{"id":51506,"date":"2025-08-10T23:39:22","date_gmt":"2025-08-10T15:39:22","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/51506.html"},"modified":"2025-08-10T23:39:22","modified_gmt":"2025-08-10T15:39:22","slug":"%e3%80%90%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84-%e5%b9%b6%e6%9f%a5%e9%9b%86%e3%80%91","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/51506.html","title":{"rendered":"\u3010\u6570\u636e\u7ed3\u6784\u2014\u2014\u5e76\u67e5\u96c6\u3011"},"content":{"rendered":"

\u5f15\u5165<\/h3>\n

\u5e76\u67e5\u96c6（Disjoint Set Union，DSU）\u662f\u4e00\u79cd\u7528\u4e8e\u7ba1\u7406\u5143\u7d20\u5206\u7ec4\u7684\u6570\u636e\u7ed3\u6784\u3002<\/p>\n

\u5408\u5e76（Union）：\u5c06\u4e24\u4e2a\u4e0d\u76f8\u4ea4\u7684\u96c6\u5408\u5408\u5e76\u4e3a\u4e00\u4e2a\u96c6\u5408\u3002
\n\u67e5\u627e（Find）：\u786e\u5b9a\u67d0\u4e2a\u5143\u7d20\u5c5e\u4e8e\u54ea\u4e2a\u96c6\u5408，\u901a\u5e38\u901a\u8fc7\u8fd4\u56de\u96c6\u5408\u7684\u201c\u4ee3\u8868\u5143\u7d20\u201d（groupID\u6216\u7236\u8282\u70b9）\u5b9e\u73b0\u3002<\/p>\n

quickFind \u548c quickUnion \u662f\u5e76\u67e5\u96c6\u7684\u4e24\u79cd\u5b9e\u73b0\u65b9\u5f0f\u3002<\/p>\n

\u6bcf\u4e2a\u5143\u7d20\u521d\u59cb\u65f6\u662f\u4e00\u4e2a\u72ec\u7acb\u7684\u96c6\u5408，\u5176groupID\u662f\u672c\u8eab\u4e0b\u6807\u6216\u7236\u8282\u70b9\u6307\u5411\u81ea\u5df1（\u5206\u522b\u8868\u660e\u5404\u81ea\u5c5e\u4e8e\u54ea\u4e2a\u96c6\u5408）\u3002
\n\u5982\u4e0b：
\n\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"
\n\u4e3b\u8981\u5c31\u662f\u5bf9\u4e24\u4e2a\u6570\u7ec4\u6240\u5b58\u7684\u5185\u5bb9\u8fdb\u884c\u64cd\u4f5c，\u7279\u522b\u662f\u4ee3\u8868\u5143\u7d20\u90e8\u5206\u3002
\n\u5bf9\u4ee3\u8868\u5143\u7d20\u8fdb\u884c\u64cd\u4f5c\u7684\u65b9\u5411（\u601d\u8003\u89d2\u5ea6）\u4e0d\u540c，\u5c31\u4f1a\u4f7f\u7528\u4e0d\u540c\u7684\u89e3\u51b3\u65b9\u6848（\u5982\u9009\u62e9quickFind\u8fd8\u662fquickUnion,）<\/p>\n

quickFind<\/h3>\n

\u6bcf\u4e2a\u5143\u7d20\u76f4\u63a5\u6307\u5411\u5176\u6240\u5c5e\u96c6\u5408\u7684\u4ee3\u8868\u5143（\u6839\u8282\u70b9），\u5408\u5e76\u64cd\u4f5c\u65f6\u9700\u8981\u904d\u5386\u6574\u4e2a\u6570\u7ec4\u66f4\u65b0\u6240\u6709\u76f8\u5173\u5143\u7d20\u3002<\/p>\n

\u65f6\u95f4\u590d\u6742\u5ea6：
\n\u67e5\u627e（Find）：O(1)，\u76f4\u63a5\u8bbf\u95ee\u6570\u7ec4\u5373\u53ef\u786e\u5b9a\u6240\u5c5e\u96c6\u5408\u3002
\n\u5408\u5e76（Union）：O(n)，\u9700\u8981\u904d\u5386\u6570\u7ec4\u66f4\u65b0\u6240\u6709\u5c5e\u4e8e\u540c\u4e00\u96c6\u5408\u7684\u5143\u7d20\u3002<\/p>\n

\u7279\u70b9：\u67e5\u627e\u901f\u5ea6\u5feb，\u4f46\u5408\u5e76\u6548\u7387\u4f4e（\u627e\u5feb\u5408\u6162）\u3002<\/p>\n

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

\u5934\u6587\u4ef6<\/h3>\n

#<\/span>pragma<\/span> once<\/span><\/span>
\ntypedef<\/span> int<\/span> Element;<\/span><\/p>\n

typedef<\/span> struct<\/span> {<\/span>
\nElement*<\/span> data;<\/span> \/\/\u5b58\u50a8\u5177\u4f53\u6570\u636e\u7ec4\u7f16\u53f7<\/span>
\nint<\/span>*<\/span> groupID;<\/span> \/\/\u5b58\u50a8\u7ec4\u7f16\u53f7<\/span>
\nint<\/span> n;<\/span> \/\/\u5143\u7d20\u4e2a\u6570<\/span>
\n}<\/span>QuickFindSet;<\/span><\/p>\n

