{"id":11818,"date":"2023-01-03T16:55:19","date_gmt":"2023-01-03T08:55:19","guid":{"rendered":"https:\/\/docs.pingcode.com\/?p=11818"},"modified":"2023-01-03T16:58:50","modified_gmt":"2023-01-03T08:58:50","slug":"%e9%ab%98%e7%ba%a7%e7%ae%97%e6%b3%95%e6%9c%89%e5%93%aa%e4%ba%9b","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/uncategorized\/11818.html","title":{"rendered":"\u9ad8\u7ea7\u7b97\u6cd5\u6709\u54ea\u4e9b"},"content":{"rendered":"\n
\n

\u9ad8\u7ea7\u7b97\u6cd5\u6709\uff1a1. \u7a77\u7aed\u641c\u7d22\uff1b2. \u8d2a\u5fc3\uff1b3. \u52a8\u6001\u89c4\u5212\uff1b4. \u56fe\u8bba\uff1b5. \u6570\u8bba\u3002\u5176\u4e2d\uff0c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\uff08DFS\uff09\u4ece\u67d0\u4e2a\u72b6\u6001\u5f00\u59cb\uff0c\u4e0d\u65ad\u8f6c\u79fb\uff0c\u76f4\u81f3\u65e0\u6cd5\u8f6c\u79fb\uff0c\u56de\u9000\u5230\u524d\u4e00\u6b65\uff0c\u518d\u7ee7\u7eed\u8f6c\u79fb\u5230\u5176\u4ed6\u72b6\u6001\uff0c\u76f4\u5230\u627e\u5230\u6700\u7ec8\u89e3\u3002<\/p>\n<\/blockquote>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

\u4e00\u3001\u9ad8\u7ea7\u7b97\u6cd5<\/strong><\/h2>\n\n\n\n

1. <\/strong>\u7a77\u7aed\u641c\u7d22<\/strong><\/h3>\n\n\n\n

\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\uff08DFS\uff09\uff1a<\/strong><\/p>\n\n\n\n

\u4ece\u67d0\u4e2a\u72b6\u6001\u5f00\u59cb\uff0c\u4e0d\u65ad\u8f6c\u79fb\uff0c\u76f4\u81f3\u65e0\u6cd5\u8f6c\u79fb\uff0c\u56de\u9000\u5230\u524d\u4e00\u6b65\uff0c\u518d\u7ee7\u7eed\u8f6c\u79fb\u5230\u5176\u4ed6\u72b6\u6001\uff0c\u76f4\u5230\u627e\u5230\u6700\u7ec8\u89e3\u3002\u901a\u5e38\u91c7\u7528\u9012\u5f52\u51fd\u6570\u6216\u8005\u6808\uff08Stack\uff09\u6765\u5b9e\u73b0\u3002<\/p>\n\n\n\n

\u5bbd\u5ea6\u4f18\u5148\u641c\u7d22\uff08BFS\uff09\uff1a<\/strong><\/p>\n\n\n\n

\u4ece\u521d\u59cb\u72b6\u6001\u5f00\u59cb\uff0c\u603b\u662f\u5148\u641c\u7d22\u81f3\u8ddd\u79bb\u521d\u59cb\u72b6\u6001\u8fd1\u7684\u72b6\u6001\u3002\u6bcf\u4e2a\u72b6\u6001\u90fd\u53ea\u7ecf\u8fc7\u4e00\u6b21\uff0c\u56e0\u6b64\u590d\u6742\u5ea6\u4e3aO(\u72b6\u6001\u6570*\u8f6c\u79fb\u65b9\u5f0f\u6570)\u3002\u901a\u5e38\u91c7\u7528\u5faa\u73af\u6216\u961f\u5217\uff08Queue\uff09\u5b9e\u73b0\u3002<\/p>\n\n\n\n

2. <\/strong>\u8d2a\u5fc3<\/strong><\/h3>\n\n\n\n

\u8d2a\u5fc3\u7b97\u6cd5\uff1a<\/strong><\/p>\n\n\n\n

\u9075\u5faa\u67d0\u79cd\u89c4\u5f8b\uff0c\u4e0d\u65ad\u8d2a\u5fc3\u9009\u53d6\u5f53\u524d\u4f18\u5f02\u7b56\u7565\u3002<\/p>\n\n\n\n

\u8d2a\u5fc3\u8bc1\u660e\uff1a<\/strong><\/p>\n\n\n\n

\u4e0e\u5176\u5b83\u9009\u62e9\u65b9\u6848\u76f8\u6bd4\uff0c\u8be5\u7b97\u6cd5\u5e76\u4e0d\u4f1a\u5f97\u5230\u66f4\u5dee\u7684\u89e3\uff08\u5f52\u7eb3\u6cd5\uff09\uff1b\u4e0d\u5b58\u5728\u5176\u4ed6\u7684\u89e3\u51b3\u65b9\u6848\uff08\u53cd\u8bc1\u6cd5\uff09\u3002<\/p>\n\n\n\n

