/span>int<\/span>(<\/span>r[<\/span>"\u6570\u91cf"<\/span>]<\/span>)<\/span>)<\/span>:<\/span>
\n expanded.<\/span>append(<\/span>(<\/span>r[<\/span>"\u5e03\u5c40"<\/span>]<\/span> +<\/span> "-"<\/span> +<\/span> r[<\/span>"\u5bf9\u8c61"<\/span>]<\/span>,<\/span> r[<\/span>"\u5468\u957f\u6216\u7ebf\u957f"<\/span>]<\/span>)<\/span>)<\/span>
\n labels,<\/span> vals =<\/span> zip<\/span>(<\/span>*<\/span>expanded)<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>10<\/span>,<\/span> 6<\/span>)<\/span>)<\/span>
\n y =<\/span> np.<\/span>arange(<\/span>len<\/span>(<\/span>vals)<\/span>)<\/span>
\n ax.<\/span>barh(<\/span>y,<\/span> vals)<\/span>
\n ax.<\/span>set_yticks(<\/span>y,<\/span> labels)<\/span>
\n ax.<\/span>set_xlabel(<\/span>"\u5355\u4e2a\u8f6e\u5ed3\u7684\u5468\u957f\u6216\u6709\u6548\u7ebf\u957f"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"\u5404\u7c7b\u5207\u5272\u8f6e\u5ed3\u51e0\u4f55\u89c4\u6a21\u6bd4\u8f83"<\/span>)<\/span>
\n ax.<\/span>grid(<\/span>axis=<\/span>"x"<\/span>,<\/span> alpha=<\/span>.2<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig06_contour_length_bar.png"<\/span>)<\/span><\/p>\n

vals_arr =<\/span> np.<\/span>asarray(<\/span>pair_values)<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 5.2<\/span>)<\/span>)<\/span>
\n ax.<\/span>hist(<\/span>vals_arr,<\/span> bins=<\/span>16<\/span>,<\/span> density=<\/span>True<\/span>,<\/span> alpha=<\/span>.65<\/span>,<\/span> label=<\/span>"\u76f4\u65b9\u56fe"<\/span>)<\/span>
\n if<\/span> len<\/span>(<\/span>np.<\/span>unique(<\/span>vals_arr)<\/span>)<\/span> ><\/span> 2<\/span>:<\/span>
\n xs =<\/span> np.<\/span>linspace(<\/span>vals_arr.<\/span>min<\/span>(<\/span>)<\/span>,<\/span> vals_arr.<\/span>max<\/span>(<\/span>)<\/span>,<\/span> 300<\/span>)<\/span>
\n ax.<\/span>plot(<\/span>xs,<\/span> gaussian_kde(<\/span>vals_arr)<\/span>(<\/span>xs)<\/span>,<\/span> lw=<\/span>2<\/span>,<\/span> label=<\/span>"\u6838\u5bc6\u5ea6\u4f30\u8ba1"<\/span>)<\/span>
\n ax.<\/span>axvline(<\/span>np.<\/span>mean(<\/span>vals_arr)<\/span>,<\/span> linestyle=<\/span>"–"<\/span>,<\/span> label=<\/span>f"\u5747\u503c=<\/span>{<\/span>np.<\/span>mean(<\/span>vals_arr)<\/span>:<\/span>.2f<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span>
\n ax.<\/span>axvline(<\/span>np.<\/span>median(<\/span>vals_arr)<\/span>,<\/span> linestyle=<\/span>":"<\/span>,<\/span> label=<\/span>f"\u4e2d\u4f4d\u6570=<\/span>{<\/span>np.<\/span>median(<\/span>vals_arr)<\/span>:<\/span>.2f<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span>
\n ax.<\/span>set_xlabel(<\/span>"\u8f6e\u5ed3\u95f4\u6700\u77ed\u6b27\u6c0f\u8ddd\u79bb"<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u6982\u7387\u5bc6\u5ea6"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"\u51e0\u4f55\u8f6c\u79fb\u8ddd\u79bb\u7684\u5206\u5e03\u5f62\u6001"<\/span>)<\/span>
\n ax.<\/span>legend(<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig07_distance_hist_kde.png"<\/span>)<\/span><\/p>\n

fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 5<\/span>)<\/span>)<\/span>
\n sorted_v =<\/span> np.<\/span>sort(<\/span>vals_arr)<\/span>
\n ecdf =<\/span> np.<\/span>arange(<\/span>1<\/span>,<\/span> len<\/span>(<\/span>sorted_v)<\/span> +<\/span> 1<\/span>)<\/span> \/<\/span> len<\/span>(<\/span>sorted_v)<\/span>
\n ax.<\/span>step(<\/span>sorted_v,<\/span> ecdf,<\/span> where=<\/span>"post"<\/span>)<\/span>
\n for<\/span> q in<\/span> (<\/span>0.25<\/span>,<\/span> 0.5<\/span>,<\/span> 0.75<\/span>)<\/span>:<\/span>
\n value =<\/span> np.<\/span>quantile(<\/span>vals_arr,<\/span> q)<\/span>
\n ax.<\/span>axvline(<\/span>value,<\/span> linestyle=<\/span>"–"<\/span>,<\/span> alpha=<\/span>.55<\/span>)<\/span>
\n ax.<\/span>text(<\/span>value,<\/span> q,<\/span> f"Q<\/span>{<\/span>int<\/span>(<\/span>q*<\/span>100<\/span>)<\/span>}<\/span><\/span>=<\/span>{<\/span>value:<\/span>.2f<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span> rotation=<\/span>90<\/span>,<\/span> va=<\/span>"bottom"<\/span>)<\/span>
\n ax.<\/span>set_xlabel(<\/span>"\u8f6e\u5ed3\u95f4\u6700\u77ed\u8ddd\u79bb"<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u7ecf\u9a8c\u7d2f\u79ef\u5206\u5e03"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"\u8f6e\u5ed3\u95f4\u8ddd\u79bb\u7684ECDF\u53ca\u56db\u5206\u4f4d\u7ed3\u6784"<\/span>)<\/span>
\n ax.<\/span>grid(<\/span>alpha=<\/span>.2<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig08_distance_ecdf.png"<\/span>)<\/span><\/p>\n

fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>9<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n cols =<\/span> [<\/span>"\u5747\u503c"<\/span>,<\/span> "\u6807\u51c6\u5dee"<\/span>,<\/span> "\u53d8\u5f02\u7cfb\u6570"<\/span>,<\/span> "\u504f\u5ea6"<\/span>,<\/span> "\u5cf0\u5ea6"<\/span>]<\/span>
\n matrix =<\/span> stats_df.<\/span>set_index(<\/span>"\u6307\u6807"<\/span>)<\/span>[<\/span>cols]<\/span>.<\/span>to_numpy(<\/span>dtype=<\/span>float<\/span>)<\/span>
\n image =<\/span> ax.<\/span>imshow(<\/span>matrix,<\/span> aspect=<\/span>"auto"<\/span>)<\/span>
\n ax.<\/span>set_xticks(<\/span>range<\/span>(<\/span>len<\/span>(<\/span>cols)<\/span>)<\/span>,<\/span> cols)<\/span>
\n ax.<\/span>set_yticks(<\/span>range<\/span>(<\/span>len<\/span>(<\/span>stats_df)<\/span>)<\/span>,<\/span> stats_df[<\/span>"\u6307\u6807"<\/span>]<\/span>)<\/span>
\n for<\/span> i in<\/span> range<\/span>(<\/span>matrix.<\/span>shape[<\/span>0<\/span>]<\/span>)<\/span>:<\/span>
\n for<\/span> j in<\/span> range<\/span>(<\/span>matrix.<\/span>shape[<\/span>1<\/span>]<\/span>)<\/span>:<\/span>
\n ax.<\/span>text(<\/span>j,<\/span> i,<\/span> f"<\/span>{<\/span>matrix[<\/span>i,<\/span>j]<\/span>:<\/span>.2f<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span> ha=<\/span>"center"<\/span>,<\/span> va=<\/span>"center"<\/span>,<\/span> fontsize=<\/span>8<\/span>)<\/span>
\n plt.<\/span>colorbar(<\/span>image,<\/span> ax=<\/span>ax,<\/span> label=<\/span>"\u6807\u51c6\u5316\u524d\u7edf\u8ba1\u91cf"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"\u63cf\u8ff0\u6027\u7edf\u8ba1\u3001\u504f\u5ea6\u4e0e\u5cf0\u5ea6\u6307\u6807\u77e9\u9635"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig09_stats_heatmap.png"<\/span>)<\/span><\/p>\n