QuickFindSet*<\/span> createQuickFindSet<\/span>(<\/span>int<\/span> n)<\/span>;<\/span>\/\/\u521b\u5efan\u4e2a\u5143\u7d20\u7684quickFind\u6811（\u5feb\u67e5\u6811）<\/span>
\nvoid<\/span> releaseQuickFindSet<\/span>(<\/span>QuickFindSet*<\/span> setQF)<\/span>;<\/span>\/\/\u91ca\u653esetQF\u8fd9\u4e2a\u6811<\/span>
\nvoid<\/span> initQuickFindSet<\/span>(<\/span>const<\/span> QuickFindSet*<\/span> setQF,<\/span> const<\/span> Element*<\/span> data,<\/span> int<\/span> n)<\/span>;<\/span>
\n \/\/\u521d\u59cb\u5316setQF\u8fd9\u4e2a\u542bn\u4e2a\u7ed3\u70b9\u7684\u5feb\u67e5\u6811，\u4ee5\u53cadata\u6570\u7ec4\u7684\u503c(groupID\u6570\u7ec4\u521d\u59cb\u65f6\u5e38\u4ee5\u4e0b\u6807\u4e3a\u503c,\u4f9d\u6b21\u8d4b\u503c\u5c31\u884c\u4e86)<\/span>
\n\/\/\u67e5,\u5224\u65ad\u4e24\u4e2a\u5143\u7d20\u662f\u4e0d\u662f\u540c\u4e00\u4e2a\u7ec4<\/span>
\nint<\/span> isSameQF<\/span>(<\/span>QuickFindSet*<\/span> setQF,<\/span> Element a,<\/span> Element b)<\/span>;<\/span>
\n\/\/\u5e76，\u5408\u5e76\u4e24\u4e2a\u5143\u7d20<\/span>
\nvoid<\/span> unionQF<\/span>(<\/span>QuickFindSet*<\/span> setQF,<\/span> Element a,<\/span> Element b)<\/span>;<\/span><\/p>\n

\u529f\u80fd\u5b9e\u73b0<\/h3>\n

\u521b\u5efa<\/h4>\n

QuickFindSet*<\/span> createQuickFindSet<\/span>(<\/span>int<\/span> n)<\/span> {<\/span>
\nQuickFindSet*<\/span> setQF =<\/span> (<\/span>QuickFindSet*<\/span>)<\/span>malloc<\/span>(<\/span>sizeof<\/span>(<\/span>QuickFindSet)<\/span>)<\/span>;<\/span>
\nif<\/span> (<\/span>setQF ==<\/span> NULL<\/span>)<\/span> {<\/span>
\nprintf<\/span>(<\/span>"setQF malloc failed!\\\\n"<\/span>)<\/span>;<\/span>
\nreturn<\/span> NULL<\/span>;<\/span>
\n}<\/span>
\n\/\/\u82e5\u7533\u8bf7\u6210\u529f，\u5c31\u4f20\u9012n\u7684\u503c\u5e76\u7ee7\u7eed\u7533\u8bf7\u4e24\u4e2a\u6570\u7ec4\u7684\u7a7a\u95f4<\/span>
\nsetQF-><\/span>n =<\/span> n;<\/span>
\nsetQF-><\/span>data =<\/span>(<\/span>Element*<\/span>)<\/span> malloc<\/span>(<\/span>sizeof<\/span>(<\/span>Element)<\/span> *<\/span> n)<\/span>;<\/span>
\nsetQF-><\/span>groupID =<\/span> (<\/span>int<\/span>*<\/span>)<\/span>malloc<\/span>(<\/span>sizeof<\/span>(<\/span>int<\/span>)<\/span> *<\/span> n)<\/span>;<\/span><\/p>\n

return<\/span> setQF;<\/span>
\n}<\/span><\/p>\n

\u91ca\u653e<\/h4>\n

void<\/span> releaseQuickFindSet<\/span>(<\/span>QuickFindSet*<\/span> setQF)<\/span> {<\/span>
\nif<\/span> (<\/span>setQF)<\/span> {<\/span>
\nif<\/span> (<\/span>setQF-><\/span>data)<\/span> {<\/span>
\nfree<\/span>(<\/span>setQF-><\/span>data)<\/span>;<\/span>
\n}<\/span>
\nif<\/span> (<\/span>setQF-><\/span>groupID)<\/span> {<\/span>
\nfree<\/span>(<\/span>setQF-><\/span>groupID)<\/span>;<\/span>
\n}<\/span>
\nfree<\/span>(<\/span>setQF)<\/span>;<\/span>
\n}<\/span>
\n}<\/span><\/p>\n

\u521d\u59cb\u5316<\/h4>\n

void<\/span> initQuickFindSet<\/span>(<\/span>const<\/span> QuickFindSet*<\/span> setQF,<\/span> const<\/span> Element*<\/span> data,<\/span> int<\/span> n)<\/span> {<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> {<\/span>
\nsetQF-><\/span>data[<\/span>i]<\/span> =<\/span> data[<\/span>i]<\/span>;<\/span>
\nsetQF-><\/span>groupID[<\/span>i]<\/span> =<\/span> i;<\/span>
\n}<\/span>
\n}<\/span><\/p>\n

