{"id":763,"date":"2009-06-05T14:41:46","date_gmt":"2009-06-05T06:41:46","guid":{"rendered":"http:\/\/www.slyar.com\/blog\/?p=763"},"modified":"2014-04-22T13:57:38","modified_gmt":"2014-04-22T05:57:38","slug":"prim-simplicity-c","status":"publish","type":"post","link":"http:\/\/www.slyar.com\/blog\/prim-simplicity-c.html","title":{"rendered":"\u6700\u5c0f\u751f\u6210\u6811Prim\u7b97\u6cd5\u6734\u7d20\u7248 C\u8bed\u8a00\u5b9e\u73b0"},"content":{"rendered":"<p>\u6587\u7ae0\u4f5c\u8005\uff1a<span style=\"color: #0000ff;\">\u59dc\u5357(Slyar) <\/span>\u6587\u7ae0\u6765\u6e90\uff1aSlyar Home (<a title=\"Slyar\" href=\"..\/..\/\" target=\"_blank\">www.slyar.com<\/a>) \u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff0c\u8c22\u8c22\u5408\u4f5c\u3002<\/p>\n<p>\u524d\u51e0\u5929\u7814\u7a76Kruskal\u7b97\u6cd5\uff0c\u76f4\u63a5\u4e0a\u624b\u5c31\u662f\u5e76\u67e5\u96c6\u4f18\u5316\uff0c\u6734\u7d20\u7b97\u6cd5\u538b\u6839\u5c31\u6ca1\u5199\u3002\u8fd9\u4e24\u5929\u770bPrim\u7b97\u6cd5\u4e5f\u60f3\u7565\u8fc7\u6734\u7d20\u7248O(n^2)\u76f4\u63a5\u7528\u4e8c\u53c9\u5806\u4f18\u5316\uff0c\u53ef\u662f\u53d1\u73b0\u4e0d\u770b\u6734\u7d20\u7b97\u6cd5\u6839\u672c\u5199\u4e0d\u51fa\u6765...\u56e7\uff0c\u770b\u6765\u8fd8\u662f\u4e0d\u80fd\u5ffd\u7565\u57fa\u7840...<\/p>\n<p>\u8349\u7a3f\u7eb8\u4e0a\u753b\u56fe\u6a21\u62df\u63a8\u6f14\u4e86\u534a\u5929\uff0c\u7ec8\u4e8e\u641e\u6e05\u695aPrim\u7b97\u6cd5\u6734\u7d20\u7248\u7684C\u8bed\u8a00\u5b9e\u73b0\uff0c\u62ff\u51fa\u90a3\u5929\u5b66Kruskal\u7684\u5c0f\u9898\u76ee\u6d4b\u8bd5\u4e86\u4e00\u4e0b\uff0c\u901a\u8fc7\u3002<\/p>\n<p>\u4ee3\u7801\u7684\u6ce8\u91ca\u6211\u5199\u5f97\u5f88\u8be6\u7ec6\uff0c\u65b9\u4fbf\u7406\u89e3\uff0c\u6709\u51e0\u70b9\u9700\u8981\u8bf4\u660e\u4e00\u4e0b\u3002<\/p>\n<p>1\u30012\u4e2afor\u5faa\u73af\u90fd\u662f\u4ece2\u5f00\u59cb\u7684\uff0c\u56e0\u4e3a\u4e00\u822c\u6211\u4eec\u9ed8\u8ba4\u5f00\u59cb\u5c31\u628a\u7b2c\u4e00\u4e2a\u8282\u70b9\u52a0\u5165\u751f\u6210\u6811\uff0c\u56e0\u6b64\u4e4b\u540e\u4e0d\u9700\u8981\u518d\u6b21\u5bfb\u627e\u5b83\u3002<\/p>\n<p>2\u3001lowcost[i]\u8bb0\u5f55\u7684\u662f\u4ee5\u8282\u70b9i\u4e3a\u7ec8\u70b9\u7684\u6700\u5c0f\u8fb9\u6743\u503c\u3002\u521d\u59cb\u5316\u65f6\u56e0\u4e3a\u9ed8\u8ba4\u628a\u7b