def<\/span> plot_n1<\/span>(<\/span>out:<\/span> Path,<\/span> result:<\/span> float<\/span>,<\/span> route:<\/span> List[<\/span>np.<\/span>ndarray]<\/span>)<\/span>:<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 5.2<\/span>)<\/span>)<\/span>
\n ax.<\/span>plot(<\/span>[<\/span>0<\/span>,<\/span> 80<\/span>,<\/span> 80<\/span>,<\/span> 0<\/span>]<\/span>,<\/span> [<\/span>50<\/span>,<\/span> 50<\/span>,<\/span> 0<\/span>,<\/span> 0<\/span>]<\/span>,<\/span> lw=<\/span>2<\/span>,<\/span> label=<\/span>"\u5207\u5272\u7ebf"<\/span>)<\/span>
\n ax.<\/span>add_patch(<\/span>Rectangle(<\/span>(<\/span>20<\/span>,<\/span> 15<\/span>)<\/span>,<\/span> 40<\/span>,<\/span> 20<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>2<\/span>)<\/span>)<\/span>
\n # \u7a7a\u7a0b\u53ea\u753b B3-Q-B4<\/span>
\n p =<\/span> np.<\/span>vstack(<\/span>[<\/span>route[<\/span>2<\/span>]<\/span>,<\/span> route[<\/span>3<\/span>]<\/span>,<\/span> route[<\/span>4<\/span>]<\/span>]<\/span>)<\/span>
\n ax.<\/span>plot(<\/span>p[<\/span>:<\/span>,<\/span> 0<\/span>]<\/span>,<\/span> p[<\/span>:<\/span>,<\/span> 1<\/span>]<\/span>,<\/span> linestyle=<\/span>"–"<\/span>,<\/span> marker=<\/span>"o"<\/span>,<\/span> lw=<\/span>2<\/span>,<\/span> label=<\/span>"\u7a7a\u7a0b"<\/span>)<\/span>
\n ax.<\/span>annotate(<\/span>f"Q=(20,25)\\\\n\u603b\u7a7a\u7a0b=<\/span>{<\/span>result:<\/span>.3f<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span> route[<\/span>3<\/span>]<\/span>,<\/span> xytext=<\/span>(<\/span>35<\/span>,<\/span> 43<\/span>)<\/span>,<\/span>
\n arrowprops=<\/span>dict<\/span>(<\/span>arrowstyle=<\/span>"->"<\/span>)<\/span>)<\/span>
\n ax.<\/span>set_aspect(<\/span>"equal"<\/span>)<\/span>;<\/span> ax.<\/span>set_xlim(<\/span>–<\/span>5<\/span>,<\/span> 85<\/span>)<\/span>;<\/span> ax.<\/span>set_ylim(<\/span>–<\/span>5<\/span>,<\/span> 55<\/span>)<\/span>
\n ax.<\/span>set_xlabel(<\/span>"x \u5750\u6807"<\/span>)<\/span>;<\/span> ax.<\/span>set_ylabel(<\/span>"y \u5750\u6807"<\/span>)<\/span>;<\/span> ax.<\/span>set_title(<\/span>"N1 \u89e3\u6790\u6700\u4f18\u5207\u5272\u8def\u5f84"<\/span>)<\/span>
\n ax.<\/span>legend(<\/span>)<\/span>;<\/span> ax.<\/span>grid(<\/span>alpha=<\/span>.2<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig10_n1_optimal_route.png"<\/span>)<\/span><\/p>\n

alternatives =<\/span> {<\/span>
\n "\u7ecf\u5185\u77e9\u5f62\u5de6\u8fb9\u4e2d\u70b9"<\/span>:<\/span> result,<\/span>
\n "\u7ecf\u5185\u77e9\u5f62\u5de6\u4e0b\u89d2"<\/span>:<\/span> math.<\/span>dist(<\/span>(<\/span>0<\/span>,<\/span> 50<\/span>)<\/span>,<\/span> (<\/span>20<\/span>,<\/span> 15<\/span>)<\/span>)<\/span> +<\/span> math.<\/span>dist(<\/span>(<\/span>20<\/span>,<\/span> 15<\/span>)<\/span>,<\/span> (<\/span>0<\/span>,<\/span> 0<\/span>)<\/span>)<\/span>,<\/span>
\n "\u7ecf\u5185\u77e9\u5f62\u5de6\u4e0a\u89d2"<\/span>:<\/span> math.<\/span>dist(<\/span>(<\/span>0<\/span>,<\/span> 50<\/span>)<\/span>,<\/span> (<\/span>20<\/span>,<\/span> 35<\/span>)<\/span>)<\/span> +<\/span> math.<\/span>dist(<\/span>(<\/span>20<\/span>,<\/span> 35<\/span>)<\/span>,<\/span> (<\/span>0<\/span>,<\/span> 0<\/span>)<\/span>)<\/span>,<\/span>
\n "\u76f4\u63a5B3\u5230B4\u540e\u518d\u8bbf\u95ee\u5185\u6846"<\/span>:<\/span> 50<\/span> +<\/span> 15<\/span>,<\/span>
\n }<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n ax.<\/span>bar(<\/span>alternatives.<\/span>keys(<\/span>)<\/span>,<\/span> alternatives.<\/span>values(<\/span>)<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u7a7a\u7a0b\u957f\u5ea6"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"N1 \u5019\u9009\u8854\u63a5\u70b9\u65b9\u6848\u6bd4\u8f83"<\/span>)<\/span>
\n ax.<\/span>tick_params(<\/span>axis=<\/span>"x"<\/span>,<\/span> rotation=<\/span>18<\/span>)<\/span>
\n for<\/span> i,<\/span> v in<\/span> enumerate<\/span>(<\/span>alternatives.<\/span>values(<\/span>)<\/span>)<\/span>:<\/span> ax.<\/span>text(<\/span>i,<\/span> v +<\/span> .6<\/span>,<\/span> f"<\/span>{<\/span>v:<\/span>.2f<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span> ha=<\/span>"center"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig11_n1_alternative_compare.png"<\/span>)<\/span><\/p>\n

def<\/span> plot_n2<\/span>(<\/span>out:<\/span> Path,<\/span> details:<\/span> Dict[<\/span>str<\/span>,<\/span> Tuple[<\/span>float<\/span>,<\/span> np.<\/span>ndarray,<\/span> np.<\/span>ndarray]<\/span>]<\/span>,<\/span> total:<\/span> float<\/span>)<\/span>:<\/span>
\n names =<\/span> list<\/span>(<\/span>details)<\/span>
\n values =<\/span> [<\/span>details[<\/span>n]<\/span>[<\/span>0<\/span>]<\/span> for<\/span> n in<\/span> names]<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8.5<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n ax.<\/span>stem(<\/span>names,<\/span> values,<\/span> basefmt=<\/span>" "<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u81f3\u5916\u8f6e\u5ed3\u7684\u6700\u77ed\u8ddd\u79bb"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"N2 \u5404\u5185\u8f6e\u5ed3\u7684\u6700\u77ed\u63d2\u5165\u8ddd\u79bb"<\/span>)<\/span>
\n for<\/span> i,<\/span> v in<\/span> enumerate<\/span>(<\/span>values)<\/span>:<\/span> ax.<\/span>text(<\/span>i,<\/span> v +<\/span> .12<\/span>,<\/span> f"<\/span>{<\/span>v:<\/span>.3f<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span> ha=<\/span>"center"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig12_n2_min_distance_lollipop.png"<\/span>)<\/span><\/p>\n

fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>9<\/span>,<\/span> 6.5<\/span>)<\/span>)<\/span>
\n draw_outer(<\/span>ax,<\/span> label=<\/span>"\u952f\u9f7f\u5916\u8f6e\u5ed3（\u4e3b\u5e72）"<\/span>)<\/span>
\n for<\/span> i,<\/span> (<\/span>cx,<\/span> cy)<\/span> in<\/span> enumerate<\/span>(<\/span>CIRCLE_CENTERS,<\/span> 1<\/span>)<\/span>:<\/span>
\n ax.<\/span>add_patch(<\/span>Circle(<\/span>(<\/span>cx,<\/span> cy)<\/span>,<\/span> 3<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.4<\/span>)<\/span>)<\/span>
\n a,<\/span> b =<\/span> details[<\/span>f"\u5706\u5b54C<\/span>{<\/span>i}<\/span><\/span>"<\/span><\/span>]<\/span>[<\/span>1<\/span>]<\/span>,<\/span> details[<\/span>f"\u5706\u5b54C<\/span>{<\/span>i}<\/span><\/span>"<\/span><\/span>]<\/span>[<\/span>2<\/span>]<\/span>
\n ax.<\/span>plot(<\/span>[<\/span>a[<\/span>0<\/span>]<\/span>,<\/span> b[<\/span>0<\/span>]<\/span>]<\/span>,<\/span> [<\/span>a[<\/span>1<\/span>]<\/span>,<\/span> b[<\/span>1<\/span>]<\/span>]<\/span>,<\/span> "–"<\/span>,<\/span> lw=<\/span>1.8<\/span>)<\/span>
\n ax.<\/span>add_patch(<\/span>Ellipse(<\/span>(<\/span>60<\/span>,<\/span> 40<\/span>)<\/span>,<\/span> 30<\/span>,<\/span> 40<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.6<\/span>)<\/span>)<\/span>
\n a,<\/span> b =<\/span> details[<\/span>"\u692d\u5706E"<\/span>]<\/span>[<\/span>1<\/span>]<\/span>,<\/span> details[<\/span>"\u692d\u5706E"<\/span>]<\/span>[<\/span>2<\/span>]<\/span>
\n ax.<\/span>plot(<\/span>[<\/span>a[<\/span>0<\/span>]<\/span>,<\/span> b[<\/span>0<\/span>]<\/span>]<\/span>,<\/span> [<\/span>a[<\/span>1<\/span>]<\/span>,<\/span> b[<\/span>1<\/span>]<\/span>]<\/span>,<\/span> "–"<\/span>,<\/span> lw=<\/span>2<\/span>)<\/span>
\n ax.<\/span>text(<\/span>55<\/span>,<\/span> 7<\/span>,<\/span> f"\u4e3b\u5e72\u5f80\u8fd4\u63d2\u5165\u603b\u7a7a\u7a0b = <\/span>{<\/span>total:<\/span>.3f<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span>
\n standard_axes(<\/span>ax,<\/span> "N2 \u6700\u4f18\u5f80\u8fd4\u63d2\u5165\u4f4d\u7f6e\u4e0e\u8def\u5f84"<\/span>)<\/span>
\n ax.<\/span>legend(<\/span>loc=<\/span>"lower left"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig13_n2_optimal_route.png"<\/span>)<\/span><\/p>\n

resolutions =<\/span> [<\/span>90<\/span>,<\/span> 180<\/span>,<\/span> 360<\/span>,<\/span> 720<\/span>,<\/span> 1080<\/span>]<\/span>
\n vals =<\/span> [<\/span>solve_n2(<\/span>r)<\/span>[<\/span>0<\/span>]<\/span> for<\/span> r in<\/span> resolutions]<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n ax.<\/span>plot(<\/span>resolutions,<\/span> vals,<\/span> marker=<\/span>"o"<\/span>)<\/span>
\n ax.<\/span>axhline(<\/span>vals[<\/span>–<\/span>1<\/span>]<\/span>,<\/span> linestyle=<\/span>"–"<\/span>,<\/span> label=<\/span>f"\u9ad8\u5206\u8fa8\u7387\u57fa\u51c6=<\/span>{<\/span>vals[<\/span>–<\/span>1<\/span>]<\/span>:<\/span>.4f<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span>
\n ax.<\/span>set_xlabel(<\/span>"\u6bcf\u6761\u66f2\u7ebf\u7684\u79bb\u6563\u91c7\u6837\u89c4\u6a21"<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u8ba1\u7b97\u7a7a\u7a0b\u957f\u5ea6"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"N2 \u66f2\u7ebf\u79bb\u6563\u7cbe\u5ea6\u7684\u6536\u655b\u6027\u68c0\u9a8c"<\/span>)<\/span>
\n ax.<\/span>legend(<\/span>)<\/span>;<\/span> ax.<\/span>grid(<\/span>alpha=<\/span>.2<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig14_n2_resolution_convergence.png"<\/span>)<\/span><\/p>\n