\u67e5\u627e\u76ee\u6807\u503c\u7684\u7d22\u5f15<\/h4>\n

static<\/span> int<\/span> findIndex<\/span>(<\/span>const<\/span> QuickFindSet*<\/span> setQF,<\/span> Element e)<\/span> {<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> setQF-><\/span>n;<\/span> ++<\/span>i)<\/span> {<\/span>
\nif<\/span> (<\/span>setQF-><\/span>data[<\/span>i]<\/span> ==<\/span> e)<\/span> {<\/span>
\nreturn<\/span> i;<\/span>
\n}<\/span>
\n}<\/span>
\nreturn<\/span> –<\/span>1<\/span>;<\/span>
\n}<\/span><\/p>\n

\u5224\u65ad\u76ee\u6807\u503c\u7d22\u5f15\u5bf9\u5e94\u7684\u7ec4ID\u662f\u5426\u76f8\u540c(a\u3001b\u5728\u4e0d\u5728\u4e00\u4e2a\u96c6\u5408)<\/h4>\n

int<\/span> isSameQF<\/span>(<\/span>QuickFindSet*<\/span> setQF,<\/span> Element a,<\/span> Element b)<\/span> {<\/span>
\nint<\/span> aIndex =<\/span> findIndex<\/span>(<\/span>setQF,<\/span> a)<\/span>;<\/span>
\nint<\/span> bIndex =<\/span> findIndex<\/span>(<\/span>setQF,<\/span> b)<\/span>;<\/span>
\nif<\/span> (<\/span>aIndex ==<\/span> –<\/span>1<\/span> ||<\/span> bIndex ==<\/span> –<\/span>1<\/span>)<\/span> {<\/span>
\nreturn<\/span> 0<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> setQF-><\/span>groupID[<\/span>aIndex]<\/span> ==<\/span> setQF-><\/span>groupID[<\/span>bIndex]<\/span>;<\/span>
\n}<\/span><\/p>\n

\u5408\u5e76\u64cd\u4f5c<\/h4>\n

void<\/span> unionQF<\/span>(<\/span>QuickFindSet*<\/span> setQF,<\/span> Element a,<\/span> Element b)<\/span> {<\/span>
\nint<\/span> aIndex =<\/span> findIndex<\/span>(<\/span>setQF,<\/span> a)<\/span>;<\/span>
\nint<\/span> bIndex =<\/span> findIndex<\/span>(<\/span>setQF,<\/span> b)<\/span>;<\/span><\/p>\n

\/\/\u5047\u8bbe\u628ab\u96c6\u5408\u4e2d\u7684\u5143\u7d20\u5408\u5e76\u5230a\u96c6\u5408\u4e0a<\/span>
\nint<\/span> gID =<\/span> setQF-><\/span>groupID[<\/span>bIndex]<\/span>;<\/span>\/\/\u5148\u5b58\u4e0bb\u7684\u7ec4\u53f7<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> setQF-><\/span>n;<\/span> ++<\/span>i)<\/span> {<\/span>
\nif<\/span> (<\/span>setQF-><\/span>groupID[<\/span>i]<\/span> ==<\/span> gID)<\/span> {<\/span> \/\/\u662fb\u7ec4\u7684\u5143\u7d20<\/span>
\nsetQF-><\/span>groupID[<\/span>i]<\/span> =<\/span> setQF-><\/span>groupID[<\/span>aIndex]<\/span>;<\/span> \/\/\u5168\u90e8\u7ec4\u53f7\u6539\u4e3aa\u7ec4\u7684\u7ec4\u53f7<\/span>
\n}<\/span>
\n}<\/span>
\n}<\/span><\/p>\n

\u529f\u80fd\u8c03\u7528<\/h3>\n

void<\/span> test250808<\/span>(<\/span>)<\/span> {<\/span>
\nint<\/span> n =<\/span> 9<\/span>;<\/span>
\nQuickFindSet*<\/span> QFSet =<\/span> createQuickFindSet<\/span>(<\/span>n)<\/span>;<\/span>
\nElement data[<\/span>9<\/span>]<\/span>;<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> sizeof<\/span>(<\/span>data)<\/span> \/<\/span> sizeof<\/span>(<\/span>data[<\/span>0<\/span>]<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> {<\/span>
\ndata[<\/span>i]<\/span> =<\/span> i;<\/span>
\n}<\/span>
\ninitQuickFindSet<\/span>(<\/span>QFSet,<\/span> data,<\/span> n)<\/span>;<\/span><\/p>\n

unionQF<\/span>(<\/span>QFSet,<\/span> 1<\/span>,<\/span> 3<\/span>)<\/span>;<\/span>
\nunionQF<\/span>(<\/span>QFSet,<\/span>3<\/span>,<\/span> 2<\/span>)<\/span>;<\/span>
\nunionQF<\/span>(<\/span>QFSet,<\/span> 2<\/span>,<\/span> 4<\/span>)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>isSameQF<\/span>(<\/span>QFSet,<\/span> 0<\/span>,<\/span> 2<\/span>)<\/span>)<\/span> {<\/span>
\nprintf<\/span>(<\/span>"Yes\\\\n"<\/span>)<\/span>;<\/span>
\n}<\/span>
\nelse<\/span> {<\/span>
\nprintf<\/span>(<\/span>"No\\\\n"<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

