{"id":65165,"date":"2025-05-03T13:42:00","date_gmt":"2025-05-03T05:42:00","guid":{"rendered":"https:\/\/fwq.ai\/blog\/65165\/"},"modified":"2025-05-03T13:42:00","modified_gmt":"2025-05-03T05:42:00","slug":"java-%e5%9b%be%e5%bd%a2%e7%bb%88%e6%9e%81%e6%8c%87%e5%8d%97%ef%bc%9a%e9%80%82%e5%90%88%e5%90%84%e4%b8%aa%e7%ba%a7%e5%88%ab%e5%bc%80%e5%8f%91%e4%ba%ba%e5%91%98%e7%9a%84%e6%b7%b1%e5%85%a5%e7%a0%94-3","status":"publish","type":"post","link":"https:\/\/fwq.ai\/blog\/65165\/","title":{"rendered":"Java \u56fe\u5f62\u7ec8\u6781\u6307\u5357\uff1a\u9002\u5408\u5404\u4e2a\u7ea7\u522b\u5f00\u53d1\u4eba\u5458\u7684\u6df1\u5165\u7814\u7a76"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/img.php.cn\/upload\/article\/001\/246\/273\/173133002950591.jpg\" class=\"aligncenter\" title=\"Java \u56fe\u5f62\u7ec8\u6781\u6307\u5357\uff1a\u9002\u5408\u5404\u4e2a\u7ea7\u522b\u5f00\u53d1\u4eba\u5458\u7684\u6df1\u5165\u7814\u7a76\u63d2\u56fe\" alt=\"Java \u56fe\u5f62\u7ec8\u6781\u6307\u5357\uff1a\u9002\u5408\u5404\u4e2a\u7ea7\u522b\u5f00\u53d1\u4eba\u5458\u7684\u6df1\u5165\u7814\u7a76\u63d2\u56fe\" \/><\/p>\n<p>\u6b22\u8fce\u6765\u5230\u5168\u9762\u7684\u56fe\u8868\u4e16\u754c\uff01\u5982\u679c\u60a8\u662f\u4e00\u540d\u5f00\u53d1\u4eba\u5458\uff0c\u5e76\u4e14\u672f\u8bed\u201c\u56fe\u8868\u201d\u53ea\u4f1a\u8ba9\u4eba\u60f3\u8d77\u997c\u56fe\u548c\u6761\u5f62\u56fe\u7684\u56fe\u50cf\uff0c\u90a3\u4e48\u8bf7\u51c6\u5907\u597d\u6269\u5c55\u60a8\u7684\u89c6\u91ce\u3002\u4ece\u6570\u636e\u7ed3\u6784\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u56fe\u662f\u8bb8\u591a\u590d\u6742\u7684\u8ba1\u7b97\u673a\u79d1\u5b66\u95ee\u9898\u548c\u73b0\u5b9e\u4e16\u754c\u5e94\u7528\u80cc\u540e\u7684\u65e0\u540d\u82f1\u96c4\u3002\u4ece\u548c\u63a8\u8350\u5f15\u64ce\u5230\u5bfb\u627e\u4ece a \u70b9\u5230 b \u70b9\u7684\u6700\u77ed\u8def\u5f84\uff0c\u56fe\u8868\u53ef\u4ee5\u505a\u5230\u8fd9\u4e00\u5207\u3002\u672c\u6307\u5357\u5c06\u6db5\u76d6\u4ece\u57fa\u7840\u77e5\u8bc6\u5230\u9ad8\u7ea7\u56fe\u5f62\u7b97\u6cd5\u7684\u6240\u6709\u5185\u5bb9\u3002\u7cfb\u597d\u5b89\u5168\u5e26\uff1b\u8fd9\u5c06\u662f\u4e00\u6b21\u5145\u6ee1\u77e5\u8bc6\u3001\u5e7d\u9ed8\u548c\u4ee3\u7801\u7247\u6bb5\u7684\u75af\u72c2\u4e4b\u65c5\uff0c\u8ba9\u60a8\u6210\u4e3a java \u56fe\u5f62\u5927\u5e08\uff01<\/p>\n<h2> 1. \u5230\u5e95\u4ec0\u4e48\u662f\u56fe\uff1f <\/h2>\n<p>\u5176\u6838\u5fc3\uff0c<strong>\u56fe<\/strong>\u662f\u7531<strong>\u8fb9<\/strong>\u8fde\u63a5\u7684<strong>\u8282\u70b9\uff08\u9876\u70b9\uff09<\/strong>\u7684\u96c6\u5408\u3002\u4e0e\u53ef\u80fd\u662f\u7ebf\u6027\u7684\u5e73\u5747\u6570\u636e\u7ed3\u6784\uff08\u5982\u6570\u7ec4\u6216\u94fe\u8868\uff09\u4e0d\u540c\uff0c\u56fe\u8868\u5141\u8bb8\u66f4\u590d\u6742\u7684\u5173\u7cfb\u3002<\/p>\n<h3> \u6b63\u5f0f\u5b9a\u4e49\uff1a <\/h3>\n<p>\u56fe ggg \u5b9a\u4e49\u4e3a g=(v,e)g = (v, e)g=(v,e) \u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>vvv \u662f\u4e00\u7ec4\u9876\u70b9\uff08\u8282\u70b9\uff09\u3002<\/li>\n<li>eee \u662f\u4e00\u7ec4\u8fde\u63a5\u9876\u70b9\u5bf9\u7684\u8fb9\u3002<\/li>\n<\/ul>\n<h3> \u4f8b\u5b50\uff1a <\/h3>\n<p>\u8003\u8651\u4e00\u4e2a\u4ee3\u8868\u53cb\u8c0a\u7684\u7b80\u5355\u56fe\u8868\uff1a<\/p>\n<p><span>\u7acb\u5373\u5b66\u4e60<\/span>\u201c\u201d\uff1b<\/p>\n<ul>\n<li>\u8282\u70b9\uff1aalice\u3001bob\u3001charlie<\/li>\n<li>\u8fb9\u7f18\uff1a\u7231\u4e3d\u4e1d-\u9c8d\u52c3\uff0c\u9c8d\u52c3-\u67e5\u7406<\/li>\n<\/ul>\n<h3> \u7b26\u53f7\u5e7d\u9ed8\uff1a <\/h3>\n<p>\u56fe\u53ef\u4ee5\u662f\u6709\u5411\u56fe\u6216\u65e0\u5411\u56fe\u3002\u5728\u6709\u5411\u56fe\u4e2d\uff0c\u5982\u679c\u7231\u4e3d\u4e1d\u6307\u5411\u9c8d\u52c3\uff0c\u8bf7\u60f3\u8c61\u7231\u4e3d\u4e1d\u8bf4\uff1a\u201c\u563f\u9c8d\u52c3\uff0c\u6211\u5173\u6ce8\u4f60\uff0c\u4f46\u4f60\u4e0d\u5173\u6ce8\u6211\u3002\u201d<\/p>\n<h2> 2. \u56fe\u7684\u7c7b\u578b <\/h2>\n<h3> 2.1. <strong>\u65e0\u5411\u56fe\u4e0e\u6709\u5411\u56fe<\/strong> <\/h3>\n<ul>\n<li> <strong>\u65e0\u5411\u56fe<\/strong>\uff1a\u8282\u70b9\u4e4b\u95f4\u7684\u5173\u7cfb\u662f\u53cc\u5411\u7684\u3002\u5982\u679c a \u548c b \u4e4b\u95f4\u6709\u8fb9\uff0c\u60a8\u53ef\u4ee5\u4ece a \u5230 b\uff0c\u518d\u4ece b \u5230 a\u3002<\/li>\n<li> <strong>\u6709\u5411\u56fe\uff08digraph\uff09<\/strong>\uff1a\u8fb9\u6709\u65b9\u5411\u3002\u5982\u679c\u4ece a \u5230 b \u6709\u4e00\u6761\u8fb9\uff0c\u4f60\u53ef\u4ee5\u4ece a \u5230 b\uff0c\u4f46\u4e0d\u4e00\u5b9a\u80fd\u8fd4\u56de\u3002<\/li>\n<\/ul>\n<h3> 2.2. <strong>\u52a0\u6743\u4e0e\u672a\u52a0\u6743\u56fe\u8868<\/strong> <\/h3>\n<ul>\n<li> <strong>\u52a0\u6743\u56fe<\/strong>\uff1a\u6bcf\u6761\u8fb9\u90fd\u6709\u4e00\u4e2a\u5173\u8054\u7684\u6743\u91cd\uff08\u5c06\u5176\u89c6\u4e3a\u8ddd\u79bb\u6216\u6210\u672c\uff09\u3002<\/li>\n<li> <strong>\u672a\u52a0\u6743\u56fe<\/strong>\uff1a\u6240\u6709\u8fb9\u90fd\u88ab\u540c\u7b49\u5bf9\u5f85\uff0c\u6ca1\u6709\u6743\u91cd\u3002<\/li>\n<\/ul>\n<h3> 