{"id":75309,"date":"2026-02-12T01:25:34","date_gmt":"2026-02-11T17:25:34","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/75309.html"},"modified":"2026-02-12T01:25:34","modified_gmt":"2026-02-11T17:25:34","slug":"%e3%80%90%e7%ae%97%e6%b3%95%e8%af%a6%e8%a7%a3%e3%80%91%e5%8f%8c%e6%8c%87%e9%92%88","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/75309.html","title":{"rendered":"\u3010\u7b97\u6cd5\u8be6\u89e3\u3011\u53cc\u6307\u9488"},"content":{"rendered":"

\u53cc\u6307\u9488<\/h2>\n

\u5f15\u8a00<\/h3>\n

\u5176\u5b9e\u5bf9\u4e8e\u53cc\u6307\u9488\u5b83\u4e0d\u592a\u50cf\u4e00\u79cd\u524d\u7f00\u548c\u4e0e\u5dee\u5206\u6709\u56fa\u5b9a\u7684\u516c\u5f0f，\u5b83\u66f4\u50cf\u662f\u4e00\u79cd\u601d\u60f3，\u5b83\u4e0d\u662f\u6211\u53bb\u7ed9\u4f60\u8bf4\u4e00\u4e2a\u516c\u5f0f\u4f60\u5c31\u80fd\u638c\u63e1，\u800c\u662f\u50cf\u6211\u4eec\u9ad8\u4e2d\u4e00\u6837\u53bb\u5237\u9898，\u638c\u63e1\u5b83\u7684\u5404\u79cd\u53d8\u5f0f，\u6240\u4ee5\u8fd9\u7bc7\u535a\u5ba2\u6211\u5c06\u4f1a\u4e3e\u4e00\u4e9b\u9898\u76ee\u7136\u540e\u4f60\u53bb\u770b\u9898\u76ee，\u53bb\u638c\u63e1\u8fd9\u79cd\u601d\u60f3<\/p>\n

\u7b2c\u4e00\u79cd\u5206\u7c7b<\/h3>\n

\u987e\u540d\u601d\u4e49\u53cc\u6307\u9488\u5c31\u662f\u6709\u4e24\u4e2a\u6307\u9488\u8fdb\u884c\u79fb\u52a8，\u5176\u4e3b\u8981\u7684\u5206\u7c7b\u4e3a\u5bf9\u649e\u6307\u9488\u548c\u5feb\u6162\u6307\u9488 \u5bf9\u649e\u6307\u9488\u5c31\u662f\u4e24\u4e2a\u6307\u9488\u76f8\u5411\u79fb\u52a8 \u5feb\u6162\u6307\u9488\u5c31\u662f\u4e24\u4e2a\u6307\u9488\u540c\u5411\u79fb\u52a8\u53ea\u4e0d\u8fc7\u4e00\u4e2a\u5728\u524d\u4e00\u4e2a\u5728\u540e \u4e00\u822c\u6765\u8bf4\u6211\u4eec\u90fd\u4f1a\u6709\u4e00\u4e2a\u5148\u79fb\u52a8\u7684\u6307\u9488，\u4e00\u4e2a\u540e\u79fb\u52a8\u7684\u6307\u9488<\/p>\n

\u7b2c\u4e8c\u79cd\u5206\u7c7b<\/h3>\n

\u6211\u4eec\u5bf9\u4e8e\u53cc\u6307\u9488\u95ee\u9898\u8fd8\u6709\u4e00\u79cd\u5206\u7c7b\u65b9\u5f0f\u5c31\u662f\u6839\u636e\u5e8f\u5217\u7684\u4e2a\u6570\u6765\u5206\u7c7b \u4e00\u4e2a\u5e8f\u5217：\u7c7b\u4f3c\u5feb\u901f\u6392\u5e8f \u4e24\u4e2a\u5e8f\u5217：\u7c7b\u4f3c\u5f52\u5e76\u6392\u5e8f<\/p>\n

\u6a21\u677f<\/h3>\n

for<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>,<\/span> j =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span>{<\/span>\/\/i j \u7684\u521d\u59cb\u5316\u4e0ei\u7684\u622a\u6b62\u8303\u56f4<\/span>
\nwhile<\/span>(<\/span>j <<\/span> i &&<\/span> check<\/span>(<\/span>i,<\/span> j)<\/span>{<\/span>\/\/i \u6307\u9488\u79fb\u52a8\u6761\u4ef6\u4e0e\u622a\u6b62\u8303\u56f4<\/span>
\nj++<\/span>;<\/span>
\n}<\/span>
\n}<\/span><\/p>\n