unionQF<\/span>(<\/span>QFSet,<\/span> 5<\/span>,<\/span> 1<\/span>)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>isSameQF<\/span>(<\/span>QFSet,<\/span> 5<\/span>,<\/span> 2<\/span>)<\/span>)<\/span> {<\/span>
\nprintf<\/span>(<\/span>"Yes\\\\n"<\/span>)<\/span>;<\/span>
\n}<\/span>
\nelse<\/span> {<\/span>
\nprintf<\/span>(<\/span>"No\\\\n"<\/span>)<\/span>;<\/span>
\n}<\/span>
\nreleaseQuickFindSet<\/span>(<\/span>QFSet)<\/span>;<\/span>
\n}<\/span><\/p>\n

int<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
\ntest250808<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

quickUnion<\/h3>\n

\u4f7f\u7528\u6811\u7ed3\u6784\u8868\u793a\u96c6\u5408(\u770b\u4e0b\u56fe\u53ea\u80fd\u4f53\u73b0\u94fe\u5f0f\u5b58\u50a8，\u540e\u9762\u7684\u5185\u5bb9\u4f1a\u8bb2\u5230\u8def\u5f84\u538b\u7f29：\u901a\u8fc7\u589e\u5927\u8282\u70b9\u7684\u5ea6\u6765\u63d0\u9ad8\u6548\u7387\u4f1a\u4f53\u73b0\u51fa\u6811\u7684\u7279\u70b9)，\u6bcf\u4e2a\u8282\u70b9\u7684parent\u6307\u5411\u5176\u7236\u8282\u70b9，\u6839\u8282\u70b9
\n\u7684parent\u6307\u5411\u81ea\u8eab,\u5408\u5e76\u65f6\u5c06\u4e00\u4e2a\u6811\u7684\u6839\u6307\u5411\u53e6\u4e00\u4e2a\u6811\u7684\u6839\u5c31\u80fd\u8fde\u63a5\u4e24\u4e2a\u6811\u3002<\/p>\n

\u65f6\u95f4\u590d\u6742\u5ea6：
\n\u67e5\u627e（Find）：O(logn)（\u5e73\u5747，\u53d6\u51b3\u4e8e\u6811\u9ad8），\u9700\u8981\u9012\u5f52\u6216\u8fed\u4ee3\u627e\u5230\u6839\u8282\u70b9\u3002
\n\u5408\u5e76（Union）：O(logn)，\u4ec5\u9700\u4fee\u6539\u6839\u8282\u70b9\u7684\u6307\u5411\u3002<\/p>\n

\u7279\u70b9：\u5408\u5e76\u6548\u7387\u9ad8，\u4f46\u67e5\u627e\u901f\u5ea6\u53d6\u51b3\u4e8e\u6811\u9ad8\u3002<\/p>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"
\n\u8fd9\u91cc\u662f\u5b50\u8282\u70b9\u6307\u5411\u7236\u8282\u70b9；\u7236\u8282\u70b9\u662f\u81ea\u5df1\u65f6\u5c31\u6307\u5411\u81ea\u5df1，\u8fd9\u79cd\u8282\u70b9\u88ab\u79f0\u4e3a\u6839\u8282\u70b9（\u59821\u548c5）\u3002
\n\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"
\nquickUnion\u67e5\u627e\u901f\u5ea6\u53d6\u51b3\u4e8e\u6811\u9ad8,\u53ef\u901a\u8fc7\u8def\u5f84\u538b\u7f29\u7b49\u8fdb\u4e00\u6b65\u63d0\u5347\u6027\u80fd：<\/p>\n

\u8def\u5f84\u538b\u7f29<\/h3>\n

\u8def\u5f84\u538b\u7f29\u5c31\u662f\u60f3\u529e\u6cd5\u628a\u6811\u53d8\u77ee\u3002\u50cf\u4e0a\u9762\u7684\u4f8b\u5b50：\u4ece1\u52304\u8fd9\u4e32\u53f3\u5b50\u6811，\u5982\u679c\u4ece\u6839\u8282\u70b9\u5f00\u59cb\u5f80\u4e0b\u904d\u5386，\u5c06\u6bcf\u4e2a\u8282\u70b9\u7684parent\u90fd\u76f4\u63a5\u6307\u5411\u6839\u8282\u70b91，\u5f53\u6839\u8282\u70b9\u67e5\u627e\u76ee\u6807\u8282\u70b9\u65f6\u4ec5\u9700\u8bbf\u95ee1\u5c42\u3002<\/p>\n