2.3. <strong>\u5faa\u73af\u56fe\u4e0e\u975e\u5faa\u73af\u56fe<\/strong> <\/h3>\n<ul>\n<li> <strong>\u5faa\u73af\u56fe<\/strong>\uff1a\u5305\u542b\u81f3\u5c11\u4e00\u4e2a\u5faa\u73af\uff08\u5728\u540c\u4e00\u8282\u70b9\u5f00\u59cb\u548c\u7ed3\u675f\u7684\u8def\u5f84\uff09\u3002<\/li>\n<li> <strong>\u975e\u5faa\u73af\u56fe<\/strong>\uff1a\u4e0d\u5b58\u5728\u5faa\u73af\u3002\u6700\u8457\u540d\u7684\u7c7b\u578b\uff1f <strong>dag<\/strong>\uff08\u6709\u5411\u65e0\u73af\u56fe\uff09\uff0c\u5b83\u662f\u62d3\u6251\u6392\u5e8f\u7684\u652f\u67f1\u3002<\/li>\n<\/ul>\n<h3> 2.4. <strong>\u8fde\u63a5\u56fe\u4e0e\u975e\u8fde\u63a5\u56fe<\/strong> <\/h3>\n<ul>\n<li> <strong>\u8fde\u901a\u56fe<\/strong>\uff1a\u6240\u6709\u8282\u70b9\u90fd\u53ef\u4ee5\u4ece\u4efb\u4f55\u5176\u4ed6\u8282\u70b9\u5230\u8fbe\u3002<\/li>\n<li> <strong>\u65ad\u5f00\u8fde\u63a5\u7684\u56fe<\/strong>\uff1a\u67d0\u4e9b\u8282\u70b9\u65e0\u6cd5\u4ece\u5176\u4ed6\u8282\u70b9\u5230\u8fbe\u3002<\/li>\n<\/ul>\n<h3> 2.5. <strong>\u7279\u6b8a\u56fe\u8868<\/strong> <\/h3>\n<ul>\n<li> <strong>\u6811<\/strong>\uff1a\u8fde\u901a\u7684\u65e0\u73af\u65e0\u5411\u56fe\u3002\u628a\u5b83\u60f3\u8c61\u6210\u4e00\u4e2a\u6ca1\u6709\u5faa\u73af\u7684\u5bb6\u8c31\u2014\u2014\u8fd9\u91cc\u6ca1\u6709\u4eba\u4e0e\u4ed6\u4eec\u7684\u8868\u5f1f\u7ed3\u5a5a\u3002<\/li>\n<li> <strong>\u4e8c\u90e8\u56fe<\/strong>\uff1a\u53ef\u4ee5\u5206\u4e3a\u4e24\u4e2a\u96c6\u5408\uff0c\u4f7f\u5f97\u540c\u4e00\u96c6\u5408\u5185\u6ca1\u6709\u4e24\u4e2a\u56fe\u9876\u70b9\u76f8\u90bb\u3002<\/li>\n<li> <strong>\u5b8c\u5168\u56fe<\/strong>\uff1a\u6bcf\u5bf9\u4e0d\u540c\u7684\u9876\u70b9\u90fd\u7531\u4e00\u6761\u8fb9\u8fde\u63a5\u3002<\/li>\n<li> <strong>\u7a00\u758f\u56fe\u4e0e\u5bc6\u96c6\u56fe<\/strong>\uff1a\u7a00\u758f\u56fe\u76f8\u5bf9\u4e8e\u8282\u70b9\u6570\u91cf\u800c\u8a00\u8fb9\u5f88\u5c11\uff1b\u5bc6\u96c6\u56fe\u5219\u76f8\u53cd\u3002<\/li>\n<\/ul>\n<h2> 3. \u5185\u5b58\u4e2d\u7684\u56fe\u5f62\u8868\u793a <\/h2>\n<h3> 3.1. <strong>\u90bb\u63a5\u77e9\u9635<\/strong> <\/h3>\n<p>\u4e8c\u7ef4\u6570\u7ec4 adj[i][j]adj[i][j]adj[i][j] \u7528\u4e8e\u4ee5\u4e0b\u4f4d\u7f6e\uff1a<\/p>\n<ul>\n<li>\n<p>\u5982\u679c\u8282\u70b9 i \u548c j \u4e4b\u95f4\u6709\u8fb9\uff0c\u5219 adj[i][j]=1adj[i][j] = 