\u4e00\u822c\u601d\u8def<\/h3>\n

\u4e00\u822c\u6211\u4eec\u4f1a\u5199\u4e00\u4e2a\u590d\u6742\u5ea6\u4e3a <\/p>\n

O<\/p>\n

(<\/p>\n

n<\/p>\n

2<\/p>\n

)<\/p>\n

O(n^2)<\/p>\n

<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u7684\u4e24\u4e2a\u6307\u9488\u518d\u4f18\u5316\u6210\u590d\u6742\u5ea6\u4e3a <\/p>\n

O<\/p>\n

(<\/p>\n

n<\/p>\n

)<\/p>\n

O(n)<\/p>\n

<\/span><\/span>O<\/span>(<\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span> \u7684\u53cc\u6307\u9488<\/p>\n

\u9898\u76ee<\/h3>\n

1. \u6700\u957f\u8fde\u7eed\u4e0d\u91cd\u590d\u5b50\u5e8f\u5217（AcWing 799）<\/h4>\n

AcWing 799 \u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a <\/p>\n

n<\/p>\n

n<\/p>\n

<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u7684\u6574\u6570\u5e8f\u5217，\u8bf7\u627e\u51fa\u6700\u957f\u7684\u4e0d\u5305\u542b\u91cd\u590d\u7684\u6570\u7684\u8fde\u7eed\u533a\u95f4，\u8f93\u51fa\u5b83\u7684\u957f\u5ea6<\/p>\n

\u8f93\u5165\u683c\u5f0f \u7b2c\u4e00\u884c\u5305\u542b\u6574\u6570 <\/p>\n

n<\/p>\n

n<\/p>\n

<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u7b2c\u4e8c\u884c\u5305\u542b <\/p>\n

n<\/p>\n

n<\/p>\n

<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6574\u6570（\u5747\u5728 <\/p>\n

0<\/p>\n

\u223c<\/p>\n

10<\/p>\n

5<\/p>\n

0\u223c10^5<\/p>\n

<\/span><\/span>0<\/span><\/span>\u223c<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8303\u56f4\u5185，\u8868\u793a\u6574\u6570\u5e8f\u5217<\/p>\n

\u8f93\u51fa\u683c\u5f0f \u5171\u4e00\u884c，\u5305\u542b\u4e00\u4e2a\u6574\u6570，\u8868\u793a\u6700\u957f\u7684\u4e0d\u5305\u542b\u91cd\u590d\u7684\u6570\u7684\u8fde\u7eed\u533a\u95f4\u7684\u957f\u5ea6\u3002<\/p>\n

\u6570\u636e\u8303\u56f4 <\/p>\n

1<\/p>\n

\u2264<\/p>\n

n<\/p>\n

\u2264<\/p>\n

10<\/p>\n

5<\/p>\n

1\\\\le n \\\\le 10^5<\/p>\n

<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8f93\u5165\u6837\u4f8b：<\/p>\n

5
\n1 2 2 3 5<\/p>\n

\u8f93\u51fa\u6837\u4f8b：<\/p>\n

3<\/p>\n

1.1 \u4e00\u822c\u601d\u8def<\/h5>\n

\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a\u8ba1\u6570\u5668\u6570\u7ec4 <\/p>\n

c<\/p>\n

o<\/p>\n

u<\/p>\n

n<\/p>\n

t<\/p>\n

[<\/p>\n

]<\/p>\n

count[]<\/p>\n

<\/span><\/span>co<\/span>u<\/span>n<\/span>t<\/span>[<\/span>]<\/span><\/span><\/span><\/span><\/span> <\/p>\n

c<\/p>\n

o<\/p>\n

u<\/p>\n

n<\/p>\n

t<\/p>\n

[<\/p>\n

a<\/p>\n

[<\/p>\n

i<\/p>\n

]<\/p>\n

]<\/p>\n

count[a[i]]<\/p>\n

<\/span><\/span>co<\/span>u<\/span>n<\/span>t<\/span>[<\/span>a<\/span>[<\/span>i<\/span>]]<\/span><\/span><\/span><\/span><\/span> \u8868\u793a <\/p>\n

a<\/p>\n

[<\/p>\n

i<\/p>\n

]<\/p>\n

a[i]<\/p>\n

<\/span><\/span>a<\/span>[<\/span>i<\/span>]<\/span><\/span><\/span><\/span><\/span> \u8fd9\u4e2a\u6570\u5b57\u51fa\u73b0\u7684\u6b21\u6570<\/p>\n