\u5982\u4f55\u5b9e\u73b0\u8fd9\u4e00\u601d\u60f3\u5462？\u904d\u5386\u8fd9\u4e9b\u8282\u70b9\u4ee5\u53ca\u5c06\u5b83\u4eec\u6bcf\u4e2a\u8282\u70b9\u7684parent\u6307\u5411\u6839\u8282\u70b9\u8fd9\u4e00\u73af\u8282\u65f6，\u53ef\u4ee5\u60f3\u8c61\u6210\u4ece\u53f6\u5b50\u8282\u70b9\u5f00\u59cb\u6328\u4e2a\u6458\u53d6\u5e76\u5b58\u4e0b\u6765（\u76f4\u63a5\u6307\u5411\u6839\u8282\u70b9\u7684\u53f6\u5b50\u8282\u70b9\u5ffd\u7565），\u904d\u5386\u5230\u6839\u8282\u70b9\u65f6\u518d\u6328\u4e2a\u53d6\u51fa\u6765\u5e76\u6328\u4e2a\u5c06\u8282\u70b9\u7684parent\u6307\u5411\u6839\u8282\u70b9\u3002<\/p>\n

\u8fd9\u79cd\u5b58\u50a8\u7279\u70b9\u5c31\u4e0d\u7531\u7684\u8054\u60f3\u8d77\u4e86\u6808，\u76f8\u5bf9\u63d0\u524d\u7533\u8bf7\u7a7a\u95f4\u7684\u987a\u5e8f\u6808，\u94fe\u5f0f\u6808\u66f4\u5408\u9002，\u7528\u591a\u5c11\u5c31\u7533\u8bf7\u591a\u5c11\u3002\u4e14\u9700\u91c7\u7528\u5934\u63d2\u6cd5\u8fdb\u884c\u5165\u6808\u64cd\u4f5c（\u65b9\u4fbf\u4fbf\u5229\u63d2\u5165\u8282\u70b9\u4e4b\u540e\u7684\u8282\u70b9\u5143\u7d20）\u3002
\n\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u4e0equickFind\u7684\u4ee3\u7801\u5f88\u76f8\u4f3c，\u4e2a\u522b\u5730\u65b9\u9700\u8c03\u6574\u3002<\/p>\n

\u5934\u6587\u4ef6<\/h3>\n

#<\/span>pragma<\/span> once<\/span><\/span>
\ntypedef<\/span> int<\/span> Element;<\/span><\/p>\n

typedef<\/span> struct<\/span> {<\/span>
\nElement*<\/span> data;<\/span>
\nint<\/span>*<\/span> parent;<\/span>
\nint<\/span>*<\/span> size;<\/span> \/\/\u8868\u793a\u5176\u4e2d\u67d0\u4e2a\u96c6\u5408\u7684\u5143\u7d20\u4e2a\u6570<\/span>
\nint<\/span> n;<\/span>\/\/\u8868\u793a\u603b\u5143\u7d20\u4e2a\u6570（\u6240\u6709\u96c6\u5408\u7684\u5143\u7d20\u4e2a\u6570\u4e4b\u548c）<\/span>
\n}<\/span>QuickUnionSet;<\/span><\/p>\n

\/\/\u4e3a\u538b\u7f29\u5b58\u50a8\u4e2d\u94fe\u5f0f\u6808\u7684\u5165\u6808\u51fa\u6808\u64cd\u4f5c\u505a\u51c6\u5907:\u5b9a\u4e49\u8282\u70b9\u7ed3\u6784<\/span>
\ntypedef<\/span> struct<\/span> _set_node<\/span> {<\/span>
\nint<\/span> index;<\/span>
\nstruct<\/span> _set_node<\/span>*<\/span> next;<\/span>
\n}<\/span>SetNode;<\/span><\/p>\n

QuickUnionSet*<\/span> createQuickUnionSet<\/span>(<\/span>int<\/span> n)<\/span>;<\/span>
\nvoid<\/span> releaseQuickUnionSet<\/span>(<\/span>QuickUnionSet*<\/span> setQU)<\/span>;<\/span>
\nvoid<\/span> initQuickUnionSet<\/span>(<\/span>QuickUnionSet*<\/span> setQU,<\/span> const<\/span> Element*<\/span> data,<\/span> int<\/span> n)<\/span>;<\/span><\/p>\n

int<\/span> isSameQU<\/span>(<\/span>const<\/span> QuickUnionSet*<\/span> setQU,<\/span> Element a,<\/span> Element b)<\/span>;<\/span>
\nvoid<\/span> unionQU<\/span>(<\/span>QuickUnionSet*<\/span> setQU,<\/span> Element a,<\/span> Element b)<\/span>;<\/span><\/p>\n

\u529f\u80fd\u5b9e\u73b0<\/h3>\n

\u521b\u5efa<\/h4>\n

QuickUnionSet*<\/span> createQuickUnionSet<\/span>(<\/span>int<\/span> n)<\/span> {<\/span>
\nQuickUnionSet*<\/span> setQU =<\/span> (<\/span>QuickUnionSet*<\/span>)<\/span>malloc<\/span>(<\/span>sizeof<\/span>(<\/span>Element)<\/span> *<\/span> n)<\/span>;<\/span>
\nif<\/span> (<\/span>setQU ==<\/span> NULL<\/span>)<\/span> {<\/span>
\nreturn<\/span> NULL<\/span>;<\/span>
\n}<\/span>
\nsetQU-><\/span>data =<\/span> (<\/span>Element*<\/span>)<\/span>malloc<\/span>(<\/span>sizeof<\/span>(<\/span>Element)<\/span> *<\/span> n)<\/span>;<\/span>
\nsetQU-><\/span>parent =<\/span> (<\/span>int<\/span>*<\/span>)<\/span>malloc<\/span>(<\/span>sizeof<\/span>(<\/span>int<\/span>)<\/span> *<\/span> n)<\/span>;<\/span>
\nsetQU-><\/span>size =<\/span> (<\/span>int<\/span>*<\/span>)<\/span>malloc<\/span>(<\/span>sizeof<\/span>(<\/span>int<\/span>)<\/span> *<\/span> n)<\/span>;<\/span>
\nsetQU-><\/span>n =<\/span> n;<\/span><\/p>\n