1adj[i][j]=1\u3002<\/p>\n<p>ii<\/p>\n<p>jj<\/p>\n<\/li>\n<li>\n<p>adj[i][j]=weightadj[i][j] = weightadj[i][j]=\u6743\u91cd\uff08\u5982\u679c\u56fe\u8868\u5df2\u52a0\u6743\uff09\u3002<\/p>\n<\/li>\n<\/ul>\n<p><strong>\u4f18\u70b9<\/strong>\uff1a<\/p>\n<ul>\n<li>\n<p>\u5feb\u901f\u67e5\u627e\uff1ao(1) \u68c0\u67e5\u8fb9\u662f\u5426\u5b58\u5728\u3002<\/p>\n<p>o(1)o(1)<\/p>\n<\/li>\n<li>\n<p>\u975e\u5e38\u9002\u5408\u5bc6\u96c6\u56fe\u5f62\u3002<\/p>\n<\/li>\n<\/ul>\n<p><strong>\u7f3a\u70b9<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5927\u578b\u7a00\u758f\u56fe\u7684\u5185\u5b58\u5bc6\u96c6\u578b\u3002<\/li>\n<\/ul>\n<h3> \u4ee3\u7801\u793a\u4f8b\uff1a <\/h3>\n<pre>int[][] adjmatrix = new int[n][n]; \/\/ n is the number of vertices\n\/\/ add an edge between vertex 1 and 2\nadjmatrix[1][2] = 1;\n\n<\/pre>\n<p> \u767b\u5f55\u540e\u590d\u5236 <\/p>\n<h3> 3.2. <strong>\u90bb\u63a5\u5217\u8868<\/strong> <\/h3>\n<p>\u4e00\u4e2a\u6570\u7ec4\u6216\u5217\u8868\uff0c\u5176\u4e2d\u6bcf\u4e2a\u7d22\u5f15 iii \u4fdd\u5b58\u8fde\u63a5\u5230\u9876\u70b9 iii \u7684\u8282\u70b9\u5217\u8868\u3002\u975e\u5e38\u9002\u5408\u7a00\u758f\u56fe\u3002<\/p>\n<p><strong>\u4f18\u70b9<\/strong>\uff1a<\/p>\n<ul>\n<li>\u8282\u7701\u7a7a\u95f4\u3002<\/li>\n<li>\u6613\u4e8e\u8fed\u4ee3\u90bb\u5c45\u3002<\/li>\n<\/ul>\n<p><strong>\u7f3a\u70b9<\/strong>\uff1a<\/p>\n<ul>\n<li>\n<p>\u67e5\u627e\u8fb9\u662f\u5426\u5b58\u5728\u9700\u8981 o(n)\u3002<\/p>\n<p>o(n)o(n)<\/p>\n<\/li>\n<\/ul>\n<h3> \u4ee3\u7801\u793a\u4f8b\uff1a <\/h3>\n<pre>list&lt;list&lt;integer&gt;&gt; adjlist = new arraylist&lt;&gt;();\nfor (int i = 0; i &lt; n; i++) {\n    adjlist.add(new arraylist&lt;&gt;());\n}\n\/\/ add an edge between vertex 1 and 2\nadjlist.get(1).add(2);\n\n<\/pre>\n<p> \u767b\u5f55\u540e\u590d\u5236 <\/p>\n<h3> 3.3. <strong>\u8fb9\u7f18\u5217\u8868<\/strong> <\/h3>\n<p>\u6240\u6709\u8fb9\u7684\u7b80\u5355\u5217\u8868\u3002\u6bcf\u6761\u8fb9\u90fd\u8868\u793a\u4e3a\u4e00\u5bf9\uff08\u6216\u52a0\u6743\u56fe\u7684\u4e09\u5143\u7ec4\uff09\u3002<\/p>\n<p><strong>\u4f18\u70b9<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5bf9\u4e8e\u7a00\u758f\u56fe\u6765\u8bf4\u975e\u5e38\u7d27\u51d1\u3002<\/li>\n<\/ul>\n<p><strong>\u7f3a\u70b9<\/strong>\uff1a<\/p>\n<ul>\n<li>\u7f13\u6162\u7684\u8fb9\u7f18\u5b58\u5728\u68c0\u67e5\u3002<\/li>\n<\/ul>\n<h3> \u4ee3\u7801\u793a\u4f8b\uff1a <\/h3>\n<pre>list&lt;edge&gt; edges = new arraylist&lt;&gt;();\nedges.add(new edge(1, 2, 10)); \/\/ edge from 1 to 2 with weight 10\n\n<\/pre>\n<p> \u767b\u5f55\u540e\u590d\u5236 <\/p>\n<h2> 4.