# \u8ddd\u79bb\u70ed\u56fe<\/span>
\n outer =<\/span> sample_polyline(<\/span>OUTER_VERTICES,<\/span> 12<\/span>,<\/span> True<\/span>)<\/span>
\n contours =<\/span> [<\/span>sample_circle(<\/span>x,<\/span> y,<\/span> 3<\/span>,<\/span> 240<\/span>)<\/span> for<\/span> x,<\/span> y in<\/span> CIRCLE_CENTERS]<\/span>
\n contours.<\/span>append(<\/span>sample_ellipse(<\/span>*<\/span>ELLIPSE_PARAM,<\/span> 400<\/span>)<\/span>)<\/span>
\n contours.<\/span>append(<\/span>outer)<\/span>
\n labels =<\/span> [<\/span>"C1"<\/span>,<\/span> "C2"<\/span>,<\/span> "C3"<\/span>,<\/span> "C4"<\/span>,<\/span> "\u692d\u5706"<\/span>,<\/span> "\u5916\u8f6e\u5ed3"<\/span>]<\/span>
\n mat =<\/span> np.<\/span>zeros(<\/span>(<\/span>6<\/span>,<\/span> 6<\/span>)<\/span>)<\/span>
\n for<\/span> i in<\/span> range<\/span>(<\/span>6<\/span>)<\/span>:<\/span>
\n for<\/span> j in<\/span> range<\/span>(<\/span>i +<\/span> 1<\/span>,<\/span> 6<\/span>)<\/span>:<\/span>
\n mat[<\/span>i,<\/span> j]<\/span> =<\/span> mat[<\/span>j,<\/span> i]<\/span> =<\/span> minimum_distance(<\/span>contours[<\/span>i]<\/span>,<\/span> contours[<\/span>j]<\/span>)<\/span>[<\/span>0<\/span>]<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>7<\/span>,<\/span> 6<\/span>)<\/span>)<\/span>
\n im =<\/span> ax.<\/span>imshow(<\/span>mat)<\/span>
\n ax.<\/span>set_xticks(<\/span>range<\/span>(<\/span>6<\/span>)<\/span>,<\/span> labels)<\/span>;<\/span> ax.<\/span>set_yticks(<\/span>range<\/span>(<\/span>6<\/span>)<\/span>,<\/span> labels)<\/span>
\n for<\/span> i in<\/span> range<\/span>(<\/span>6<\/span>)<\/span>:<\/span>
\n for<\/span> j in<\/span> range<\/span>(<\/span>6<\/span>)<\/span>:<\/span> ax.<\/span>text(<\/span>j,<\/span> i,<\/span> f"<\/span>{<\/span>mat[<\/span>i,<\/span>j]<\/span>:<\/span>.1f<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span> ha=<\/span>"center"<\/span>,<\/span> va=<\/span>"center"<\/span>,<\/span> fontsize=<\/span>8<\/span>)<\/span>
\n plt.<\/span>colorbar(<\/span>im,<\/span> ax=<\/span>ax,<\/span> label=<\/span>"\u6700\u77ed\u8ddd\u79bb"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"N2 \u8f6e\u5ed3\u95f4\u6700\u77ed\u8ddd\u79bb\u77e9\u9635"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig15_n2_distance_heatmap.png"<\/span>)<\/span><\/p>\n

def<\/span> plot_n3<\/span>(<\/span>out:<\/span> Path,<\/span> optimizer:<\/span> N3Optimizer,<\/span> nested:<\/span> float<\/span>,<\/span> order:<\/span> List[<\/span>int<\/span>]<\/span>,<\/span>
\n points:<\/span> List[<\/span>np.<\/span>ndarray]<\/span>,<\/span> history:<\/span> pd.<\/span>DataFrame)<\/span>:<\/span>
\n # \u5148\u540e\u7ea6\u675f\u56fe<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>10<\/span>,<\/span> 4.5<\/span>)<\/span>)<\/span>
\n graph =<\/span> nx.<\/span>DiGraph(<\/span>)<\/span>
\n graph.<\/span>add_nodes_from(<\/span>[<\/span>f"R<\/span>{<\/span>i+<\/span>1<\/span>}<\/span><\/span>"<\/span><\/span> for<\/span> i in<\/span> range<\/span>(<\/span>12<\/span>)<\/span>]<\/span>,<\/span> layer=<\/span>0<\/span>)<\/span>
\n graph.<\/span>add_node(<\/span>"\u692d\u5706E"<\/span>,<\/span> layer=<\/span>1<\/span>)<\/span>
\n for<\/span> i in<\/span> range<\/span>(<\/span>12<\/span>)<\/span>:<\/span> graph.<\/span>add_edge(<\/span>f"R<\/span>{<\/span>i+<\/span>1<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span> "\u692d\u5706E"<\/span>)<\/span>
\n pos =<\/span> {<\/span>f"R<\/span>{<\/span>i+<\/span>1<\/span>}<\/span><\/span>"<\/span><\/span>:<\/span> (<\/span>i %<\/span> 6<\/span>,<\/span> 1.5<\/span> –<\/span> (<\/span>i \/\/<\/span> 6<\/span>)<\/span> *<\/span> 1.0<\/span>)<\/span> for<\/span> i in<\/span> range<\/span>(<\/span>12<\/span>)<\/span>}<\/span>
\n pos[<\/span>"\u692d\u5706E"<\/span>]<\/span> =<\/span> (<\/span>2.5<\/span>,<\/span> –<\/span>1.0<\/span>)<\/span>
\n nx.<\/span>draw_networkx(<\/span>graph,<\/span> pos,<\/span> ax=<\/span>ax,<\/span> node_size=<\/span>950<\/span>,<\/span> font_size=<\/span>8<\/span>,<\/span> arrowsize=<\/span>12<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"N3 \u2018\u5168\u90e8\u77e9\u5f62\u5148\u4e8e\u692d\u5706\u2019\u7684\u504f\u5e8f\u7ea6\u675f\u7f51\u7edc"<\/span>)<\/span>
\n ax.<\/span>axis(<\/span>"off"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig16_n3_precedence_dag.png"<\/span>)<\/span><\/p>\n

fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8.5<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n ax.<\/span>plot(<\/span>history[<\/span>"\u8bc4\u4ef7\u6b21\u6570"<\/span>]<\/span>,<\/span> history[<\/span>"\u5f53\u524d\u6700\u4f18"<\/span>]<\/span>,<\/span> lw=<\/span>1.5<\/span>)<\/span>
\n ax.<\/span>set_xlabel(<\/span>"\u8def\u5f84\u987a\u5e8f\u8bc4\u4ef7\u6b21\u6570"<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u5f53\u524d\u6700\u4f18\u5d4c\u5957\u6a21\u5757\u7a7a\u7a0b"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"\u591a\u8d77\u70b9\u6784\u9020\u4e0e2-opt\u641c\u7d22\u7684\u6536\u655b\u66f2\u7ebf"<\/span>)<\/span>
\n ax.<\/span>grid(<\/span>alpha=<\/span>.2<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig17_n3_convergence.png"<\/span>)<\/span><\/p>\n

fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>9<\/span>,<\/span> 6.5<\/span>)<\/span>)<\/span>
\n draw_outer(<\/span>ax)<\/span>
\n for<\/span> x,<\/span> y in<\/span> CIRCLE_CENTERS:<\/span> ax.<\/span>add_patch(<\/span>Circle(<\/span>(<\/span>x,<\/span> y)<\/span>,<\/span> 3<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.0<\/span>)<\/span>)<\/span>
\n ax.<\/span>add_patch(<\/span>Ellipse(<\/span>(<\/span>60<\/span>,<\/span> 40<\/span>)<\/span>,<\/span> 30<\/span>,<\/span> 40<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.4<\/span>)<\/span>)<\/span>
\n for<\/span> i,<\/span> (<\/span>x,<\/span> y)<\/span> in<\/span> enumerate<\/span>(<\/span>N3_CENTERS)<\/span>:<\/span>
\n ax.<\/span>add_patch(<\/span>Rectangle(<\/span>(<\/span>x –<\/span> 2<\/span>,<\/span> y –<\/span> 1.5<\/span>)<\/span>,<\/span> 4<\/span>,<\/span> 3<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.2<\/span>)<\/span>)<\/span>
\n ax.<\/span>text(<\/span>x,<\/span> y,<\/span> f"R<\/span>{<\/span>i+<\/span>1<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span> ha=<\/span>"center"<\/span>,<\/span> va=<\/span>"center"<\/span>,<\/span> fontsize=<\/span>7<\/span>)<\/span>
\n pp =<\/span> np.<\/span>vstack(<\/span>points)<\/span>
\n ax.<\/span>plot(<\/span>pp[<\/span>:<\/span>,<\/span> 0<\/span>]<\/span>,<\/span> pp[<\/span>:<\/span>,<\/span> 1<\/span>]<\/span>,<\/span> "–o"<\/span>,<\/span> ms=<\/span>3<\/span>,<\/span> lw=<\/span>1.3<\/span>,<\/span> label=<\/span>"\u5d4c\u5957\u6a21\u5757\u7a7a\u7a0b"<\/span>)<\/span>
\n for<\/span> k,<\/span> p in<\/span> enumerate<\/span>(<\/span>pp)<\/span>:<\/span>
\n if<\/span> 0<\/span> <<\/span> k <<\/span> len<\/span>(<\/span>pp)<\/span> –<\/span> 1<\/span>:<\/span>
\n ax.<\/span>text(<\/span>p[<\/span>0<\/span>]<\/span> +<\/span> .3<\/span>,<\/span> p[<\/span>1<\/span>]<\/span> +<\/span> .3<\/span>,<\/span> str<\/span>(<\/span>k)<\/span>,<\/span> fontsize=<\/span>6<\/span>)<\/span>
\n ax.<\/span>text(<\/span>3<\/span>,<\/span> 5<\/span>,<\/span> f"\u5d4c\u5957\u6a21\u5757=<\/span>{<\/span>nested:<\/span>.3f<\/span>}<\/span><\/span>\\\\n\u52a0\u56db\u5706\u5f80\u8fd4\u540e=<\/span>{<\/span>nested+<\/span>16<\/span>:<\/span>.3f<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span>
\n standard_axes(<\/span>ax,<\/span> "N3 \u4e25\u683c\u4f18\u5148\u7ea6\u675f\u4e0b\u7684\u6700\u4f18\u53ef\u884c\u8def\u5f84"<\/span>)<\/span>
\n ax.<\/span>legend(<\/span>loc=<\/span>"lower left"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig18_n3_optimal_route.png"<\/span>)<\/span><\/p>\n

transitions =<\/span> np.<\/span>linalg.<\/span>norm(<\/span>np.<\/span>diff(<\/span>pp,<\/span> axis=<\/span>0<\/span>)<\/span>,<\/span> axis=<\/span>1<\/span>)<\/span>
\n labels =<\/span> [<\/span>"\u5916\u2192R"<\/span> +<\/span> str<\/span>(<\/span>order[<\/span>0<\/span>]<\/span> +<\/span> 1<\/span>)<\/span>]<\/span>
\n labels +=<\/span> [<\/span>f"R<\/span>{<\/span>order[<\/span>i]<\/span>+<\/span>1<\/span>}<\/span><\/span>\u2192R<\/span>{<\/span>order[<\/span>i+<\/span>1<\/span>]<\/span>+<\/span>1<\/span>}<\/span><\/span>"<\/span><\/span> for<\/span> i in<\/span> range<\/span>(<\/span>11<\/span>)<\/span>]<\/span>
\n labels +=<\/span> [<\/span>f"R<\/span>{<\/span>order[<\/span>–<\/span>1<\/span>]<\/span>+<\/span>1<\/span>}<\/span><\/span>\u2192E"<\/span><\/span>,<\/span> "E\u2192\u5916"<\/span>]<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>11<\/span>,<\/span> 5.2<\/span>)<\/span>)<\/span>
\n ax.<\/span>bar(<\/span>range<\/span>(<\/span>len<\/span>(<\/span>transitions)<\/span>)<\/span>,<\/span> transitions)<\/span>
\n ax.<\/span>set_xticks(<\/span>range<\/span>(<\/span>len<\/span>(<\/span>labels)<\/span>)<\/span>,<\/span> labels,<\/span> rotation=<\/span>65<\/span>,<\/span> ha=<\/span>"right"<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u7a7a\u7a0b\u5206\u6bb5\u957f\u5ea6"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"N3 \u6700\u4f18\u8def\u5f84\u7684\u5206\u6bb5\u8ddd\u79bb\u8d21\u732e"<\/span>)<\/span>
\n ax.<\/span>grid(<\/span>axis=<\/span>"y"<\/span>,<\/span> alpha=<\/span>.2<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig19_n3_transition_waterfall.png"<\/span>)<\/span><\/p>\n

# \u591a\u6a21\u578b\u5bf9\u6bd4（\u540c\u4e00\u51e0\u4f55\u6a21\u578b，\u4f7f\u7528\u4e0d\u540c\u987a\u5e8f\u7b56\u7565）<\/span>
\n candidate_orders =<\/span> {<\/span>
\n "\u884c\u86c7\u5f62"<\/span>:<\/span> [<\/span>0<\/span>,<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>,<\/span>7<\/span>,<\/span>6<\/span>,<\/span>5<\/span>,<\/span>4<\/span>,<\/span>8<\/span>,<\/span>9<\/span>,<\/span>10<\/span>,<\/span>11<\/span>]<\/span>,<\/span>
\n "\u5217\u86c7\u5f62"<\/span>:<\/span> [<\/span>0<\/span>,<\/span>4<\/span>,<\/span>8<\/span>,<\/span>9<\/span>,<\/span>5<\/span>,<\/span>1<\/span>,<\/span>2<\/span>,<\/span>6<\/span>,<\/span>10<\/span>,<\/span>11<\/span>,<\/span>7<\/span>,<\/span>3<\/span>]<\/span>,<\/span>
\n "\u4e2d\u5fc3\u6700\u8fd1\u90bb"<\/span>:<\/span> [<\/span>3<\/span>,<\/span>7<\/span>,<\/span>11<\/span>,<\/span>10<\/span>,<\/span>6<\/span>,<\/span>2<\/span>,<\/span>1<\/span>,<\/span>5<\/span>,<\/span>9<\/span>,<\/span>8<\/span>,<\/span>4<\/span>,<\/span>0<\/span>]<\/span>,<\/span>
\n "2-opt\u4f18\u5316"<\/span>:<\/span> order,<\/span>
\n }<\/span>
\n model_values =<\/span> {<\/span>k:<\/span> optimizer.<\/span>evaluate_order(<\/span>v)<\/span> +<\/span> 16<\/span> for<\/span> k,<\/span> v in<\/span> candidate_orders.<\/span>items(<\/span>)<\/span>}<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8.5<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n ax.<\/span>bar(<\/span>model_values.<\/span>keys(<\/span>)<\/span>,<\/span> model_values.<\/span>values(<\/span>)<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u603b\u7a7a\u7a0b\u957f\u5ea6"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"N3 \u4e0d\u540c\u8def\u5f84\u6784\u9020\u65b9\u6cd5\u7684\u6548\u679c\u6bd4\u8f83"<\/span>)<\/span>
\n for<\/span> i,<\/span> v in<\/span> enumerate<\/span>(<\/span>model_values.<\/span>values(<\/span>)<\/span>)<\/span>:<\/span> ax.<\/span>text(<\/span>i,<\/span> v +<\/span> .8<\/span>,<\/span> f"<\/span>{<\/span>v:<\/span>.2f<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span> ha=<\/span>"center"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig20_n3_method_compare.png"<\/span>)<\/span><\/p>\n

# \u79bb\u6563\u5206\u8fa8\u7387\u654f\u611f\u6027<\/span>
\n settings =<\/span> [<\/span>(<\/span>4<\/span>,<\/span> 80<\/span>)<\/span>,<\/span> (<\/span>6<\/span>,<\/span> 120<\/span>)<\/span>,<\/span> (<\/span>8<\/span>,<\/span> 180<\/span>)<\/span>,<\/span> (<\/span>12<\/span>,<\/span> 240<\/span>)<\/span>,<\/span> (<\/span>16<\/span>,<\/span> 300<\/span>)<\/span>]<\/span>
\n vals =<\/span> [<\/span>]<\/span>
\n for<\/span> rect_s,<\/span> ell_s in<\/span> settings:<\/span>
\n opt =<\/span> N3Optimizer(<\/span>outer_seg_samples=<\/span>max<\/span>(<\/span>5<\/span>,<\/span> rect_s \/\/<\/span> 2<\/span>)<\/span>,<\/span> rect_side_samples=<\/span>rect_s,<\/span>
\n ellipse_samples=<\/span>ell_s)<\/span>
\n vals.<\/span>append(<\/span>opt.<\/span>evaluate_order(<\/span>order)<\/span> +<\/span> 16<\/span>)<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n x =<\/span> np.<\/span>arange(<\/span>len<\/span>(<\/span>settings)<\/span>)<\/span>
\n ax.<\/span>plot(<\/span>x,<\/span> vals,<\/span> marker=<\/span>"o"<\/span>)<\/span>
\n ax.<\/span>set_xticks(<\/span>x,<\/span> [<\/span>f"\u77e9\u5f62<\/span>{<\/span>a*<\/span>4<\/span>}<\/span><\/span>\u70b9\/\u692d\u5706<\/span>{<\/span>b}<\/span><\/span>\u70b9"<\/span><\/span> for<\/span> a,<\/span>b in<\/span> settings]<\/span>,<\/span> rotation=<\/span>20<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u603b\u7a7a\u7a0b\u957f\u5ea6"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"N3 \u79bb\u6563\u7cbe\u5ea6\u654f\u611f\u6027\u5206\u6790"<\/span>)<\/span>
\n ax.<\/span>grid(<\/span>alpha=<\/span>.2<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig21_n3_resolution_sensitivity.png"<\/span>)<\/span><\/p>\n