return<\/span> setQU;<\/span>
\n}<\/span><\/p>\n

\u91ca\u653e<\/h4>\n

void<\/span> releaseQuickUnionSet<\/span>(<\/span>QuickUnionSet*<\/span> setQU)<\/span> {<\/span>
\nif<\/span> (<\/span>setQU)<\/span> {<\/span>
\nif<\/span> (<\/span>setQU-><\/span>data)<\/span> {<\/span>
\nfree<\/span>(<\/span>setQU-><\/span>data)<\/span>;<\/span>
\n}<\/span>
\nif<\/span> (<\/span>setQU-><\/span>parent)<\/span> {<\/span>
\nfree<\/span>(<\/span>setQU-><\/span>parent)<\/span>;<\/span>
\n}<\/span>
\nif<\/span> (<\/span>setQU-><\/span>size)<\/span> {<\/span>
\nfree<\/span>(<\/span>setQU-><\/span>size)<\/span>;<\/span>
\n}<\/span>
\n}<\/span>
\n}<\/span><\/p>\n

\u521d\u59cb\u5316<\/h4>\n

void<\/span> initQuickUnionSet<\/span>(<\/span>QuickUnionSet*<\/span> setQU,<\/span> const<\/span> Element*<\/span> data,<\/span> int<\/span> n)<\/span> {<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span> {<\/span>
\nsetQU-><\/span>data[<\/span>i]<\/span> =<\/span> data[<\/span>i]<\/span>;<\/span>
\nsetQU-><\/span>parent[<\/span>i]<\/span> =<\/span> i;<\/span>
\nsetQU-><\/span>size[<\/span>i]<\/span> =<\/span> 1<\/span>;<\/span>
\n}<\/span>
\n}<\/span><\/p>\n

\u67e5\u627e\u76ee\u6807\u503c\u7d22\u5f15<\/h4>\n

static<\/span> int<\/span> findIndex<\/span>(<\/span>const<\/span> QuickUnionSet*<\/span> setQU,<\/span> Element e)<\/span> {<\/span>
\nfor<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> setQU-><\/span>n;<\/span> ++<\/span>i)<\/span> {<\/span>
\nif<\/span> (<\/span>setQU-><\/span>data[<\/span>i]<\/span> ==<\/span> e)<\/span> {<\/span>
\nreturn<\/span> i;<\/span>
\n}<\/span>
\n}<\/span>
\nreturn<\/span> –<\/span>1<\/span>;<\/span>
\n}<\/span><\/p>\n

\u8def\u5f84\u538b\u7f29<\/h4>\n

#<\/span>define<\/span> PATH_COMPRESS<\/span><\/span>
\n#<\/span>ifndef<\/span> PATH_COMPRESS<\/span><\/span>
\nstatic<\/span> int<\/span> findRootIndex<\/span>(<\/span>const<\/span> QuickUnionSet*<\/span> setQU,<\/span> Element e)<\/span> {<\/span>
\nint<\/span> curIndex =<\/span> findIndex<\/span>(<\/span>setQU,<\/span> e)<\/span>;<\/span>
\nif<\/span> (<\/span>curIndex ==<\/span> –<\/span>1<\/span>)<\/span> {<\/span>
\nreturn<\/span> –<\/span>1<\/span>;<\/span>
\n}<\/span>
\n\/\/\u82e5\u627e\u5230\u5219\u5411\u4e0a\u904d\u5386，\u76f4\u5230\u7236\u8282\u70b9\u548c\u81ea\u8eab\u7d22\u5f15\u4e00\u81f4（\u627e\u5230\u6839\u8282\u70b9）<\/span>
\nwhile<\/span>(<\/span>setQU-><\/span>parent[<\/span>curIndex]<\/span>!=<\/span>curIndex)<\/span> {<\/span>
\ncurIndex =<\/span> setQU-><\/span>parent[<\/span>curIndex]<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> curIndex;<\/span>
\n}<\/span>
\n#<\/span>else<\/span><\/span>
\nstatic<\/span> SetNode*<\/span> push<\/span>(<\/span>SetNode*<\/span> stack,<\/span> int<\/span> index)<\/span> {<\/span>
\n\/\/\u4f20\u5165\u7684stack\u662f\u4e00\u4e2a\u7a7a\u6307\u9488，\u76f8\u5f53\u4e8e\u65e0\u5934\u7ed3\u70b9\u3001\u5934\u6307\u9488\u94fe\u5f0f\u7ed3\u6784\u7684\u5934\u63d2\u64cd\u4f5c<\/span>
\nSetNode*<\/span> node =<\/span> (<\/span>SetNode*<\/span>)<\/span>malloc<\/span>(<\/span>sizeof<\/span>(<\/span>SetNode)<\/span>)<\/span>;<\/span>
\nnode-><\/span>index =<\/span> index;<\/span>
\nnode-><\/span>next =<\/span> stack;<\/span>
\nreturn<\/span> node;<\/span>
\n}<\/span><\/p>\n