#<\/span>include<\/span><bits\/stdc++.h><\/span><\/span>
\nusing<\/span> namespace<\/span> std;<\/span><\/p>\n

const<\/span> int<\/span> n =<\/span> 1010<\/span>;<\/span>
\nint<\/span> a[<\/span>N]<\/span>,<\/span>count[<\/span>N]<\/span>;<\/span><\/p>\n

int<\/span> main<\/span>(<\/span>)<\/span>{<\/span>
\nint<\/span> n;<\/span>
\ncin >><\/span> n;<\/span>
\nfor<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span>{<\/span>
\ncin >><\/span>a[<\/span>i]<\/span>;<\/span>
\ncount[<\/span>a[<\/span>i]<\/span>]<\/span>++<\/span>;<\/span>
\n}<\/span>
\n}<\/span><\/p>\n

<\/p>\n

c<\/p>\n

o<\/p>\n

u<\/p>\n

n<\/p>\n

t<\/p>\n

[<\/p>\n

]<\/p>\n

count[]<\/p>\n

<\/span><\/span>co<\/span>u<\/span>n<\/span>t<\/span>[<\/span>]<\/span><\/span><\/span><\/span><\/span> \u7528\u6765\u7edf\u8ba1\u6570\u5b57\u51fa\u73b0\u6b21\u6570 \u5b9a\u4e49 <\/p>\n

i<\/p>\n

,<\/p>\n

j<\/p>\n

i,j<\/p>\n

<\/span><\/span>i<\/span>,<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span> \u6307\u9488\u6307\u5411\u6570\u7ec4\u7684\u9996\u4f4d\u7f6e \u4e00\u5f00\u59cb\u6211\u4eec\u5411\u53f3\u79fb\u52a8 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6307\u9488\u5e76\u7edf\u8ba1 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6307\u5411\u7684\u7684\u6570\u5b57\u5728 <\/p>\n

[<\/p>\n

j<\/p>\n

,<\/p>\n

i<\/p>\n

]<\/p>\n

[j,i]<\/p>\n

<\/span><\/span>[<\/span>j<\/span>,<\/span><\/span>i<\/span>]<\/span><\/span><\/span><\/span><\/span> \u8fd9\u4e2a\u533a\u95f4\u7684\u51fa\u73b0\u6b21\u6570，\u6b64\u65f6<\/p>\n

c<\/p>\n

o<\/p>\n

u<\/p>\n

n<\/p>\n

t<\/p>\n

[<\/p>\n

a<\/p>\n

[<\/p>\n

i<\/p>\n

]<\/p>\n

]<\/p>\n

+<\/p>\n

+<\/p>\n

count[a[i]]++<\/p>\n

<\/span><\/span>co<\/span>u<\/span>n<\/span>t<\/span>[<\/span>a<\/span>[<\/span>i<\/span>]]<\/span><\/span>+<\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span> \u5f53\u67d0\u4e2a\u6570\u51fa\u73b0\u7b2c\u4e8c\u6b21\u65f6\u6211\u4eec\u505c\u6b62 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6307\u9488，\u5f00\u59cb\u79fb\u52a8 <\/p>\n

j<\/p>\n

j<\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span> \u6307\u9488，\u6b64\u65f6 <\/p>\n

c<\/p>\n

o<\/p>\n

u<\/p>\n

n<\/p>\n

t<\/p>\n

[<\/p>\n

a<\/p>\n

[<\/p>\n

j<\/p>\n

]<\/p>\n

]<\/p>\n

\u2212<\/p>\n

\u2212<\/p>\n

count[a[j]]–<\/p>\n

<\/span><\/span>co<\/span>u<\/span>n<\/span>t<\/span>[<\/span>a<\/span>[<\/span>j<\/span>]]<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span> \u4e00\u76f4\u5230\u6307\u5411\u4e0e <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u505c\u6b62\u65f6\u6307\u5411\u7684\u5143\u7d20，\u5c06\u5c06\u5176\u5728 <\/p>\n

[<\/p>\n

j<\/p>\n

,<\/p>\n

i<\/p>\n

]<\/p>\n

[j,i]<\/p>\n

<\/span><\/span>[<\/span>j<\/span>,<\/span><\/span>i<\/span>]<\/span><\/span><\/span><\/span><\/span> \u533a\u95f4\u51fa\u73b0\u7684\u6b21\u6570\u51cf\u4e3a <\/p>\n

1<\/p>\n

1<\/p>\n

<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u6211\u4eec\u7ee7\u7eed\u79fb\u52a8 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u77e5\u9053\u5b83\u505c\u6b62 \u6ce8\u610f\u6bcf\u6b21\u5728 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6307\u9488\u505c\u6b62\u65f6\u6211\u4eec\u5c06\u7b54\u6848\u5224\u65ad\u5927\u5c0f\u4e00\u6b21 \u9898\u76ee\u4ee3\u7801<\/p>\n