2c\u4e00\u4e2a\u8282\u70b9\u52a0\u5165\u751f\u6210\u6811\uff0c\u56e0\u6b64lowcost[i] = graph[1][i]\uff0c\u5373\u6700\u5c0f\u8fb9\u6743\u503c\u5c31\u662f\u5404\u8282\u70b9\u52301\u53f7\u8282\u70b9\u7684\u8fb9\u6743\u503c\u3002<\/p>\n<p>3\u3001mst[i]\u8bb0\u5f55\u7684\u662flowcost[i]\u5bf9\u5e94\u7684\u8d77\u70b9\uff0c\u8fd9\u6837\u6709\u8d77\u70b9\uff0c\u6709\u7ec8\u70b9\uff0c\u5373\u53ef\u552f\u4e00\u786e\u5b9a\u4e00\u6761\u8fb9\u4e86\u3002\u521d\u59cb\u5316\u65f6mst[i] = 1\uff0c\u5373\u6bcf\u6761\u8fb9\u90fd\u662f\u4ece1\u53f7\u8282\u70b9\u51fa\u53d1\u3002<\/p>\n<p>\u7f16\u5199\u7a0b\u5e8f:\u5bf9\u4e8e\u5982\u4e0b\u4e00\u4e2a\u5e26\u6743\u65e0\u5411\u56fe\uff0c\u7ed9\u51fa\u8282\u70b9\u4e2a\u6570\u4ee5\u53ca\u6240\u6709\u8fb9\u6743\u503c\uff0c\u7528Prim\u7b97\u6cd5\u6c42\u6700\u5c0f\u751f\u6210\u6811\u3002<\/p>\n<p><!--more--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-749\" title=\"kruskal\" src=\"http:\/\/www.slyar.com\/blog\/wp-content\/uploads\/2009\/06\/kruskal.png\" alt=\"kruskal\" width=\"600\" height=\"445\" srcset=\"http:\/\/www.slyar.com\/blog\/wp-content\/uploads\/2009\/06\/kruskal.png 600w, http:\/\/www.slyar.com\/blog\/wp-content\/uploads\/2009\/06\/kruskal-150x111.png 150w, http:\/\/www.slyar.com\/blog\/wp-content\/uploads\/2009\/06\/kruskal-300x223.png 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>\u8f93\u5165\u6570\u636e:<\/p>\n<p>7 11<br \/>\nA B 7<br \/>\nA D 5<br \/>\nB C 8<br \/>\nB D 9<br \/>\nB E 7<br \/>\nC E 5<br \/>\nD E 15<br \/>\nD F 6<br \/>\nE F 8<br \/>\nE G 9<br \/>\nF G 11<\/p>\n<p>\u8f93\u51fa:<\/p>\n<p>A - D : 5<br \/>\nD - F : 6<br \/>\nA - B : 7<br \/>\nB - E : 7<br \/>\nE - C : 5<br \/>\nE - G : 9<br \/>\nTotal:39<\/p>\n<p>\u6700\u5c0f\u751f\u6210\u6811Prim\u7b97\u6cd5\u6734\u7d20\u7248 C\u8bed\u8a00\u5b9e\u73b0 \u4ee3\u7801\u5982\u4e0b<\/p>\n<pre lang=\"c\" line=\"1\">\r\n#include <stdio.h>\r\n#include <stdlib.h>\r\n\r\n#define MAX 100\r\n#define MAXCOST 0x7fffffff\r\n\r\nint graph[MAX][MAX];\r\n\r\nint Prim(int graph[][MAX], int n)\r\n{\r\n\t\/* lowcost[i]\u8bb0\u5f55\u4ee5i\u4e3a\u7ec8\u70b9\u7684\u8fb9\u7684\u6700\u5c0f\u6743\u503c\uff0c\u5f53lowcost[i]=0\u65f6\u8868\u793a\u7ec8\u70b9i\u52a0\u5165\u751f\u6210\u6811 *\/\r\n\tint