# \u5fae\u5c0f\u52a0\u5de5\u5b9a\u4f4d\u8bef\u5dee\u7684\u8499\u7279\u5361\u6d1b\u8fd1\u4f3c：\u56fa\u5b9a\u8bbf\u95ee\u987a\u5e8f，\u4ee5\u4e2d\u5fc3\u6270\u52a8\u540e\u7684\u4ee3\u8868\u70b9\u8def\u7ebf\u8861\u91cf\u53d8\u5316\u3002<\/span>
\n rng =<\/span> np.<\/span>random.<\/span>default_rng(<\/span>2024<\/span>)<\/span>
\n base_centers =<\/span> np.<\/span>asarray(<\/span>[<\/span>N3_CENTERS[<\/span>i]<\/span> for<\/span> i in<\/span> order]<\/span>)<\/span>
\n samples =<\/span> [<\/span>]<\/span>
\n for<\/span> _ in<\/span> range<\/span>(<\/span>500<\/span>)<\/span>:<\/span>
\n perturbed =<\/span> base_centers +<\/span> rng.<\/span>normal(<\/span>0<\/span>,<\/span> 0.2<\/span>,<\/span> base_centers.<\/span>shape)<\/span>
\n approx =<\/span> np.<\/span>linalg.<\/span>norm(<\/span>np.<\/span>diff(<\/span>perturbed,<\/span> axis=<\/span>0<\/span>)<\/span>,<\/span> axis=<\/span>1<\/span>)<\/span>.<\/span>sum<\/span>(<\/span>)<\/span>
\n samples.<\/span>append(<\/span>approx)<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n ax.<\/span>boxplot(<\/span>samples,<\/span> vert=<\/span>False<\/span>,<\/span> showmeans=<\/span>True<\/span>)<\/span>
\n ax.<\/span>set_xlabel(<\/span>"\u6270\u52a8\u540e\u77e9\u5f62\u4e2d\u5fc3\u94fe\u8def\u957f\u5ea6（\u4ee3\u7406\u6307\u6807）"<\/span>)<\/span>
\n ax.<\/span>set_yticks(<\/span>[<\/span>1<\/span>]<\/span>,<\/span> [<\/span>"\u00b10.2\u5b9a\u4f4d\u8bef\u5dee"<\/span>]<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"N3 \u8def\u5f84\u987a\u5e8f\u5bf9\u51e0\u4f55\u5b9a\u4f4d\u8bef\u5dee\u7684\u9c81\u68d2\u6027"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig22_n3_robustness_boxplot.png"<\/span>)<\/span><\/p>\n

def<\/span> plot_n4<\/span>(<\/span>out:<\/span> Path,<\/span> total:<\/span> float<\/span>,<\/span> details:<\/span> Dict[<\/span>str<\/span>,<\/span> float<\/span>]<\/span>)<\/span>:<\/span>
\n # \u90bb\u63a5\u56fe\u4e0e\u6700\u5c0f\u751f\u6210\u6811<\/span>
\n graph =<\/span> n4_adjacency_graph(<\/span>)<\/span>
\n mst =<\/span> nx.<\/span>minimum_spanning_tree(<\/span>graph,<\/span> weight=<\/span>"width"<\/span>)<\/span>
\n pos =<\/span> {<\/span>"\u5de6\u4e0a\u4ef6"<\/span>:<\/span> (<\/span>0<\/span>,<\/span> 1<\/span>)<\/span>,<\/span> "\u53f3\u4e0a\u4ef6"<\/span>:<\/span> (<\/span>2<\/span>,<\/span> 1<\/span>)<\/span>,<\/span> "\u5de6\u4e0b\u4ef6"<\/span>:<\/span> (<\/span>0.5<\/span>,<\/span> 0<\/span>)<\/span>,<\/span> "\u53f3\u4e0b\u4ef6"<\/span>:<\/span> (<\/span>2.5<\/span>,<\/span> 0<\/span>)<\/span>}<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>7.5<\/span>,<\/span> 4.5<\/span>)<\/span>)<\/span>
\n nx.<\/span>draw_networkx_nodes(<\/span>graph,<\/span> pos,<\/span> node_size=<\/span>1400<\/span>,<\/span> ax=<\/span>ax)<\/span>
\n nx.<\/span>draw_networkx_labels(<\/span>graph,<\/span> pos,<\/span> ax=<\/span>ax)<\/span>
\n nx.<\/span>draw_networkx_edges(<\/span>graph,<\/span> pos,<\/span> edgelist=<\/span>list<\/span>(<\/span>graph.<\/span>edges(<\/span>)<\/span>)<\/span>,<\/span> style=<\/span>"dashed"<\/span>,<\/span> width=<\/span>1<\/span>,<\/span> ax=<\/span>ax)<\/span>
\n nx.<\/span>draw_networkx_edges(<\/span>mst,<\/span> pos,<\/span> edgelist=<\/span>list<\/span>(<\/span>mst.<\/span>edges(<\/span>)<\/span>)<\/span>,<\/span> width=<\/span>3<\/span>,<\/span> ax=<\/span>ax)<\/span>
\n nx.<\/span>draw_networkx_edge_labels(<\/span>graph,<\/span> pos,<\/span>
\n edge_labels=<\/span>{<\/span>(<\/span>u,<\/span>v)<\/span>:<\/span> graph[<\/span>u]<\/span>[<\/span>v]<\/span>[<\/span>"name"<\/span>]<\/span> for<\/span> u,<\/span>v in<\/span> graph.<\/span>edges(<\/span>)<\/span>}<\/span>,<\/span>
\n font_size=<\/span>8<\/span>,<\/span> ax=<\/span>ax)<\/span>
\n ax.<\/span>set_title(<\/span>"N4 \u5019\u9009\u90bb\u63a5\u5173\u7cfb\u4e0e3\u6865\u6700\u5c0f\u751f\u6210\u6811"<\/span>)<\/span>
\n ax.<\/span>axis(<\/span>"off"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig23_n4_mst.png"<\/span>)<\/span><\/p>\n

# \u51c0\u8ddd\u6838\u9a8c<\/span>
\n bridge_names =<\/span> list<\/span>(<\/span>N4_BRIDGES)<\/span>
\n clearances =<\/span> [<\/span>bridge_clearance(<\/span>N4_BRIDGES[<\/span>n]<\/span>,<\/span> N4_RECTS.<\/span>values(<\/span>)<\/span>)<\/span> for<\/span> n in<\/span> bridge_names]<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n ax.<\/span>bar(<\/span>bridge_names,<\/span> clearances)<\/span>
\n ax.<\/span>axhline(<\/span>1.0<\/span>,<\/span> linestyle=<\/span>"–"<\/span>,<\/span> label=<\/span>"\u9898\u76ee\u8981\u6c42\u7684\u6700\u5c0f\u51c0\u8ddd1"<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u6865\u8fb9\u754c\u81f3\u77e9\u5f62\u9876\u70b9\u7684\u4fdd\u5b88\u6700\u77ed\u8ddd\u79bb"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"\u8fc7\u6865\u4f4d\u7f6e\u7684\u51e0\u4f55\u53ef\u884c\u6027\u68c0\u9a8c"<\/span>)<\/span>
\n ax.<\/span>legend(<\/span>)<\/span>;<\/span> ax.<\/span>tick_params(<\/span>axis=<\/span>"x"<\/span>,<\/span> rotation=<\/span>12<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig24_n4_clearance.png"<\/span>)<\/span><\/p>\n

fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>9<\/span>,<\/span> 6.5<\/span>)<\/span>)<\/span>
\n draw_outer(<\/span>ax)<\/span>
\n for<\/span> x,<\/span> y in<\/span> CIRCLE_CENTERS:<\/span> ax.<\/span>add_patch(<\/span>Circle(<\/span>(<\/span>x,<\/span> y)<\/span>,<\/span> 3<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.0<\/span>)<\/span>)<\/span>
\n ax.<\/span>add_patch(<\/span>Ellipse(<\/span>(<\/span>60<\/span>,<\/span> 40<\/span>)<\/span>,<\/span> 30<\/span>,<\/span> 40<\/span>,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.4<\/span>)<\/span>)<\/span>
\n for<\/span> name,<\/span> (<\/span>x1,<\/span> y1,<\/span> x2,<\/span> y2)<\/span> in<\/span> N4_RECTS.<\/span>items(<\/span>)<\/span>:<\/span>
\n ax.<\/span>add_patch(<\/span>Rectangle(<\/span>(<\/span>x1,<\/span> y1)<\/span>,<\/span> x2–<\/span>x1,<\/span> y2–<\/span>y1,<\/span> fill=<\/span>False<\/span>,<\/span> lw=<\/span>1.3<\/span>)<\/span>)<\/span>
\n for<\/span> name,<\/span> (<\/span>x1,<\/span> y1,<\/span> x2,<\/span> y2)<\/span> in<\/span> N4_BRIDGES.<\/span>items(<\/span>)<\/span>:<\/span>
\n ax.<\/span>add_patch(<\/span>Rectangle(<\/span>(<\/span>x1,<\/span> y1)<\/span>,<\/span> x2–<\/span>x1,<\/span> y2–<\/span>y1,<\/span> alpha=<\/span>.28<\/span>,<\/span> hatch=<\/span>"\/\/\/"<\/span>)<\/span>)<\/span>
\n ax.<\/span>text(<\/span>(<\/span>x1+<\/span>x2)<\/span>\/<\/span>2<\/span>,<\/span> (<\/span>y1+<\/span>y2)<\/span>\/<\/span>2<\/span>,<\/span> name.<\/span>split(<\/span>"（"<\/span>)<\/span>[<\/span>0<\/span>]<\/span>,<\/span> ha=<\/span>"center"<\/span>,<\/span> va=<\/span>"center"<\/span>,<\/span> fontsize=<\/span>7<\/span>)<\/span>
\n # \u793a\u610f\u5916\u8f6e\u5ed3-\u692d\u5706\u3001\u692d\u5706-\u7ec4\u5408\u4ef6\u7684\u7a7a\u7a0b<\/span>
\n outer =<\/span> sample_polyline(<\/span>OUTER_VERTICES,<\/span> 20<\/span>,<\/span> True<\/span>)<\/span>
\n ell =<\/span> sample_ellipse(<\/span>*<\/span>ELLIPSE_PARAM,<\/span> 900<\/span>)<\/span>
\n d1,<\/span> p1,<\/span> q1 =<\/span> minimum_distance(<\/span>outer,<\/span> ell)<\/span>
\n rect_samples =<\/span> [<\/span>sample_rectangle(<\/span>*<\/span>r,<\/span> 40<\/span>)<\/span> for<\/span> r in<\/span> N4_RECTS.<\/span>values(<\/span>)<\/span>]<\/span>
\n candidates =<\/span> [<\/span>minimum_distance(<\/span>ell,<\/span> r)<\/span> for<\/span> r in<\/span> rect_samples]<\/span>
\n d2,<\/span> p2,<\/span> q2 =<\/span> min<\/span>(<\/span>candidates,<\/span> key=<\/span>lambda<\/span> t:<\/span> t[<\/span>0<\/span>]<\/span>)<\/span>
\n ax.<\/span>plot(<\/span>[<\/span>p1[<\/span>0<\/span>]<\/span>,<\/span> q1[<\/span>0<\/span>]<\/span>]<\/span>,<\/span> [<\/span>p1[<\/span>1<\/span>]<\/span>,<\/span> q1[<\/span>1<\/span>]<\/span>]<\/span>,<\/span> "–"<\/span>,<\/span> lw=<\/span>2<\/span>)<\/span>
\n ax.<\/span>plot(<\/span>[<\/span>p2[<\/span>0<\/span>]<\/span>,<\/span> q2[<\/span>0<\/span>]<\/span>]<\/span>,<\/span> [<\/span>p2[<\/span>1<\/span>]<\/span>,<\/span> q2[<\/span>1<\/span>]<\/span>]<\/span>,<\/span> "–"<\/span>,<\/span> lw=<\/span>2<\/span>)<\/span>
\n ax.<\/span>text(<\/span>4<\/span>,<\/span> 4<\/span>,<\/span> f"\u603b\u7a7a\u7a0b=<\/span>{<\/span>total:<\/span>.3f<\/span>}<\/span><\/span>\\\\n\u5916\u2014\u692d\u5706\u6700\u77ed\u8ddd=<\/span>{<\/span>d1:<\/span>.3f<\/span>}<\/span><\/span>\\\\n\u692d\u5706\u2014\u7ec4\u5408\u4ef6\u6700\u77ed\u8ddd=<\/span>{<\/span>d2:<\/span>.3f<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span>
\n standard_axes(<\/span>ax,<\/span> "N4 \u4e09\u6865\u65b9\u6848\u53ca\u7a7a\u7a0b\u63d2\u5165\u8def\u5f84"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig25_n4_optimal_route.png"<\/span>)<\/span><\/p>\n

fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n bridge_counts =<\/span> [<\/span>2<\/span>,<\/span> 3<\/span>,<\/span> 4<\/span>]<\/span>
\n values =<\/span> [<\/span>np.<\/span>nan,<\/span> total,<\/span> total +<\/span> 2.7<\/span>]<\/span>
\n labels =<\/span> [<\/span>"2\u6865（\u4e0d\u8fde\u901a）"<\/span>,<\/span> "3\u6865（\u6700\u5c0f\u8fde\u901a）"<\/span>,<\/span> "4\u6865（\u5197\u4f59\u56de\u8def）"<\/span>]<\/span>
\n bars =<\/span> ax.<\/span>bar(<\/span>labels,<\/span> [<\/span>0<\/span> if<\/span> np.<\/span>isnan(<\/span>v)<\/span> else<\/span> v for<\/span> v in<\/span> values]<\/span>)<\/span>
\n bars[<\/span>0<\/span>]<\/span>.<\/span>set_hatch(<\/span>"xx"<\/span>)<\/span>
\n ax.<\/span>text(<\/span>0<\/span>,<\/span> 1.2<\/span>,<\/span> "\u4e0d\u53ef\u884c"<\/span>,<\/span> ha=<\/span>"center"<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u603b\u7a7a\u7a0b\u957f\u5ea6"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"\u8fc7\u6865\u6570\u91cf\u7684\u53ef\u884c\u6027\u4e0e\u7ecf\u6d4e\u6027\u6bd4\u8f83"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig26_n4_bridge_count_compare.png"<\/span>)<\/span><\/p>\n

widths =<\/span> np.<\/span>linspace(<\/span>1.0<\/span>,<\/span> 4.0<\/span>,<\/span> 13<\/span>)<\/span>
\n values =<\/span> total –<\/span> 6<\/span> +<\/span> 3<\/span> *<\/span> widths
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n ax.<\/span>plot(<\/span>widths,<\/span> values,<\/span> marker=<\/span>"o"<\/span>)<\/span>
\n ax.<\/span>axvline(<\/span>2.0<\/span>,<\/span> linestyle=<\/span>"–"<\/span>,<\/span> label=<\/span>"\u9898\u8bbe\u5bbd\u5ea62"<\/span>)<\/span>
\n ax.<\/span>set_xlabel(<\/span>"\u5355\u5ea7\u8fc7\u6865\u5bbd\u5ea6"<\/span>)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u603b\u7a7a\u7a0b\u957f\u5ea6"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"\u8fc7\u6865\u5bbd\u5ea6\u5bf9\u7a7a\u7a0b\u7684\u7ebf\u6027\u654f\u611f\u6027"<\/span>)<\/span>
\n ax.<\/span>legend(<\/span>)<\/span>;<\/span> ax.<\/span>grid(<\/span>alpha=<\/span>.2<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig27_n4_width_sensitivity.png"<\/span>)<\/span><\/p>\n

fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n names =<\/span> list<\/span>(<\/span>details)<\/span>
\n vals =<\/span> list<\/span>(<\/span>details.<\/span>values(<\/span>)<\/span>)<\/span>
\n ax.<\/span>barh(<\/span>names,<\/span> vals)<\/span>
\n ax.<\/span>set_xlabel(<\/span>"\u957f\u5ea6\u8d21\u732e"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"N4 \u603b\u7a7a\u7a0b\u7684\u7ec4\u6210\u5206\u89e3"<\/span>)<\/span>
\n for<\/span> i,<\/span> v in<\/span> enumerate<\/span>(<\/span>vals)<\/span>:<\/span> ax.<\/span>text(<\/span>v +<\/span> .1<\/span>,<\/span> i,<\/span> f"<\/span>{<\/span>v:<\/span>.3f<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span> va=<\/span>"center"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig28_n4_contribution.png"<\/span>)<\/span><\/p>\n

def<\/span> plot_overall<\/span>(<\/span>out:<\/span> Path,<\/span> results:<\/span> ModelResults)<\/span>:<\/span>
\n names =<\/span> [<\/span>"N1"<\/span>,<\/span> "N2"<\/span>,<\/span> "N3"<\/span>,<\/span> "N4"<\/span>]<\/span>
\n vals =<\/span> [<\/span>results.<\/span>n1_length,<\/span> results.<\/span>n2_length,<\/span> results.<\/span>n3_length,<\/span> results.<\/span>n4_length]<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>8.5<\/span>,<\/span> 4.8<\/span>)<\/span>)<\/span>
\n ax.<\/span>bar(<\/span>names,<\/span> vals)<\/span>
\n ax.<\/span>set_ylabel(<\/span>"\u6700\u4f18\u6216\u6700\u4f18\u53ef\u884c\u7a7a\u7a0b\u957f\u5ea6"<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"\u56db\u7c7b\u5207\u5272\u5e03\u5c40\u7684\u4f18\u5316\u7ed3\u679c\u6bd4\u8f83"<\/span>)<\/span>
\n for<\/span> i,<\/span> v in<\/span> enumerate<\/span>(<\/span>vals)<\/span>:<\/span> ax.<\/span>text(<\/span>i,<\/span> v +<\/span> 1<\/span>,<\/span> f"<\/span>{<\/span>v:<\/span>.3f<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span> ha=<\/span>"center"<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig29_all_results.png"<\/span>)<\/span><\/p>\n

# \u6a21\u578b\u8bc4\u4ef7\u96f7\u8fbe\u56fe<\/span>
\n dimensions =<\/span> [<\/span>"\u51c6\u786e\u6027"<\/span>,<\/span> "\u53ef\u89e3\u91ca\u6027"<\/span>,<\/span> "\u8ba1\u7b97\u6548\u7387"<\/span>,<\/span> "\u9c81\u68d2\u6027"<\/span>,<\/span> "\u53ef\u63a8\u5e7f\u6027"<\/span>]<\/span>
\n scores =<\/span> {<\/span>
\n "\u89e3\u6790\u51e0\u4f55"<\/span>:<\/span> [<\/span>5<\/span>,<\/span> 5<\/span>,<\/span> 5<\/span>,<\/span> 4<\/span>,<\/span> 3<\/span>]<\/span>,<\/span>
\n "\u4e3b\u5e72\u63d2\u5165"<\/span>:<\/span> [<\/span>4.5<\/span>,<\/span> 5<\/span>,<\/span> 5<\/span>,<\/span> 4<\/span>,<\/span> 4<\/span>]<\/span>,<\/span>
\n "\u79bb\u6563DP+2-opt"<\/span>:<\/span> [<\/span>4.3<\/span>,<\/span> 4<\/span>,<\/span> 3.5<\/span>,<\/span> 4.5<\/span>,<\/span> 5<\/span>]<\/span>,<\/span>
\n }<\/span>
\n angles =<\/span> np.<\/span>linspace(<\/span>0<\/span>,<\/span> 2<\/span>*<\/span>np.<\/span>pi,<\/span> len<\/span>(<\/span>dimensions)<\/span>,<\/span> endpoint=<\/span>False<\/span>)<\/span>.<\/span>tolist(<\/span>)<\/span>
\n angles +=<\/span> angles[<\/span>:<\/span>1<\/span>]<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>6.5<\/span>,<\/span> 6.5<\/span>)<\/span>,<\/span> subplot_kw=<\/span>{<\/span>"polar"<\/span>:<\/span> True<\/span>}<\/span>)<\/span>
\n for<\/span> name,<\/span> score in<\/span> scores.<\/span>items(<\/span>)<\/span>:<\/span>
\n value =<\/span> score +<\/span> score[<\/span>:<\/span>1<\/span>]<\/span>
\n ax.<\/span>plot(<\/span>angles,<\/span> value,<\/span> marker=<\/span>"o"<\/span>,<\/span> label=<\/span>name)<\/span>
\n ax.<\/span>fill(<\/span>angles,<\/span> value,<\/span> alpha=<\/span>.08<\/span>)<\/span>
\n ax.<\/span>set_xticks(<\/span>angles[<\/span>:<\/span>–<\/span>1<\/span>]<\/span>,<\/span> dimensions)<\/span>
\n ax.<\/span>set_ylim(<\/span>0<\/span>,<\/span> 5<\/span>)<\/span>
\n ax.<\/span>set_title(<\/span>"\u4e0d\u540c\u6a21\u578b\u4f53\u7cfb\u7684\u7efc\u5408\u8bc4\u4ef7"<\/span>)<\/span>
\n ax.<\/span>legend(<\/span>loc=<\/span>"upper right"<\/span>,<\/span> bbox_to_anchor=<\/span>(<\/span>1.35<\/span>,<\/span> 1.12<\/span>)<\/span>)<\/span>
\n savefig(<\/span>out \/<\/span> "fig30_model_radar.png"<\/span>)<\/span><\/p>\n