#<\/span>include<\/span><bits\/stdc++.h><\/span><\/span>
\nusing<\/span> namespace<\/span> std;<\/span>
\nconst<\/span> int<\/span> N =<\/span> 1e5<\/span> +<\/span> 10<\/span>;<\/span>
\nint<\/span> a[<\/span>N]<\/span>,<\/span> count[<\/span>N]<\/span>;<\/span>
\nint<\/span> main<\/span>(<\/span>)<\/span>{<\/span>
\nint<\/span> n;<\/span>
\ncin >><\/span> n;<\/span>
\nfor<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span>cin >><\/span> a[<\/span>i]<\/span>;<\/span><\/p>\n

int<\/span> ans =<\/span> 0<\/span>;<\/span>
\nfor<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>,<\/span> j =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span>{<\/span>
\ncount[<\/span>a[<\/span>i]<\/span>]<\/span>++<\/span>;<\/span>
\nwhile<\/span>(<\/span>count[<\/span>a[<\/span>i]<\/span>]<\/span> ><\/span> 1<\/span>)<\/span>{<\/span>
\ncount[<\/span>a[<\/span>j]<\/span>]<\/span>—<\/span>;<\/span>
\nj++<\/span>;<\/span>
\n}<\/span>
\nans =<\/span> max<\/span>(<\/span>ans,<\/span> i –<\/span> j +<\/span> 1<\/span>)<\/span>;<\/span>
\n}<\/span>
\nreturn<\/span> 0<\/span>;<\/span>
\n}<\/span><\/p>\n

1.2 \u56fe\u89e3<\/h5>\n

i = 0, j = 0 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" i++ \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" j++ \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" i++\u540ej++\u5c31\u662f\u8bf4\u5f53\u5982\u679c\u5728\u4e00\u4e2a\u76f8\u7b49\u7684\u533a\u95f4\u5185 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u79fb\u52a8\u4e4b\u540e <\/p>\n

j<\/p>\n

j<\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span> \u4e5f\u4f1a\u7d27\u63a5\u7740\u79fb\u52a8i \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" i++ \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

2. \u8fde\u7eed\u6b63\u6574\u6570\u548c (Luogu P1147)<\/h4>\n

Luogu P1147<\/p>\n

\u7ed9\u5b9a\u4e00\u4e2a\u6b63\u6574\u6570 <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span>，\u6c42\u51fa\u6240\u6709\u7684\u8fde\u7eed\u7684\u6b63\u6574\u6570\u6bb5（\u6bcf\u4e00\u6bb5\u81f3\u5c11\u6709\u4e24\u4e2a\u6570），\u4f7f\u5f97\u8fd9\u4e9b\u8fde\u7eed\u7684\u6b63\u6574\u6570\u6bb5\u4e2d\u7684\u5168\u90e8\u6570\u4e4b\u548c\u4e3a <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u4f8b\u5982，<\/p>\n

1998<\/p>\n

+<\/p>\n

1999<\/p>\n

+<\/p>\n

2000<\/p>\n

+<\/p>\n

2001<\/p>\n

+<\/p>\n

2002<\/p>\n

=<\/p>\n

10000<\/p>\n

1998+1999+2000+2001+2002=10000<\/p>\n

<\/span><\/span>1998<\/span><\/span>+<\/span><\/span><\/span><\/span>1999<\/span><\/span>+<\/span><\/span><\/span><\/span>2000<\/span><\/span>+<\/span><\/span><\/span><\/span>2001<\/span><\/span>+<\/span><\/span><\/span><\/span>2002<\/span><\/span>=<\/span><\/span><\/span><\/span>10000<\/span><\/span><\/span><\/span><\/span>，\u6240\u4ee5\u4ece <\/p>\n

1998<\/p>\n

1998<\/p>\n

<\/span><\/span>1998<\/span><\/span><\/span><\/span><\/span> \u5230 <\/p>\n

2002<\/p>\n

2002<\/p>\n

<\/span><\/span>2002<\/span><\/span><\/span><\/span><\/span> \u7684\u4e00\u4e2a\u6b63\u6574\u6570\u6bb5\u4e3a <\/p>\n

M<\/p>\n

=<\/p>\n

10000<\/p>\n

M=10000<\/p>\n

<\/span><\/span>M<\/span><\/span>=<\/span><\/span><\/span><\/span>10000<\/span><\/span><\/span><\/span><\/span> \u7684\u4e00\u4e2a\u89e3\u3002<\/p>\n