3. <\/strong>\u52a8\u6001\u89c4\u5212<\/strong><\/h3>\n\n\n\n

\u52a8\u6001\u89c4\u5212\uff08DP\uff09\uff1a<\/strong><\/p>\n\n\n\n

\u901a\u8fc7\u5b9a\u4e49\u67d0\u79cd\u4f18\u5f02\u5b50\u72b6\u6001\uff0c\u8fdb\u884c\u72b6\u6001\u95f4\u8f6c\u79fb\u8fbe\u5230\u6700\u7ec8\u89e3\u3002<\/p>\n\n\n\n

\u8bb0\u5fc6\u5316\u641c\u7d22\uff1a<\/p>\n\n\n\n

\u5c06\u91cd\u590d\u72b6\u6001\u901a\u8fc7\u6807\u8bb0\u964d\u4f4e\u590d\u6742\u5ea6\u3002<\/p>\n\n\n\n

\u591a\u79cd\u5f62\u5f0f\u7684DP\uff1a<\/strong><\/p>\n\n\n\n

\u641c\u7d22\u7684\u8bb0\u5fc6\u5316\u6216\u5229\u7528\u9012\u63a8\u5173\u7cfb\u7684DP\uff0c\u6216\u4ece\u72b6\u6001\u8f6c\u79fb\u8003\u8651\u7684DP\u3002\u72b6\u6001\u5b9a\u4e49\u548c\u5faa\u73af\u987a\u5e8f\u90fd\u4f1a\u5f71\u54cd\u590d\u6742\u5ea6\u3002<\/p>\n\n\n\n

4. <\/strong>\u56fe\u8bba<\/strong><\/h3>\n\n\n\n

\u56fe\uff1a<\/strong><\/p>\n\n\n\n

\u9876\u70b9\u96c6\u5408\u4e3aV\u3001\u8fb9\u96c6\u4e3aE\u7684\u56fe\u8bb0\u4f5cG=(V,E)\uff0c\u4eceu\u5230v\u7684\u8fb9\u8bb0\u4f5ce=(u,v)\u3002\u6839\u636e\u8fb9\u662f\u5426\u6709\u5411\u5206\u4e3a\u6709\u5411\u56fe\u548c\u65e0\u5411\u56fe\uff0c\u6839\u636e\u662f\u5426\u6709\u73af\u5206\u4e3a\u6709\u73af\u56fe\u548c\u65e0\u73af\u56fe\u3002\u56fe\u53ef\u7531\u90bb\u63a5\u8868\u548c\u90bb\u63a5\u77e9\u9635\u4e24\u79cd\u65b9\u5f0f\u8868\u793a\u3002<\/p>\n\n\n\n

Bellman-Ford<\/strong>\u7b97\u6cd5\uff08\u5355\u6e90\u6700\u77ed\u8def\uff09\uff1a<\/strong><\/p>\n\n\n\n

\u8bb0\u5f55\u8d77\u70b9\u5230\u6bcf\u4e2a\u70b9i\u7684\u6700\u77ed\u8ddd\u79bbd[i]\uff0c\u7528\u6240\u6709\u7684\u8fb9\u6761\u4ef6\u6301\u7eed\u66f4\u65b0d[i]\uff0c\u76f4\u5230\u6bcf\u4e2ad[i]\u90fd\u5df2\u7ecf\u4e3a\u6700\u5c0f\u65e0\u6cd5\u66f4\u65b0\u3002\u56fe\u53ef\u5305\u542b\u8d1f\u6743\u8fb9\uff0c\u5305\u542b\u8d1f\u73af\u7684\u5224\u65ad\u65b9\u6cd5\u4e3a\u5c06\u6240\u6709d[i]\u521d\u59cb\u5316\u4e3a0\uff0c\u7b2cV\u6b21d[i]\u662f\u5426\u4ecd\u5b58\u5728\u66f4\u65b0\u3002\u590d\u6742\u5ea6\u4e3aO(EV)\u3002<\/p>\n\n\n\n

Dijkstra<\/strong>\u7b97\u6cd5\uff08\u5355\u6e90\u6700\u77ed\u8def\uff09\uff1a<\/strong><\/p>\n\n\n\n