lowcost[MAX];\r\n\t\r\n\t\/* mst[i]\u8bb0\u5f55\u5bf9\u5e94lowcost[i]\u7684\u8d77\u70b9\uff0c\u5f53mst[i]=0\u65f6\u8868\u793a\u8d77\u70b9i\u52a0\u5165\u751f\u6210\u6811 *\/\r\n\tint mst[MAX];\r\n\t\r\n\tint i, j, min, minid, sum = 0;\r\n\t\r\n\t\/* \u9ed8\u8ba4\u9009\u62e91\u53f7\u8282\u70b9\u52a0\u5165\u751f\u6210\u6811\uff0c\u4ece2\u53f7\u8282\u70b9\u5f00\u59cb\u521d\u59cb\u5316 *\/\r\n\tfor (i = 2; i <= n; i++)\r\n\t{\r\n\t\t\/* \u6700\u77ed\u8ddd\u79bb\u521d\u59cb\u5316\u4e3a\u5176\u4ed6\u8282\u70b9\u52301\u53f7\u8282\u70b9\u7684\u8ddd\u79bb *\/\r\n\t\tlowcost[i] = graph[1][i];\r\n\t\t\r\n\t\t\/* \u6807\u8bb0\u6240\u6709\u8282\u70b9\u7684\u8d77\u70b9\u7686\u4e3a\u9ed8\u8ba4\u76841\u53f7\u8282\u70b9 *\/\r\n\t\tmst[i] = 1;\r\n\t}\r\n\t\r\n\t\/* \u6807\u8bb01\u53f7\u8282\u70b9\u52a0\u5165\u751f\u6210\u6811 *\/\r\n\tmst[1] = 0;\r\n\t\r\n\t\/* n\u4e2a\u8282\u70b9\u81f3\u5c11\u9700\u8981n-1\u6761\u8fb9\u6784\u6210\u6700\u5c0f\u751f\u6210\u6811 *\/\r\n\tfor (i = 2; i <= n; i++)\r\n\t{\r\n\t\tmin = MAXCOST;\r\n\t\tminid = 0;\r\n\t\t\r\n\t\t\/* \u627e\u6ee1\u8db3\u6761\u4ef6\u7684\u6700\u5c0f\u6743\u503c\u8fb9\u7684\u8282\u70b9minid *\/\r\n\t\tfor (j = 2; j <= n; j++)\r\n\t\t{\r\n\t\t\t\/* \u8fb9\u6743\u503c\u8f83\u5c0f\u4e14\u4e0d\u5728\u751f\u6210\u6811\u4e2d *\/\r\n\t\t\tif (lowcost[j] < min && lowcost[j] != 0)\r\n\t\t\t{\r\n\t\t\t\tmin = lowcost[j];\r\n\t\t\t\tminid = j;\r\n\t\t\t}\r\n\t\t}\r\n\t\t\/* \u8f93\u51fa\u751f\u6210\u6811\u8fb9\u7684\u4fe1\u606f:\u8d77\u70b9\uff0c\u7ec8\u70b9\uff0c\u6743\u503c *\/\r\n\t\tprintf(\"%c - %c : %d\\n\", mst[minid] + 'A' - 1, minid + 'A' - 1, min);\r\n\t\t\r\n\t\t\/* \u7d2f\u52a0\u6743\u503c *\/\r\n\t\tsum += min;\r\n\t\t\r\n\t\t\/* \u6807\u8bb0\u8282\u70b9minid\u52a0\u5165\u751f\u6210\u6811 *\/\r\n\t\tlowcost[minid] = 0;\r\n\t\t\r\n\t\t\/* \u66f4\u65b0\u5f53\u524d\u8282\u70b9minid\u5230\u5176\u4ed6\u8282\u70b9\u7684\u6743\u503c *\/\r\n\t\tfor (j = 2; j <= n; j++)\r\n\t\t{\r\n\t\t\t\/* \u53d1\u73b0\u66f4\u5c0f\u7684\u6743\u503c *\/\r\n\t\t\tif (graph[minid][j] < lowcost[j])\r\n\t\t\t{\r\n\t\t\t\t\/* \u66f4\u65b0\u6743\u503c\u4fe1\u606f *\/\r\n\t\t\t\tlowcost[j] = graph[minid][j];\r\n\t\t\t\t\r\n\t\t\t\t\/* \u66f4\u65b0\u6700\u5c0f\u6743\u503c\u8fb9\u7684\u8d77\u70b9 *\/\r\n\t\t\t\tmst[j] = minid;\r\n\t\t\t}\r\n\t\t}\r\n\t}\r\n\t\/* \u8fd4\u56de\u6700\u5c0f\u6743\u503c\u548c *\/\r\n\treturn sum;\r\n}\r\n\r\nint main()\r\n{\r\n\tint i, j, k, m, n;\r\n\tint x, y, cost;\r\n\tchar chx, chy;\r\n\t\r\n\t\/* \u8bfb\u53d6\u8282\u70b9\u548c\u8fb9\u7684\u6570\u76ee *\/\r\n\tscanf(\"%d%d\", &m, &n);\r\n\tgetchar();\r\n\t\r\n\t\/* \u521d\u59cb\u5316\u56fe\uff0c\u6240\u6709\u8282\u70b9\u95f4\u8ddd\u79bb\u4e3a\u65e0\u7a77\u5927 *\/\r\n\tfor (i = 1; i <= m; i++)\r\n\t{\r\n\t\tfor (j = 1; j <= m; j++)\r\n\t\t{\r\n\t\t\tgraph[i][j] = MAXCOST;\r\n\t\t}\r\n\t}\r\n \r\n\t\/* \u8bfb\u53d6\u8fb9\u4fe1\u606f *\/\r\n\tfor (k = 0; k < n; k++)\r\n\t{\r\n\t\tscanf(\"%c %c %d\", &chx, &chy, &cost);\r\n\t\tgetchar();\r\n\t\ti = chx - 'A' + 1;\r\n\t\tj = chy - 'A' + 1;\r\n\t\tgraph[i][j] = cost;\r\n\t\tgraph[j][i] = cost;\r\n\t}\r\n\t\r\n\t\/* \u6c42\u89e3\u6700\u5c0f\u751f\u6210\u6811 *\/\r\n\tcost = Prim(graph, m);\r\n\t\r\n\t\/* \u8f93\u51fa\u6700\u5c0f\u6743\u503c\u548c *\/\r\n\tprintf(\"Total:%d\\n\", cost);\r\n\t\r\n\t\/\/system(\"pause\");\r\n\treturn 0;\t\r\n}\r\n<\/pre>\n<p>\u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff1a<a href=\"http:\/\/www.slyar.com\/blog\">Slyar Home<\/a> &raquo; <a href=\"http:\/\/www.slyar.com\/blog\/prim-simplicity-c.html\">\u6700\u5c0f\u751f\u6210\u6811Prim\u7b97\u6cd5\u6734\u7d20\u7248 C\u8bed\u8a00\u5b9e\u73b0<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u4f5c\u8005\uff1a\u59dc\u5357(Slyar) \u6587\u7ae0\u6765\u6e90\uff1aSlyar Home (www.slyar.com) \u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff0c\u8c22\u8c22\u5408\u4f5c\u3002 \u524d\u51e0\u5929\u7814\u7a76Kruskal\u7b97\u6cd5\uff0c\u76f4\u63a5\u4e0a\u624b\u5c31\u662f\u5e76\u67e5\u96c6\u4f18\u5316\uff0c\u6734\u7d20\u7b97\u6cd5\u538b\u6839\u5c31\u6ca1\u5199\u3002\u8fd9\u4e24\u5929\u770bPrim\u7b97\u6cd5\u4e5f\u60f3\u7565\u8fc7\u6734\u7d20\u7248O(n^2)\u76f4\u63a5\u7528\u4e8c\u53c9\u5806 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17],"tags":[1010,913],"class_list":["post-763","post","type-post","status-publish","format-standard","hentry","category-programing","tag-prim","tag-913"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.2.1 - 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