\u8f93\u5165\u683c\u5f0f<\/p>\n

\u8f93\u5165\u4e00\u884c\u4e00\u4e2a\u6b63\u6574\u6570，\u8868\u793a <\/p>\n

M<\/p>\n

M<\/p>\n

<\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u7684\u503c（<\/p>\n

10<\/p>\n

\u2264<\/p>\n

M<\/p>\n

\u2264<\/p>\n

2<\/p>\n

\u00d7<\/p>\n

10<\/p>\n

6<\/p>\n

10\\\\le M\\\\le 2\\\\times 10^6<\/p>\n

<\/span><\/span>10<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>M<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>2<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）\u3002<\/p>\n

\u8f93\u51fa\u683c\u5f0f<\/p>\n

\u8f93\u51fa\u6bcf\u884c\u5305\u542b\u4e24\u4e2a\u6b63\u6574\u6570，\u8868\u793a\u4e00\u4e2a\u6ee1\u8db3\u6761\u4ef6\u7684\u8fde\u7eed\u6b63\u6574\u6570\u6bb5\u7684\u5de6\u53f3\u7aef\u70b9，\u4e24\u6570\u4e4b\u95f4\u7528\u4e00\u4e2a\u7a7a\u683c\u9694\u5f00\u3002<\/p>\n

\u8f93\u51fa\u6309\u5de6\u7aef\u70b9\u5927\u5c0f\u5347\u5e8f\u6392\u5217\u3002<\/p>\n

\u8f93\u5165<\/p>\n

10000<\/p>\n

\u8f93\u51fa<\/p>\n

18 142
\n297 328
\n388 412
\n1998 2002<\/p>\n

2.1 \u4e00\u822c\u601d\u8def<\/h5>\n

\u5b9a\u4e49 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6307\u9488\u5f00\u59cb\u5411\u53f3\u79fb\u52a8 \u5b9a\u4e49 <\/p>\n

s<\/p>\n

u<\/p>\n

m<\/p>\n

=<\/p>\n

a<\/p>\n

j<\/p>\n

+<\/p>\n

a<\/p>\n

j<\/p>\n

+<\/p>\n

1<\/p>\n

+<\/p>\n

\u22ef<\/p>\n

+<\/p>\n

a<\/p>\n

i<\/p>\n

sum =a_j +a_{j+1}+\\\\dots+a_i<\/p>\n

<\/span><\/span>s<\/span>u<\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>a<\/span><\/span>j<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u22ef<\/span><\/span>+<\/span><\/span><\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5982\u679c <\/p>\n

s<\/p>\n

u<\/p>\n

m<\/p>\n

=<\/p>\n

m<\/p>\n

sum=m<\/p>\n

<\/span><\/span>s<\/span>u<\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u6211\u4eec\u5c31\u8f93\u51fa\u6b64\u65f6\u7684 <\/p>\n

i<\/p>\n

,<\/p>\n

j<\/p>\n

i,j<\/p>\n

<\/span><\/span>i<\/span>,<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span> \u5982\u679c <\/p>\n

s<\/p>\n

u<\/p>\n

m<\/p>\n

<<\/p>\n

m<\/p>\n

sum < m<\/p>\n

<\/span><\/span>s<\/span>u<\/span>m<\/span><\/span><<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u6211\u4eec\u5c31 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6307\u9488\u53f3\u79fb\u52a8，\u6b64\u65f6 <\/p>\n

s<\/p>\n

u<\/p>\n

m<\/p>\n

sum<\/p>\n

<\/span><\/span>s<\/span>u<\/span>m<\/span><\/span><\/span><\/span><\/span> \u4f1a\u589e\u5927 \u5982\u679c <\/p>\n

s<\/p>\n

u<\/p>\n

m<\/p>\n

><\/p>\n

m<\/p>\n

sum > m<\/p>\n

<\/span><\/span>s<\/span>u<\/span>m<\/span><\/span>><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u6211\u4eec\u5c31 <\/p>\n

j<\/p>\n

j<\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span> \u6307\u9488\u53f3\u79fb\u52a8，\u6b64\u65f6 <\/p>\n

s<\/p>\n

u<\/p>\n

m<\/p>\n

sum<\/p>\n

<\/span><\/span>s<\/span>u<\/span>m<\/span><\/span><\/span><\/span><\/span> \u4f1a\u51cf\u5c0f \u6ce8\u610f\u8f93\u51fa\u653e\u5728\u524d\u9762<\/p>\n