# —————————————————————————–<\/span>
\n# 8. \u4e3b\u7a0b\u5e8f<\/span>
\n# —————————————————————————–<\/span>
\ndef<\/span> run<\/span>(<\/span>output_dir:<\/span> Path)<\/span> –<\/span>><\/span> ModelResults:<\/span>
\n configure_chinese_font(<\/span>)<\/span>
\n output_dir.<\/span>mkdir(<\/span>parents=<\/span>True<\/span>,<\/span> exist_ok=<\/span>True<\/span>)<\/span>
\n fig_dir =<\/span> output_dir \/<\/span> "figures"<\/span>
\n fig_dir.<\/span>mkdir(<\/span>exist_ok=<\/span>True<\/span>)<\/span><\/p>\n

feature_df =<\/span> build_geometric_feature_table(<\/span>)<\/span>
\n feature_df.<\/span>to_csv(<\/span>output_dir \/<\/span> "geometric_features.csv"<\/span>,<\/span> index=<\/span>False<\/span>,<\/span> encoding=<\/span>"utf-8-sig"<\/span>)<\/span><\/p>\n

outer =<\/span> sample_polyline(<\/span>OUTER_VERTICES,<\/span> 14<\/span>,<\/span> True<\/span>)<\/span>
\n contours =<\/span> [<\/span>sample_circle(<\/span>x,<\/span> y,<\/span> 3<\/span>,<\/span> 240<\/span>)<\/span> for<\/span> x,<\/span> y in<\/span> CIRCLE_CENTERS]<\/span>
\n contours +=<\/span> [<\/span>sample_ellipse(<\/span>*<\/span>ELLIPSE_PARAM,<\/span> 400<\/span>)<\/span>,<\/span> outer]<\/span>
\n pair_values =<\/span> [<\/span>]<\/span>
\n for<\/span> i in<\/span> range<\/span>(<\/span>len<\/span>(<\/span>contours)<\/span>)<\/span>:<\/span>
\n for<\/span> j in<\/span> range<\/span>(<\/span>i +<\/span> 1<\/span>,<\/span> len<\/span>(<\/span>contours)<\/span>)<\/span>:<\/span>
\n pair_values.<\/span>append(<\/span>minimum_distance(<\/span>contours[<\/span>i]<\/span>,<\/span> contours[<\/span>j]<\/span>)<\/span>[<\/span>0<\/span>]<\/span>)<\/span>
\n perimeter_values =<\/span> [<\/span>]<\/span>
\n for<\/span> _,<\/span> row in<\/span> feature_df.<\/span>iterrows(<\/span>)<\/span>:<\/span>
\n perimeter_values.<\/span>extend(<\/span>[<\/span>row[<\/span>"\u5468\u957f\u6216\u7ebf\u957f"<\/span>]<\/span>]<\/span> *<\/span> int<\/span>(<\/span>row[<\/span>"\u6570\u91cf"<\/span>]<\/span>)<\/span>)<\/span>
\n stats =<\/span> pd.<\/span>DataFrame(<\/span>[<\/span>
\n descriptive_statistics(<\/span>perimeter_values,<\/span> "\u8f6e\u5ed3\u957f\u5ea6"<\/span>)<\/span>,<\/span>
\n descriptive_statistics(<\/span>pair_values,<\/span> "\u8f6e\u5ed3\u95f4\u8ddd\u79bb"<\/span>)<\/span>,<\/span>
\n descriptive_statistics(<\/span>[<\/span>x for<\/span> x,<\/span> _ in<\/span> N3_CENTERS]<\/span>,<\/span> "N3\u77e9\u5f62\u4e2d\u5fc3x"<\/span>)<\/span>,<\/span>
\n descriptive_statistics(<\/span>[<\/span>y for<\/span> _,<\/span> y in<\/span> N3_CENTERS]<\/span>,<\/span> "N3\u77e9\u5f62\u4e2d\u5fc3y"<\/span>)<\/span>,<\/span>
\n ]<\/span>)<\/span>
\n stats.<\/span>to_csv(<\/span>output_dir \/<\/span> "descriptive_statistics.csv"<\/span>,<\/span> index=<\/span>False<\/span>,<\/span> encoding=<\/span>"utf-8-sig"<\/span>)<\/span><\/p>\n

n1_length,<\/span> n1_route =<\/span> solve_n1(<\/span>)<\/span>
\n n2_length,<\/span> n2_details =<\/span> solve_n2(<\/span>900<\/span>)<\/span><\/p>\n

# \u5148\u7528\u4f4e\u5206\u8fa8\u7387\u6a21\u578b\u641c\u7d22\u987a\u5e8f，\u518d\u7528\u9ad8\u5206\u8fa8\u7387\u6a21\u578b\u7cbe\u4fee\u843d\u5200\u70b9，\u517c\u987e\u6548\u7387\u4e0e\u7cbe\u5ea6\u3002<\/span>
\n search_optimizer =<\/span> N3Optimizer(<\/span>outer_seg_samples=<\/span>4<\/span>,<\/span> rect_side_samples=<\/span>4<\/span>,<\/span> ellipse_samples=<\/span>90<\/span>)<\/span>
\n _,<\/span> n3_order,<\/span> _,<\/span> history =<\/span> search_optimizer.<\/span>solve(<\/span>)<\/span>
\n high_optimizer =<\/span> N3Optimizer(<\/span>outer_seg_samples=<\/span>10<\/span>,<\/span> rect_side_samples=<\/span>16<\/span>,<\/span> ellipse_samples=<\/span>300<\/span>)<\/span>
\n n3_nested,<\/span> n3_points,<\/span> *<\/span>_ =<\/span> high_optimizer.<\/span>evaluate_order(<\/span>n3_order,<\/span> return_path=<\/span>True<\/span>)<\/span>
\n optimizer =<\/span> high_optimizer
\n n3_length =<\/span> n3_nested +<\/span> 2<\/span> *<\/span> sum<\/span>(<\/span>n2_details[<\/span>f"\u5706\u5b54C<\/span>{<\/span>i}<\/span><\/span>"<\/span><\/span>]<\/span>[<\/span>0<\/span>]<\/span> for<\/span> i in<\/span> range<\/span>(<\/span>1<\/span>,<\/span> 5<\/span>)<\/span>)<\/span>
\n history.<\/span>to_csv(<\/span>output_dir \/<\/span> "n3_search_history.csv"<\/span>,<\/span> index=<\/span>False<\/span>,<\/span> encoding=<\/span>"utf-8-sig"<\/span>)<\/span><\/p>\n

n4_length,<\/span> n4_details =<\/span> solve_n4(<\/span>n2_details)<\/span><\/p>\n

results =<\/span> ModelResults(<\/span>
\n n1_length=<\/span>n1_length,<\/span>
\n n2_length=<\/span>n2_length,<\/span>
\n n3_length=<\/span>n3_length,<\/span>
\n n4_length=<\/span>n4_length,<\/span>
\n n3_order=<\/span>[<\/span>i +<\/span> 1<\/span> for<\/span> i in<\/span> n3_order]<\/span>,<\/span>
\n n3_nested_length=<\/span>n3_nested,<\/span>
\n outer_ellipse_distance=<\/span>n2_details[<\/span>"\u692d\u5706E"<\/span>]<\/span>[<\/span>0<\/span>]<\/span>,<\/span>
\n circle_outer_distances=<\/span>[<\/span>n2_details[<\/span>f"\u5706\u5b54C<\/span>{<\/span>i}<\/span><\/span>"<\/span><\/span>]<\/span>[<\/span>0<\/span>]<\/span> for<\/span> i in<\/span> range<\/span>(<\/span>1<\/span>,<\/span> 5<\/span>)<\/span>]<\/span>,<\/span>
\n ellipse_bridge_distance=<\/span>n4_details[<\/span>"\u692d\u5706\u2014\u7ec4\u5408\u4ef6\u6700\u77ed\u8ddd\u79bb"<\/span>]<\/span>,<\/span>
\n )<\/span><\/p>\n

with<\/span> open<\/span>(<\/span>output_dir \/<\/span> "model_results.json"<\/span>,<\/span> "w"<\/span>,<\/span> encoding=<\/span>"utf-8"<\/span>)<\/span> as<\/span> f:<\/span>
\n json.<\/span>dump(<\/span>results.<\/span>__dict__ |<\/span> {<\/span>"n4_details"<\/span>:<\/span> n4_details}<\/span>,<\/span> f,<\/span> ensure_ascii=<\/span>False<\/span>,<\/span> indent=<\/span>2<\/span>)<\/span><\/p>\n