static<\/span> SetNode*<\/span> pop<\/span>(<\/span>SetNode*<\/span> stack,<\/span> int<\/span>*<\/span> index)<\/span> {<\/span>
\nSetNode*<\/span> tmp =<\/span> stack;<\/span>
\n\/\/\u4e3b\u8981\u4efb\u52a1\u662f\u83b7\u5f97\u6808\u9876\u5143\u7d20\u7684\u7d22\u5f15<\/span>
\n*<\/span>index =<\/span> stack-><\/span>index;<\/span>
\n\/\/\u4e4b\u540e\u66f4\u65b0\u6808\u9876\u7d22\u5f15<\/span>
\nstack =<\/span> stack-><\/span>next;<\/span>
\nfree<\/span>(<\/span>tmp)<\/span>;<\/span>
\nreturn<\/span> stack;<\/span>
\n}<\/span><\/p>\n

static<\/span> int<\/span> findRootIndex<\/span>(<\/span>const<\/span> QuickUnionSet*<\/span> setQU,<\/span> Element e)<\/span> {<\/span>
\nint<\/span> curIndex =<\/span> findIndex<\/span>(<\/span>setQU,<\/span> e)<\/span>;<\/span>
\nif<\/span> (<\/span>curIndex ==<\/span> –<\/span>1<\/span>)<\/span>
\nreturn<\/span> –<\/span>1<\/span>;<\/span>
\n\/\/\u627e\u6839\u7684\u8def\u5f84：\u4ece\u76ee\u6807\u8282\u70b9\u5f00\u59cb\u5f80\u4e0a\u627e，\u9014\u7ecf\u7684\u8282\u70b9\u90fd\u6328\u4e2a\u5165\u6808，\u5230\u6839\u8282\u70b9\u4e3a\u6b62<\/span>
\nSetNode*<\/span> path =<\/span> NULL<\/span>;<\/span>
\nwhile<\/span> (<\/span>setQU-><\/span>parent[<\/span>curIndex]<\/span> !=<\/span> curIndex)<\/span> {<\/span>
\npath =<\/span> push<\/span>(<\/span>path,<\/span> curIndex)<\/span>;<\/span>
\ncurIndex =<\/span> setQU-><\/span>parent[<\/span>curIndex]<\/span>;<\/span>
\n}<\/span>
\n\/\/\u51fa\u6808，\u5e76\u5c06\u51fa\u6808\u7684\u6bcf\u4e2a\u8282\u70b9\u7684parent\u90fd\u6307\u5411\u6839\u8282\u70b9<\/span>
\nwhile<\/span> (<\/span>path)<\/span> {<\/span>
\nint<\/span> pos;<\/span>
\npath =<\/span> pop<\/span>(<\/span>path,<\/span> &<\/span>pos)<\/span>;<\/span>
\nsetQU-><\/span>parent[<\/span>pos]<\/span> =<\/span> curIndex;<\/span>
\n}<\/span>
\nreturn<\/span> curIndex;<\/span>
\n}<\/span>
\n#<\/span>endif<\/span> \/\/ !PATH_COMPRESS<\/span><\/span><\/p>\n

\u5224\u65ad\u4e24\u96c6\u5408\u6839\u7684\u5f02\u540c<\/h4>\n

int<\/span> isSameQU<\/span>(<\/span>const<\/span> QuickUnionSet*<\/span> setQU,<\/span> Element a,<\/span> Element b)<\/span> {<\/span>
\nint<\/span> aRoot =<\/span> findRootIndex<\/span>(<\/span>setQU,<\/span> a)<\/span>;<\/span>
\nint<\/span> bRoot =<\/span> findRootIndex<\/span>(<\/span>setQU,<\/span> b)<\/span>;<\/span>
\nif<\/span> (<\/span>aRoot ==<\/span> –<\/span>1<\/span> ||<\/span> bRoot ==<\/span> –<\/span>1<\/span>)<\/span> {<\/span>
\nreturn<\/span> 0<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> aRoot ==<\/span> bRoot;<\/span>
\n}<\/span><\/p>\n

\u5408\u5e76<\/h4>\n

\/* \u5c06\u5143\u7d20a\u548c\u5143\u7d20b\u8fdb\u884c\u5408\u5e76
\n * 1. \u627e\u5230a\u548cb\u7684\u6839\u8282\u70b9，\u539f\u672c\u662fb\u7684\u7236\u8282\u70b9\u6307\u5411a\u7684\u7236\u8282\u70b9
\n * 2. \u5f15\u5165\u6839\u8282\u70b9\u7684size\u6709\u6548\u89c4\u5219，\u8c01\u7684\u5143\u7d20\u591a，\u8ba9\u53e6\u5916\u4e00\u4e2a\u63a5\u5165\u5143\u7d20\u591a\u7684\u7ec4
\n *\/<\/span><\/p>\n