#<\/span>include<\/span><bits\/stdc++.h><\/span><\/span>
\nusing<\/span> namespace<\/span> std;<\/span><\/p>\n

const<\/span> int<\/span> N =<\/span> 2e6<\/span> +<\/span> 10<\/span>;<\/span>
\nint<\/span> a[<\/span>N]<\/span>,<\/span> count[<\/span>N]<\/span>;<\/span><\/p>\n

int<\/span> main<\/span>(<\/span>)<\/span>{<\/span>
\n int<\/span> m;<\/span>
\n cin >><\/span> m;<\/span><\/p>\n

int<\/span> sum =<\/span> 0<\/span>;<\/span>
\n int<\/span> i =<\/span> 1<\/span>,<\/span> j =<\/span> 1<\/span>;<\/span>
\n while<\/span>(<\/span>i <<\/span> m \/<\/span> 2<\/span> )<\/span>{<\/span>
\n if<\/span>(<\/span>sum <<\/span> m)<\/span>{<\/span>
\n sum +=<\/span> i;<\/span>
\n i++<\/span>;<\/span>
\n }<\/span>
\n while<\/span>(<\/span>j <<\/span> i &&<\/span> sum >=<\/span> m)<\/span>{<\/span>
\n if<\/span>(<\/span>sum ==<\/span> m)<\/span> printf<\/span>(<\/span>"%d %d\\\\n"<\/span>,<\/span> j,<\/span> i)<\/span>;<\/span>
\n sum -=<\/span> j;<\/span>
\n j++<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

3. \u6570\u7ec4\u5143\u7d20\u7684\u76ee\u6807\u548c (AcWing 800)<\/h4>\n

AcWing 800 \u7ed9\u5b9a\u4e24\u4e2a\u5347\u5e8f\u6392\u5e8f\u7684\u6709\u5e8f\u6570\u7ec4 <\/p>\n

A<\/p>\n

A<\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u548c <\/p>\n

B<\/p>\n

B<\/p>\n

<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> ，\u4ee5\u53ca\u4e00\u4e2a\u76ee\u6807\u503c <\/p>\n

x<\/p>\n

x<\/p>\n

<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u6570\u7ec4\u4e0b\u6807\u4ece <\/p>\n

0<\/p>\n

0<\/p>\n

<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u5f00\u59cb \u8bf7\u4f60\u6c42\u51fa\u6ee1\u8db3 <\/p>\n

A<\/p>\n

[<\/p>\n

i<\/p>\n

]<\/p>\n

+<\/p>\n

B<\/p>\n

[<\/p>\n

j<\/p>\n

]<\/p>\n

=<\/p>\n

x<\/p>\n

A[i]+B[j]=x<\/p>\n

<\/span><\/span>A<\/span>[<\/span>i<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>B<\/span>[<\/span>j<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7684\u6570\u5bf9 <\/p>\n

(<\/p>\n

i<\/p>\n

,<\/p>\n

j<\/p>\n

)<\/p>\n

(i,j)<\/p>\n

<\/span><\/span>(<\/span>i<\/span>,<\/span><\/span>j<\/span>)<\/span><\/span><\/span><\/span><\/span> \u6570\u636e\u4fdd\u8bc1\u6709\u552f\u4e00\u89e3\u3002<\/p>\n

\u8f93\u5165\u683c\u5f0f \u7b2c\u4e00\u884c\u5305\u542b\u4e09\u4e2a\u6574\u6570 <\/p>\n

n<\/p>\n

,<\/p>\n

m<\/p>\n

,<\/p>\n

x<\/p>\n

n,m,x<\/p>\n

<\/span><\/span>n<\/span>,<\/span><\/span>m<\/span>,<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>，\u5206\u522b\u8868\u793a <\/p>\n

A<\/p>\n

A<\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u7684\u957f\u5ea6，<\/p>\n

B<\/p>\n

B<\/p>\n

<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u7684\u957f\u5ea6\u4ee5\u53ca\u76ee\u6807\u503c <\/p>\n

x<\/p>\n

x<\/p>\n

<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u7b2c\u4e8c\u884c\u5305\u542b <\/p>\n

n<\/p>\n

n<\/p>\n

<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6574\u6570，\u8868\u793a\u6570\u7ec4 <\/p>\n

A<\/p>\n

A<\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u7b2c\u4e09\u884c\u5305\u542b <\/p>\n

m<\/p>\n

m<\/p>\n

<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6574\u6570，\u8868\u793a\u6570\u7ec4 <\/p>\n

B<\/p>\n

B<\/p>\n

<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8f93\u51fa\u683c\u5f0f \u5171\u4e00\u884c，\u5305\u542b\u4e24\u4e2a\u6574\u6570 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u548c <\/p>\n

j<\/p>\n

j<\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6570\u636e\u8303\u56f4 \u6570\u7ec4\u957f\u5ea6\u4e0d\u8d85\u8fc7 <\/p>\n