\u56fe\u7684\u76ee\u7684\u548c\u5b9e\u9645\u5e94\u7528 <\/h2>\n<ul>\n<li> <strong>\u793e\u4ea4\u7f51\u7edc<\/strong>\uff1a\u7528\u6237\u662f\u8282\u70b9\uff0c\u53cb\u8c0a\u662f\u8fb9\u3002<\/li>\n<li> <strong>\u7f51\u7edc\u722c\u884c<\/strong>\uff1a\u9875\u9762\u662f\u8282\u70b9\uff0c\u8d85\u94fe\u63a5\u662f\u8fb9\u3002<\/li>\n<li> <strong>\u8def\u7ebf\u7b97\u6cd5<\/strong>\uff1agoogle \u5730\u56fe\uff0c\u6709\u4eba\u77e5\u9053\u5417\uff1f\u4ee5\u57ce\u5e02\u4e3a\u8282\u70b9\uff0c\u9053\u8def\u4e3a\u8fb9\u7f18\u3002<\/li>\n<li> <strong>\u63a8\u8350\u7cfb\u7edf<\/strong>\uff1a\u4ea7\u54c1\u662f\u8282\u70b9\uff1b \u201c\u8d2d\u4e70 x \u7684\u987e\u5ba2\u4e5f\u8d2d\u4e70\u4e86 y\u201d\u5f62\u6210\u8fb9\u3002<\/li>\n<li> <strong>\u7f51\u7edc\u5206\u6790<\/strong>\uff1a\u8bc6\u522b\u96c6\u7fa4\u3001\u5bfb\u627e\u5f71\u54cd\u8005\u7b49<\/li>\n<\/ul>\n<h2> 5.\u56fe\u7b97\u6cd5 <\/h2>\n<h3> 5.1. <strong>\u56fe\u904d\u5386\u7b97\u6cd5<\/strong> <\/h3>\n<ul>\n<li>\n<p><strong>\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22 (bfs)<\/strong>:<\/p>\n<ul>\n<li>\u5c42\u5e8f\u904d\u5386\u3002<\/li>\n<li>\u975e\u5e38\u9002\u5408\u5728\u672a\u52a0\u6743\u56fe\u4e2d\u67e5\u627e\u6700\u77ed\u8def\u5f84\u3002<\/li>\n<li>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1ao(v+e)\u3002<\/p>\n<p>o(v+e)o(v + e)<\/p>\n<\/li>\n<\/ul>\n<pre>void bfs(int start) {\n    queue&lt;integer&gt; queue = new linkedlist();\n    boolean[] visited = new boolean[n]; \/\/ n = number of vertices\n    queue.add(start);\n    visited[start] = true;\n\n    while (!queue.isempty()) {\n        int node = queue.poll();\n        system.out.println(node);\n\n        for (int neighbor : adjlist.get(node)) {\n            if (!visited[neighbor]) {\n                queue.add(neighbor);\n                visited[neighbor] = true;\n            }\n        }\n    }\n}\n\n&lt;\/integer&gt;<\/pre>\n<p> \u767b\u5f55\u540e\u590d\u5236 <\/li>\n<li>\n<p><strong>\u6df1\u5ea6\u4f18\u5148\u641c\u7d22 (dfs)<\/strong>:<\/p>\n<ul>\n<li>\u5728\u56de\u6eaf\u4e4b\u524d\u5c3d\u53ef\u80fd\u6df1\u5165\u3002<\/li>\n<li>\u5bf9\u4e8e\u5bfb\u8def\u548c\u5faa\u73af\u68c0\u6d4b\u5f88\u6709\u7528\u3002<\/li>\n<li>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1ao(v+e)\u3002<\/p>\n<p>o(v+e)o(v + e)<\/p>\n<\/li>\n<\/ul>\n<pre>void dfs(int node, boolean[] visited) {\n    if (visited[node]) return;\n\n    visited[node] = true;\n    System.out.println(node);\n\n    for (int neighbor : adjList.get(node)) {\n        if (!visited[neighbor]) {\n            dfs(neighbor, visited);\n        }\n    }\n}\n\n<\/pre>\n<p> \u767b\u5f55\u540e\u590d\u5236 <\/li>\n<\/ul>\n<h3> 5.2. <strong>\u6700\u77ed\u8def\u5f84\u7b97\u6cd5<\/strong> <\/h3>\n<ul>\n<li> <strong>dijkstra \u7b97\u6cd5<\/strong>\uff1a\u9002\u7528\u4e8e\u5177\u6709\u975e\u8d1f\u6743\u91cd\u7684\u56fe\u8868\u3002<\/li>\n<li> <strong>\u8d1d\u5c14\u66fc-\u798f\u7279\u7b97\u6cd5<\/strong>\uff1a\u53ef\u4ee5\u5904\u7406\u8d1f\u6743\u91cd\uff0c\u4f46\u6bd4 dijkstra \u6162\u3002<\/li>\n<li> <strong>floyd-warshall \u7b97\u6cd5<\/strong>\uff1a\u67e5\u627e\u6240\u6709\u8282\u70b9\u5bf9\u4e4b\u95f4\u7684\u6700\u77ed\u8def\u5f84\uff1b\u5bf9\u4e8e\u5bc6\u96c6\u56fe\u5f88\u6709\u7528\u3002<\/li>\n<\/ul>\n<h3> 5.3. <strong>\u6700\u5c0f\u751f\u6210\u6811 (mst)<\/strong> <\/h3>\n<ul>\n<li> <strong>kruskal \u7b97\u6cd5<\/strong>\uff1a\u4f7f\u7528 union-find \u8fdb\u884c\u5faa\u73af\u68c0\u6d4b\u7684\u8d2a\u5fc3\u7b97\u6cd5\u3002<\/li>\n<li> <strong>prim \u7b97\u6cd5<\/strong>\uff1a\u901a\u8fc7\u6dfb\u52a0\u751f\u957f\u6811\u4e2d\u6700\u4fbf\u5b9c\u7684\u8fb9\u6765\u6784\u5efa mst\u3002<\/li>\n<\/ul>\n<h3> 5.4. <strong>\u62d3\u6251\u6392\u5e8f<\/strong> <\/h3>\n<ul>\n<li>\u7528\u4e8e\u6709\u5411\u65e0\u73af\u56fe\uff08dag\uff09\u3002\u975e\u5e38\u9002\u5408\u4f5c\u4e1a\u8c03\u5ea6\u7b49\u4f9d\u8d56\u5173\u7cfb\u89e3\u51b3\u3002<\/li>\n<\/ul>\n<h3> 5.5. <strong>\u68c0\u6d4b\u5468\u671f<\/strong> <\/h3>\n<ul>\n<li> <strong>\u57fa\u4e8e dfs \u7684\u65b9\u6cd5<\/strong>\uff1a\u8ddf\u8e2a\u5f53\u524d dfs \u5806\u6808\u4e2d\u7684\u8282\u70b9\u3002<\/li>\n<li> <strong>\u5e76\u67e5\u6cd5<\/strong>\uff1a\u6709\u6548\u7528\u4e8e\u65e0\u5411\u56fe\u3002<\/li>\n<\/ul>\n<h2> 6. \u56fe\u95ee\u9898\u7684\u6280\u672f\u548c\u6280\u5de7 <\/h2>\n<h3> 6.1. <strong>\u591a\u6e90 bfs<\/strong> <\/h3>\n<p>\u975e\u5e38\u9002\u5408\u50cf\u201c\u5230\u7279\u5b9a\u7c7b\u578b\u8282\u70b9\u7684\u6700\u77ed\u8ddd\u79bb\u201d\u8fd9\u6837\u6709\u591a\u4e2a\u8d77\u70b9\u7684\u95ee\u9898\u3002<\/p>\n<h3> 6.2. <strong>\u5e76\u67e5\uff08\u4e0d\u76f8\u4ea4\u96c6\uff09<\/strong> <\/h3>\n<p>\u5bf9\u4e8e\u5904\u7406\u65e0\u5411\u56fe\u4e2d\u7684\u8fde\u901a\u5206\u91cf\u548c\u5faa\u73af\u68c0\u6d4b\u529f\u80fd\u5f3a\u5927\u3002<\/p>\n<h3> 