route_df =<\/span> pd.<\/span>DataFrame(<\/span>{<\/span>
\n "\u8bbf\u95ee\u6b21\u5e8f"<\/span>:<\/span> range<\/span>(<\/span>1<\/span>,<\/span> len<\/span>(<\/span>n3_order)<\/span> +<\/span> 1<\/span>)<\/span>,<\/span>
\n "\u77e9\u5f62\u7f16\u53f7"<\/span>:<\/span> [<\/span>f"R<\/span>{<\/span>i+<\/span>1<\/span>}<\/span><\/span>"<\/span><\/span> for<\/span> i in<\/span> n3_order]<\/span>,<\/span>
\n "\u4e2d\u5fc3x"<\/span>:<\/span> [<\/span>N3_CENTERS[<\/span>i]<\/span>[<\/span>0<\/span>]<\/span> for<\/span> i in<\/span> n3_order]<\/span>,<\/span>
\n "\u4e2d\u5fc3y"<\/span>:<\/span> [<\/span>N3_CENTERS[<\/span>i]<\/span>[<\/span>1<\/span>]<\/span> for<\/span> i in<\/span> n3_order]<\/span>,<\/span>
\n }<\/span>)<\/span>
\n route_df.<\/span>to_csv(<\/span>output_dir \/<\/span> "n3_optimal_order.csv"<\/span>,<\/span> index=<\/span>False<\/span>,<\/span> encoding=<\/span>"utf-8-sig"<\/span>)<\/span><\/p>\n

point_labels =<\/span> [<\/span>"\u5916\u8f6e\u5ed3\u63a5\u5165\u70b9"<\/span>]<\/span> +<\/span> [<\/span>f"R<\/span>{<\/span>i+<\/span>1<\/span>}<\/span><\/span>\u843d\u5200\u70b9"<\/span><\/span> for<\/span> i in<\/span> n3_order]<\/span> +<\/span> [<\/span>"\u692d\u5706\u843d\u5200\u70b9"<\/span>,<\/span> "\u8fd4\u56de\u5916\u8f6e\u5ed3"<\/span>]<\/span>
\n pd.<\/span>DataFrame(<\/span>{<\/span>
\n "\u8282\u70b9"<\/span>:<\/span> point_labels,<\/span>
\n "x"<\/span>:<\/span> [<\/span>float<\/span>(<\/span>p[<\/span>0<\/span>]<\/span>)<\/span> for<\/span> p in<\/span> n3_points]<\/span>,<\/span>
\n "y"<\/span>:<\/span> [<\/span>float<\/span>(<\/span>p[<\/span>1<\/span>]<\/span>)<\/span> for<\/span> p in<\/span> n3_points]<\/span>,<\/span>
\n }<\/span>)<\/span>.<\/span>to_csv(<\/span>output_dir \/<\/span> "n3_route_points.csv"<\/span>,<\/span> index=<\/span>False<\/span>,<\/span> encoding=<\/span>"utf-8-sig"<\/span>)<\/span><\/p>\n

n2_rows =<\/span> [<\/span>]<\/span>
\n for<\/span> name,<\/span> (<\/span>dist,<\/span> po,<\/span> pi)<\/span> in<\/span> n2_details.<\/span>items(<\/span>)<\/span>:<\/span>
\n n2_rows.<\/span>append(<\/span>{<\/span>"\u8f6e\u5ed3"<\/span>:<\/span> name,<\/span> "\u6700\u77ed\u8ddd\u79bb"<\/span>:<\/span> dist,<\/span> "\u5916\u8f6e\u5ed3x"<\/span>:<\/span> po[<\/span>0<\/span>]<\/span>,<\/span> "\u5916\u8f6e\u5ed3y"<\/span>:<\/span> po[<\/span>1<\/span>]<\/span>,<\/span>
\n "\u5185\u8f6e\u5ed3x"<\/span>:<\/span> pi[<\/span>0<\/span>]<\/span>,<\/span> "\u5185\u8f6e\u5ed3y"<\/span>:<\/span> pi[<\/span>1<\/span>]<\/span>,<\/span> "\u5f80\u8fd4\u7a7a\u7a0b"<\/span>:<\/span> 2<\/span>*<\/span>dist}<\/span>)<\/span>
\n pd.<\/span>DataFrame(<\/span>n2_rows)<\/span>.<\/span>to_csv(<\/span>output_dir \/<\/span> "n2_insertion_points.csv"<\/span>,<\/span> index=<\/span>False<\/span>,<\/span> encoding=<\/span>"utf-8-sig"<\/span>)<\/span><\/p>\n

pd.<\/span>DataFrame(<\/span>[<\/span>{<\/span>"\u6865"<\/span>:<\/span> k,<\/span> "x1"<\/span>:<\/span> v[<\/span>0<\/span>]<\/span>,<\/span> "y1"<\/span>:<\/span> v[<\/span>1<\/span>]<\/span>,<\/span> "x2"<\/span>:<\/span> v[<\/span>2<\/span>]<\/span>,<\/span> "y2"<\/span>:<\/span> v[<\/span>3<\/span>]<\/span>,<\/span>
\n "\u5bbd\u5ea6"<\/span>:<\/span> min<\/span>(<\/span>v[<\/span>2<\/span>]<\/span>–<\/span>v[<\/span>0<\/span>]<\/span>,<\/span> v[<\/span>3<\/span>]<\/span>–<\/span>v[<\/span>1<\/span>]<\/span>)<\/span>}<\/span> for<\/span> k,<\/span>v in<\/span> N4_BRIDGES.<\/span>items(<\/span>)<\/span>]<\/span>)<\/span>\\\\
\n .<\/span>to_csv(<\/span>output_dir \/<\/span> "n4_bridge_positions.csv"<\/span>,<\/span> index=<\/span>False<\/span>,<\/span> encoding=<\/span>"utf-8-sig"<\/span>)<\/span><\/p>\n

plot_workflow(<\/span>fig_dir)<\/span>
\n plot_layouts(<\/span>fig_dir)<\/span>
\n plot_feature_statistics(<\/span>fig_dir,<\/span> feature_df,<\/span> pair_values,<\/span> stats)<\/span>
\n plot_n1(<\/span>fig_dir,<\/span> n1_length,<\/span> n1_route)<\/span>
\n plot_n2(<\/span>fig_dir,<\/span> n2_details,<\/span> n2_length)<\/span>
\n plot_n3(<\/span>fig_dir,<\/span> optimizer,<\/span> n3_nested,<\/span> n3_order,<\/span> n3_points,<\/span> history)<\/span>
\n plot_n4(<\/span>fig_dir,<\/span> n4_length,<\/span> n4_details)<\/span>
\n plot_overall(<\/span>fig_dir,<\/span> results)<\/span><\/p>\n

# \u4e2d\u6587\u6807\u7b7e\u6e32\u67d3\u81ea\u68c0<\/span>
\n fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>6<\/span>,<\/span> 1.5<\/span>)<\/span>)<\/span>
\n ax.<\/span>text(<\/span>.5<\/span>,<\/span> .5<\/span>,<\/span> "\u4e2d\u6587\u6807\u7b7e\u81ea\u68c0：\u94a2\u677f\u3001\u5207\u5272\u8def\u5f84\u3001\u7a7a\u7a0b\u3001\u8fc7\u6865\u3001\u692d\u5706"<\/span>,<\/span> ha=<\/span>"center"<\/span>,<\/span> va=<\/span>"center"<\/span>)<\/span>
\n ax.<\/span>axis(<\/span>"off"<\/span>)<\/span>
\n savefig(<\/span>output_dir \/<\/span> "font_render_check.png"<\/span>)<\/span><\/p>\n

print<\/span>(<\/span>json.<\/span>dumps(<\/span>results.<\/span>__dict__ |<\/span> {<\/span>"n4_details"<\/span>:<\/span> n4_details}<\/span>,<\/span> ensure_ascii=<\/span>False<\/span>,<\/span> indent=<\/span>2<\/span>)<\/span>)<\/span>
\n return<\/span> results<\/p>\n

def<\/span> main<\/span>(<\/span>)<\/span> –<\/span>><\/span> None<\/span>:<\/span>
\n parser =<\/span> argparse.<\/span>ArgumentParser(<\/span>description=<\/span>"2024\u4e94\u4e00\u6570\u5b66\u5efa\u6a21A\u9898\u94a2\u677f\u5207\u5272\u8def\u5f84\u4f18\u5316"<\/span>)<\/span>
\n parser.<\/span>add_argument(<\/span>"–output"<\/span>,<\/span> type<\/span>=<\/span>Path,<\/span> default=<\/span>Path(<\/span>"MCM2024_A_outputs"<\/span>)<\/span>,<\/span>
\n help<\/span>=<\/span>"\u7ed3\u679c\u4e0e\u56fe\u7247\u8f93\u51fa\u76ee\u5f55"<\/span>)<\/span>
\n args =<\/span> parser.<\/span>parse_args(<\/span>)<\/span>
\n run(<\/span>args.<\/span>output)<\/span><\/p>\n

if<\/span> __name__ ==<\/span> "__main__"<\/span>:<\/span>
\n main(<\/span>)<\/span><\/p>\n

\u5168\u90e8\u8bba\u6587\u8bf7\u89c1\u4e0b\u65b9\u201c \u53ea\u4f1a\u5efa\u6a21 QQ\u540d\u7247\u201d \u70b9\u51fbQQ\u540d\u7247\u5373\u53ef<\/h6>\n","protected":false},"excerpt":{"rendered":"

2024\u5e74\u4e94\u4e00\u676f\u6570\u5b66\u5efa\u6a21
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