10<\/p>\n

5<\/p>\n

10^5<\/p>\n

<\/span><\/span>1<\/span>0<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u540c\u4e00\u6570\u7ec4\u5185\u5143\u7d20\u5404\u4e0d\u76f8\u540c\u3002 <\/p>\n

1<\/p>\n

\u2264<\/p>\n

\u6570\u7ec4\u5143\u7d20<\/p>\n

\u2264<\/p>\n

10<\/p>\n

9<\/p>\n

1\u2264\u6570\u7ec4\u5143\u7d20\u226410^9<\/p>\n

<\/span><\/span>1<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>\u6570\u7ec4\u5143\u7d20<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8f93\u5165\u6837\u4f8b：<\/p>\n

4 5 6
\n1 2 4 7
\n3 4 6 8 9<\/p>\n

\u8f93\u51fa\u6837\u4f8b：<\/p>\n

1 1<\/p>\n

3. 1 \u4e00\u822c\u601d\u8def<\/h5>\n

\u4e00\u822c\u6765\u8bf4，\u6211\u4eec\u5bf9\u4e8e\u8fd9\u9053\u9898\u4f1a\u8003\u8651 \u5c06 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6307\u9488\u6307\u5411\u5728 <\/p>\n

a<\/p>\n

[<\/p>\n

]<\/p>\n

a[ ]<\/p>\n

<\/span><\/span>a<\/span>[<\/span>]<\/span><\/span><\/span><\/span><\/span> \u6570\u7ec4\u91cc\u9762\u7b2c\u4e00\u4e2a\u5143\u7d20 \u5c06 <\/p>\n

j<\/p>\n

j<\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span> \u6307\u9488\u6307\u5411\u5728 <\/p>\n

b<\/p>\n

[<\/p>\n

]<\/p>\n

b[ ]<\/p>\n

<\/span><\/span>b<\/span>[<\/span>]<\/span><\/span><\/span><\/span><\/span>\u6570\u7ec4\u91cc\u9762\u6700\u540e\u4e00\u4e2a\u5143\u7d20 \u5982\u679c <\/p>\n

a<\/p>\n

[<\/p>\n

i<\/p>\n

]<\/p>\n

+<\/p>\n

b<\/p>\n

[<\/p>\n

j<\/p>\n

]<\/p>\n

=<\/p>\n

x<\/p>\n

a[i] + b[j]=x<\/p>\n

<\/span><\/span>a<\/span>[<\/span>i<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>b<\/span>[<\/span>j<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u6211\u4eec\u5c31\u8f93\u51fa \u5982\u679c <\/p>\n

a<\/p>\n

[<\/p>\n

i<\/p>\n

]<\/p>\n

+<\/p>\n

b<\/p>\n

[<\/p>\n

j<\/p>\n

]<\/p>\n

<<\/p>\n

x<\/p>\n

a[i] + b[j]<x<\/p>\n

<\/span><\/span>a<\/span>[<\/span>i<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>b<\/span>[<\/span>j<\/span>]<\/span><\/span><<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u6211\u4eec\u5c31\u8ba9 <\/p>\n

i<\/p>\n

i<\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u6307\u9488\u53f3\u79fb\u52a8 \u5982\u679c <\/p>\n

a<\/p>\n

[<\/p>\n

i<\/p>\n

]<\/p>\n

+<\/p>\n

b<\/p>\n

[<\/p>\n

j<\/p>\n

]<\/p>\n

><\/p>\n

x<\/p>\n

a[i] + b[j]>x<\/p>\n

<\/span><\/span>a<\/span>[<\/span>i<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>b<\/span>[<\/span>j<\/span>]<\/span><\/span>><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u6211\u4eec\u5c31\u8ba9 <\/p>\n

j<\/p>\n

j<\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span> \u6307\u9488\u5de6\u79fb\u52a8<\/p>\n

#<\/span>include<\/span><bits\/stdc++.h><\/span><\/span>
\nusing<\/span> namespace<\/span> std;<\/span><\/p>\n

const<\/span> int<\/span> N =<\/span> 1e5<\/span> +<\/span> 10<\/span>;<\/span>
\nint<\/span> a[<\/span>N]<\/span>,<\/span>b[<\/span>N]<\/span>;<\/span><\/p>\n

int<\/span> main<\/span>(<\/span>)<\/span>{<\/span>
\n int<\/span> n,<\/span> m,<\/span> x;<\/span>
\n cin >><\/span> n >><\/span> m >><\/span> x;<\/span>
\n for<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span> cin >><\/span> a[<\/span>i]<\/span>;<\/span>
\n for<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> m;<\/span> i++<\/span>)<\/span> cin >><\/span> b[<\/span>i]<\/span>;<\/span><\/p>\n