\u4ece\u8d77\u70b9\u51fa\u53d1\u51fa\u53d1\uff0c\u66f4\u65b0s\u6240\u6709\u53ef\u5230\u8fbe\u7684\u8fb9j\uff0c\u82e5d[j]\u6709\u66f4\u65b0\uff0c\u5219\u52a0\u5165\u6700\u5c0f\u5806\uff0c\u4ee5\u4fbf\u4e0b\u6b21\u627e\u5230\u5269\u4f59\u96c6\u5408\u4e2dd[i]\u6700\u5c0f\u7684\u70b9i\uff0c\u518d\u4ecei\u51fa\u53d1BFS\uff0c\u76f4\u5230\u5230\u8fbe\u7ec8\u70b9t\u3002\u4e0d\u80fd\u5904\u7406\u5305\u542b\u8d1f\u6743\u8fb9\u7684\u56fe\u3002\u590d\u6742\u5ea6\u4e3aO(ElogV)\u3002<\/p>\n\n\n\n

Floyd-Warshall<\/strong>\u7b97\u6cd5\uff08\u591a\u6e90\u6700\u77ed\u8def\uff09\uff1a<\/strong><\/p>\n\n\n\n

\u5b9a\u4e49\u4ecei\u5230j\u4e14\u7ecf\u8fc7k\u7684\u6700\u77ed\u8def\u4e3ad[i][j]\u7528d[i][k]+d[k][j]\u6765\u66f4\u65b0\uff0c\u4e09\u91cd\u5faa\u73af\u76f4\u63a5\u5f97\u5230\u4efb\u610f\u4e24\u70b9\u95f4\u7684\u6700\u77ed\u8def\u3002\u56fe\u53ef\u5305\u542b\u8d1f\u6743\u8fb9\uff0c\u5305\u542b\u8d1f\u73af\u7684\u5224\u65ad\u65b9\u6cd5\u4e3a\u662f\u5426\u5b58\u5728\u9876\u70b9i\u4f7fd[i][i]\u4e3a\u8d1f\u3002\u590d\u6742\u5ea6O(V^3)\u3002<\/p>\n\n\n\n

Prim<\/strong>\u7b97\u6cd5\uff08\u6700\u5c0f\u751f\u6210\u6811\uff09\uff1a<\/strong><\/p>\n\n\n\n

\u5047\u8bbeV\u7684\u5b50\u96c6X\u5df2\u7ecf\u6784\u9020\u4e86\u90e8\u5206\u6700\u5c0f\u751f\u6210\u6811\uff0c\u90a3\u4e48\u63a5\u4e0b\u6765\u5c31\u662f\u9009\u53d6\u4eceX\u5230X\u7684\u8865\u96c6\u4e2d\u6743\u503c\u6700\u5c0f\u7684\u8fb9\u52a0\u5165\u3002\u53ef\u4f7f\u7528\u6700\u5c0f\u5806\u7ef4\u62a4\u5f85\u9009\u7684\u8fb9\uff0c\u590d\u6742\u5ea6\u4e3aO(ElogV)\u3002<\/p>\n\n\n\n

Kruskal<\/strong>\u7b97\u6cd5\uff08\u6700\u5c0f\u751f\u6210\u6811\uff09\uff1a<\/strong><\/p>\n\n\n\n

\u5c06\u6240\u6709\u8fb9\u5347\u5e8f\u6392\u5217\uff0c\u4f9d\u6b21\u53d6\u51fa\u6bcf\u6761\u6700\u5c0f\u7684\u8fb9\uff0c\u82e5\u8be5\u8fb9\u7684\u4e24\u4e2a\u7aef\u70b9\u4e0d\u5728\u76f8\u540c\u5e76\u67e5\u96c6\u5185\uff0c\u5219\u5c06\u8be5\u8fb9\u52a0\u5165\u6700\u5c0f\u751f\u6210\u6811\uff0c\u5e76\u5c06\u4e24\u70b9\u7528\u5e76\u67e5\u96c6\u8fde\u63a5\u3002\u8017\u65f6\u975e\u5e38\u591a\u7684\u64cd\u4f5c\u4e3a\u8fb9\u7684\u6392\u5e8f\uff0c\u590d\u6742\u5ea6O(ElogE)\u3002<\/p>\n\n\n\n

5. <\/strong>\u6570\u8bba<\/strong><\/h3>\n\n\n\n

\u8f97\u8f6c\u76f8\u9664\u7b97\u6cd5\uff08\u6700\u5c0f\u516c\u7ea6\u6570\uff09\uff1a<\/strong><\/p>\n\n\n\n

gcd(a,b)=gcd(b,a%b)\uff0c\u5faa\u73af\u81f3b\u4e3a0\uff0c\u6b64\u65f6\u5f97\u5230\u6700\u5c0f\u516c\u7ea6\u6570\u4e3aa\u3002<\/p>\n\n\n\n