void<\/span> unionQU<\/span>(<\/span>QuickUnionSet*<\/span> setQU,<\/span> Element a,<\/span> Element b)<\/span> {<\/span>
\nint<\/span> aRoot =<\/span> findRootIndex<\/span>(<\/span>setQU,<\/span> a)<\/span>;<\/span>
\nint<\/span> bRoot =<\/span> findRootIndex<\/span>(<\/span>setQU,<\/span> b)<\/span>;<\/span>
\nif<\/span> (<\/span>aRoot ==<\/span> –<\/span>1<\/span> ||<\/span> bRoot ==<\/span> –<\/span>1<\/span>)<\/span> {<\/span>
\nreturn<\/span>;<\/span>
\n}<\/span>
\nif<\/span> (<\/span>aRoot !=<\/span> bRoot)<\/span> {<\/span> \/\/ a\u548cb\u4e0d\u5728\u4e00\u4e2a\u96c6\u5408\u91cc<\/span>
\n\/\/ \u6839\u636e\u6839\u8282\u70b9\u7684\u7d22\u5f15\u627e\u5230\u5bf9\u5e94size\u7a7a\u95f4\u91cc\u4fdd\u5b58\u7684\u6839\u6240\u5728\u6811\u7684\u603b\u8282\u70b9\u6570<\/span>
\n\/\/\u521d\u59cb\u65f6size\u90fd\u4e3a1,\u8282\u70b9\u90fd\u662f\u5355\u72ec\u5360\u4e00\u4e2a\u96c6\u5408,\u7ed3\u5408\u65f6\u518d\u5c06\u4e24\u96c6\u5408\u7684size\u76f8\u52a0<\/span>
\nint<\/span> aSize =<\/span> setQU-><\/span>size[<\/span>aRoot]<\/span>;<\/span>
\nint<\/span> bSize =<\/span> setQU-><\/span>size[<\/span>bRoot]<\/span>;<\/span>
\nif<\/span> (<\/span>aSize >=<\/span> bSize)<\/span> {<\/span>\/\/ \u5c06b\u5143\u7d20\u7684\u6839\u8282\u70b9\u6307\u5411a\u5143\u7d20\u7684\u6839\u8282\u70b9<\/span>
\nsetQU-><\/span>parent[<\/span>bRoot]<\/span> =<\/span> aRoot;<\/span>
\nsetQU-><\/span>size[<\/span>aRoot]<\/span> +=<\/span> bSize;<\/span>
\n}<\/span>
\nelse<\/span> {<\/span>
\nsetQU-><\/span>parent[<\/span>aRoot]<\/span> =<\/span> bRoot;<\/span>
\nsetQU-><\/span>size[<\/span>bRoot]<\/span> +=<\/span> aSize;<\/span>
\n}<\/span>
\n}<\/span>
\n}<\/span><\/p>\n

\u529f\u80fd\u8c03\u7528<\/h4>\n

void<\/span> test250810<\/span>(<\/span>)<\/span> {<\/span>
\nint<\/span> n =<\/span> 9<\/span>;<\/span>
\nQuickUnionSet*<\/span> QUSet =<\/span> createQuickUnionSet<\/span>(<\/span>n)<\/span>;<\/span>
\nElement data[<\/span>9<\/span>]<\/span>;<\/span>
\nfor<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> sizeof<\/span>(<\/span>data)<\/span> \/<\/span> sizeof<\/span>(<\/span>data[<\/span>0<\/span>]<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> {<\/span>
\ndata[<\/span>i]<\/span> =<\/span> i;<\/span>
\n}<\/span>
\ninitQuickUnionSet<\/span>(<\/span>QUSet,<\/span> data,<\/span> n)<\/span>;<\/span><\/p>\n

unionQU<\/span>(<\/span>QUSet,<\/span>1<\/span>,<\/span> 3<\/span>)<\/span>;<\/span>
\nunionQU<\/span>(<\/span>QUSet,<\/span> 3<\/span>,<\/span> 2<\/span>)<\/span>;<\/span>
\nunionQU<\/span>(<\/span>QUSet,<\/span> 2<\/span>,<\/span> 4<\/span>)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>isSameQU<\/span>(<\/span>QUSet,<\/span> 0<\/span>,<\/span> 2<\/span>)<\/span>)<\/span> {<\/span>
\nprintf<\/span>(<\/span>"Yes\\\\n"<\/span>)<\/span>;<\/span>
\n}<\/span>
\nelse<\/span> {<\/span>
\nprintf<\/span>(<\/span>"No\\\\n"<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

unionQU<\/span>(<\/span>QUSet,<\/span> 5<\/span>,<\/span> 1<\/span>)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>isSameQU<\/span>(<\/span>QUSet,<\/span> 5<\/span>,<\/span> 2<\/span>)<\/span>)<\/span> {<\/span>
\nprintf<\/span>(<\/span>"Yes\\\\n"<\/span>)<\/span>;<\/span>
\n}<\/span>
\nelse<\/span> {<\/span>
\nprintf<\/span>(<\/span>"No\\\\n"<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

releaseQuickUnionSet<\/span>(<\/span>QUSet)<\/span>;<\/span>
\n}<\/span>
\nint<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
\ntest250810<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

\u62dc\u62dc~<\/p>\n","protected":false},"excerpt":{"rendered":"

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