int<\/span> i =<\/span> 0<\/span>,<\/span> j =<\/span> m –<\/span> 1<\/span>;<\/span>
\n while<\/span>(<\/span>i <<\/span> n &&<\/span> j >=<\/span> 0<\/span>)<\/span>{<\/span>
\n if<\/span>(<\/span>a[<\/span>i]<\/span> +<\/span> b[<\/span>j]<\/span> ==<\/span> x)<\/span> {<\/span>
\n printf<\/span>(<\/span>"%d %d"<\/span>,<\/span> i,<\/span> j)<\/span>;<\/span>
\n i++<\/span>;<\/span>
\n j—<\/span>;<\/span>
\n break<\/span>;<\/span>
\n }<\/span>
\n else<\/span> if<\/span>(<\/span>a[<\/span>i]<\/span> +<\/span> b[<\/span>j]<\/span> <<\/span> x)<\/span> i++<\/span>;<\/span>
\n else<\/span> j—<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\u603b\u7ed3<\/h3>\n

\u4e00\u822c\u6211\u4eec\u662f<\/p>\n

i, j \u521d\u59cb\u5316
\nwhile(i\u7684\u8303\u56f4 && j\u7684\u8303\u56f4){
\nif(\u6761\u4ef6){\u8f93\u51fa(\u53ef\u80fd\u4f1a\u6709\u79fb\u52a8)}
\nelse if(i\u79fb\u52a8\u6761\u4ef6) i\u7684\u79fb\u52a8;
\nelse j\u7684\u79fb\u52a8;
\n}<\/p>\n

\u4e5f\u53ef\u4ee5\u662f<\/p>\n

for(i, j\u521d\u59cb\u5316; \u5feb\u6307\u9488\u8303\u56f4; \u5feb\u6307\u9488\u79fb\u52a8){
\nif(\u6162\u6307\u9488\u7684\u8303\u56f4 && \u6162\u6307\u9488\u79fb\u52a8\u7684\u6761\u4ef6){
\n\u6162\u6307\u9488\u7684\u79fb\u52a8;
\n}
\nif(\u8f93\u51fa\u6761\u4ef6){
\n\u8f93\u51fa
\n}
\n}<\/p>\n

\u4f46\u662f\u65e0\u8bba\u662f\u600e\u6837\u7684\u683c\u5f0f，\u6211\u4eec\u4e3b\u8981\u5b66\u7684\u662f\u8fd9\u79cd\u601d\u60f3<\/p>\n

\u7ec3\u4e60\u9898<\/h3>\n

AcWing 2816. \u5224\u65ad\u5b50\u5e8f\u5217 \u4ee3\u7801<\/p>\n

#<\/span>include<\/span><bits\/stdc++.h><\/span><\/span>
\nusing<\/span> namespace<\/span> std;<\/span><\/p>\n

const<\/span> int<\/span> N =<\/span> 1e5<\/span> +<\/span> 10<\/span>;<\/span>
\nint<\/span> a[<\/span>N]<\/span>,<\/span> b[<\/span>N]<\/span>;<\/span><\/p>\n

int<\/span> main<\/span>(<\/span>)<\/span>{<\/span>
\n int<\/span> n,<\/span> m;<\/span>
\n cin >><\/span> n >><\/span> m;<\/span>
\n for<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span> cin >><\/span> a[<\/span>i]<\/span>;<\/span>
\n for<\/span>(<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> m;<\/span> i++<\/span>)<\/span> cin >><\/span> b[<\/span>i]<\/span>;<\/span>
\n int<\/span> i =<\/span> 0<\/span>,<\/span> j =<\/span> 0<\/span>;<\/span>
\n int<\/span> s =<\/span> 0<\/span>;<\/span>
\n while<\/span>(<\/span>i <<\/span> n &&<\/span> j <<\/span> m)<\/span>{<\/span>
\n if<\/span>(<\/span>a[<\/span>i]<\/span> ==<\/span> b[<\/span>j]<\/span>)<\/span>{<\/span>
\n i++<\/span>;<\/span>
\n j++<\/span>;<\/span>
\n s++<\/span>;<\/span>
\n }<\/span>
\n else<\/span> j++<\/span>;<\/span>
\n if<\/span>(<\/span>s ==<\/span> n)<\/span>{<\/span>
\n printf<\/span>(<\/span>"Yes"<\/span>)<\/span>;<\/span>
\n return<\/span> 0<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n printf<\/span>(<\/span>"No"<\/span>)<\/span>;<\/span>
\n return<\/span> 0<\/span>;<\/span>
\n}<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

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