\u6269\u5c55\u6b27\u51e0\u91cc\u5fb7\u7b97\u6cd5\uff08\u89e3\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\uff09\uff1a<\/strong><\/p>\n\n\n\n

\u6c42\u89e3ax+by=gcd(a,b)\uff0c\u7c7b\u4f3c\u8f97\u8f6c\u76f8\u9664\u6cd5\u3002\u6c42extgcd(a,b,&x,&y)\u65f6\uff0c\u9012\u5f52\u6c42\u5f97d=extgcd(b,a%b,y,x)\u7684\u89e3\u5b58\u5165y\u548cx\u3002\u5219ax+by=gcd(a,b)\u7684\u89e3\u4e3ax\u548cy-(a\/b)*x\u3002<\/p>\n\n\n\n

\u7d20\u6570\u7b5b\u6cd5\uff1a<\/strong><\/p>\n\n\n\n

\u901a\u8fc7\u5df2\u6c42\u5f97\u7684\u7d20\u6570\uff0c\u5c06\u6240\u6c42\u8303\u56f4\u5185\u6240\u6709\u8be5\u7d20\u6570\u7684\u500d\u6570\u90fd\u6807\u8bb0\u4e3a\u5408\u6570\u3002\u4f9d\u5e8f\u904d\u5386\u7a7a\u95f4\uff0c\u672a\u88ab\u7b5b\u6389\u7684\u5373\u4e3a\u65b0\u7684\u7d20\u6570\u3002\u590d\u6742\u5ea6O(nloglogn)\uff0c\u53ef\u770b\u4f5c\u7ebf\u6027\u7684\u3002<\/p>\n\n\n\n

\u53cd\u590d\u5e73\u65b9\u6cd5\uff08\u5feb\u901f\u5e42\uff09\uff1a\u6c42x\u7684n\u6b21\u5e42\uff0c\u53ef\u4e8c\u5206\u9012\u5f52\u6c42x\u7684n\/2\u6b21\u5e42\uff0c\u5373x^n=(x^(n\/2))^2 *<\/p>\n\n\n\n

x^(n&1)\u3002\u590d\u6742\u5ea6\u4e3aO(logn)\u3002<\/p>\n\n\n\n

\u5ef6\u4f38\u9605\u8bfb\uff1a<\/strong><\/p>\n\n\n\n

\u4e8c\u3001 \u5206\u6cbb\u6cd5\u7279\u5f81<\/strong><\/h2>\n\n\n\n

\u8be5\u95ee\u9898\u7684\u89c4\u6a21\u7f29\u5c0f\u5230\u4e00\u5b9a\u7684\u7a0b\u5ea6\u5c31\u53ef\u4ee5\u5bb9\u6613\u5730\u89e3\u51b3 \u3002
\u8be5\u95ee\u9898\u53ef\u4ee5\u5206\u89e3\u4e3a\u82e5\u5e72\u4e2a\u89c4\u6a21\u8f83\u5c0f\u7684\u76f8\u540c\u95ee\u9898\uff0c\u5373\u8be5\u95ee\u9898\u5177\u6709\u4f18\u5f02\u5b50\u7ed3\u6784\u6027\u8d28\u3002
\u5229\u7528\u8be5\u95ee\u9898\u5206\u89e3\u51fa\u7684\u5b50\u95ee\u9898\u7684\u89e3\u53ef\u4ee5\u5408\u5e76\u4e3a\u8be5\u95ee\u9898\u7684\u89e3\u3002
\u8be5\u95ee\u9898\u6240\u5206\u89e3\u51fa\u7684\u5404\u4e2a\u5b50\u95ee\u9898\u662f\u76f8\u4e92\u72ec\u7acb\u7684\uff0c\u5373\u5b50\u95ee\u9898\u4e4b\u95f4\u4e0d\u5305\u542b\u516c\u5171\u7684\u5b50\u95ee\u9898\u3002<\/p>\n\n\n\n

\u4ee5\u4e0a\u5c31\u662f\u5173\u4e8e\u9ad8\u7ea7\u7b97\u6cd5\u7684\u5185\u5bb9\u5e0c\u671b\u5bf9\u5927\u5bb6\u6709\u5e2e\u52a9\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u9ad8\u7ea7\u7b97\u6cd5\u6709\uff1a1. \u7a77\u7aed\u641c\u7d22\uff1b2. \u8d2a\u5fc3\uff1b3. \u52a8\u6001\u89c4\u5212\uff1b4. \u56fe\u8bba\uff1b5. \u6570\u8bba\u3002\u5176\u4e2d\uff0c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\uff08DFS\uff09\u4ece […]","protected":false},"author":1,"featured_media":11819,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/11818"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=11818"}],"version-history":[{"count":0,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/11818\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/11819"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=11818"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=11818"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=11818"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}