6.3. <strong>\u56fe\u4e0a\u7684\u8bb0\u5fc6\u5316\u548c dp<\/strong> <\/h3>\n<p>\u52a8\u6001\u89c4\u5212\u53ef\u4ee5\u4e0e\u56fe\u904d\u5386\u76f8\u7ed3\u5408\uff0c\u4f18\u5316\u91cd\u590d\u5b50\u95ee\u9898\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n<h3> 6.4. <em>\u57fa\u4e8e\u542f\u53d1\u5f0f\u7684\u641c\u7d22\uff08\u4e00\u79cd\u7b97\u6cd5\uff09<\/em> <\/h3>\n<p>\u7528\u4e8e\u901a\u8fc7\u77e5\u60c5\u731c\u6d4b\uff08\u542f\u53d1\u5f0f\uff09\u8fdb\u884c\u5bfb\u8def\u3002\u4e0e dijkstra \u7c7b\u4f3c\uff0c\u4f46\u4f18\u5148\u8003\u8651\u9760\u8fd1\u76ee\u7684\u5730\u7684\u8def\u5f84\u3002<\/p>\n<h2> 7. \u5982\u4f55\u8bc6\u522b\u56fe\u95ee\u9898 <\/h2>\n<h3> \u5173\u952e\u6307\u6807\uff1a <\/h3>\n<ul>\n<li> <strong>\u7c7b\u7f51\u7edc\u7ed3\u6784<\/strong>\uff1a\u5b9e\u4f53\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/li>\n<li> <strong>\u5bfb\u8def<\/strong>\uff1a\u201c\u627e\u5230\u4ecex\u5230y\u7684\u6700\u77ed\u8def\u7ebf\u3002\u201d<\/li>\n<li> <strong>\u8fde\u63a5\u7684\u7ec4\u4ef6<\/strong>\uff1a\u201c\u8ba1\u7b97\u5b64\u7acb\u7684\u7ec4\u3002\u201d<\/li>\n<li> <strong>\u4f9d\u8d56\u94fe<\/strong>\uff1a\u201c\u4f9d\u8d56\u4e8e\u5176\u4ed6\u4efb\u52a1\u7684\u4efb\u52a1\u3002\u201d<\/li>\n<li> <strong>\u904d\u5386\u573a\u666f<\/strong>\uff1a\u201c\u8bbf\u95ee\u6240\u6709\u623f\u95f4\u201d\u6216\u201c\u63a2\u7d22\u6240\u6709\u9009\u9879\u3002\u201d<\/li>\n<\/ul>\n<h2> 8. \u5fae\u7b11\u7ed3\u675f <\/h2>\n<p>\u5982\u679c\u60a8\u5df2\u7ecf\u5b8c\u6210\u4e86\u8fd9\u4e00\u6b65\uff0c\u90a3\u4e48\u606d\u559c\u60a8\uff01\u60a8\u4e0d\u4ec5\u5728\u56fe\u8868\u7684\u75af\u72c2\u4e4b\u65c5\u4e2d\u5e78\u5b58\u4e0b\u6765\uff0c\u800c\u4e14\u8fd8\u4e3a\u81ea\u5df1\u914d\u5907\u4e86\u89e3\u51b3\u9047\u5230\u7684\u4efb\u4f55\u4e0e\u56fe\u8868\u76f8\u5173\u7684\u95ee\u9898\u7684\u77e5\u8bc6\u3002\u65e0\u8bba\u60a8\u662f\u7f16\u7801\u7ade\u8d5b\u8ff7\u3001\u7b97\u6cd5\u7231\u597d\u8005\uff0c\u8fd8\u662f\u53ea\u662f\u60f3\u901a\u8fc7\u6570\u636e\u7ed3\u6784\u8bfe\u7a0b\u7684\u4eba\uff0c\u672c\u6307\u5357\u90fd\u6db5\u76d6\u4e86\u60a8\u6240\u9700\u7684\u4e00\u5207\u3002<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u5728\u56fe\u8868\u7684\u4e16\u754c\u4e2d\uff0c\u5982\u679c\u60a8\u8ff7\u8def\u4e86\uff0c\u53ea\u9700\u8fd4\u56de\u672c\u6307\u5357\u5373\u53ef\uff01<\/p>\n<p>\u4ee5\u4e0a\u5c31\u662fJava \u56fe\u5f62\u7ec8\u6781\u6307\u5357\uff1a\u9002\u5408\u5404\u4e2a\u7ea7\u522b\u5f00\u53d1\u4eba\u5458\u7684\u6df1\u5165\u7814\u7a76\u7684\u8be6\u7ec6\u5185\u5bb9\uff0c\u66f4\u591a\u8bf7\u5173\u6ce8IDCBABY\u5176\u5b83\u76f8\u5173\u6587\u7ae0\uff01<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6b22\u8fce\u6765\u5230\u5168\u9762\u7684\u56fe\u8868\u4e16\u754c\uff01\u5982\u679c\u60a8\u662f\u4e00\u540d\u5f00\u53d1\u4eba\u5458\uff0c\u5e76\u4e14\u672f\u8bed\u201c\u56fe\u8868\u201d\u53ea\u4f1a\u8ba9\u4eba\u60f3\u8d77\u997c\u56fe\u548c\u6761\u5f62\u56fe\u7684\u56fe\u50cf\uff0c\u90a3\u4e48\u8bf7\u51c6\u5907\u597d\u6269\u5c55\u60a8\u7684\u89c6\u91ce\u3002\u4ece\u6570\u636e\u7ed3\u6784\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u56fe\u662f\u8bb8\u591a\u590d\u6742\u7684\u8ba1\u7b97\u673a\u79d1\u5b66\u95ee\u9898\u548c\u73b0\u5b9e\u4e16\u754c\u5e94\u7528\u80cc\u540e\u7684\u65e0\u540d\u82f1\u96c4\u3002\u4ece\u548c\u63a8\u8350\u5f15\u64ce\u5230\u5bfb\u627e\u4ece a \u70b9\u5230 b \u70b9\u7684\u6700\u77ed\u8def\u5f84\uff0c\u56fe\u8868\u53ef\u4ee5\u505a\u5230\u8fd9\u4e00\u5207\u3002\u672c\u6307\u5357\u5c06\u6db5\u76d6\u4ece\u57fa\u7840\u77e5\u8bc6\u5230\u9ad8\u7ea7\u56fe\u5f62\u7b97\u6cd5\u7684\u6240\u6709\u5185\u5bb9\u3002\u7cfb\u597d\u5b89\u5168\u5e26\uff1b\u8fd9\u5c06\u662f\u4e00\u6b21\u5145\u6ee1\u77e5\u8bc6\u3001\u5e7d\u9ed8\u548c\u4ee3\u7801\u7247\u6bb5\u7684\u75af\u72c2\u4e4b\u65c5\uff0c\u8ba9\u60a8\u6210\u4e3a java \u56fe\u5f62\u5927\u5e08\uff01 1. \u5230\u5e95\u4ec0\u4e48\u662f\u56fe\uff1f \u5176\u6838\u5fc3\uff0c\u56fe\u662f\u7531\u8fb9\u8fde\u63a5\u7684\u8282\u70b9\uff08\u9876\u70b9\uff09\u7684\u96c6\u5408\u3002\u4e0e\u53ef\u80fd\u662f\u7ebf\u6027\u7684\u5e73\u5747\u6570\u636e\u7ed3\u6784\uff08\u5982\u6570\u7ec4\u6216\u94fe\u8868\uff09\u4e0d\u540c\uff0c\u56fe\u8868\u5141\u8bb8\u66f4\u590d\u6742\u7684\u5173\u7cfb\u3002 \u6b63\u5f0f\u5b9a\u4e49\uff1a \u56fe ggg \u5b9a\u4e49\u4e3a g=(v,e)g = (v, e)g=(v,e) \u5176\u4e2d\uff1a vvv \u662f\u4e00\u7ec4\u9876\u70b9\uff08\u8282\u70b9\uff09\u3002 eee \u662f\u4e00\u7ec4\u8fde\u63a5\u9876\u70b9\u5bf9\u7684\u8fb9\u3002 \u4f8b\u5b50\uff1a \u8003\u8651\u4e00\u4e2a\u4ee3\u8868\u53cb\u8c0a\u7684\u7b80\u5355\u56fe\u8868\uff1a \u7acb\u5373\u5b66\u4e60\u201c\u201d\uff1b \u8282\u70b9\uff1aalice\u3001bob\u3001charlie \u8fb9\u7f18\uff1a\u7231\u4e3d\u4e1d-\u9c8d\u52c3\uff0c\u9c8d\u52c3-\u67e5\u7406 \u7b26\u53f7\u5e7d\u9ed8\uff1a \u56fe\u53ef\u4ee5\u662f\u6709\u5411\u56fe\u6216\u65e0\u5411\u56fe\u3002\u5728\u6709\u5411\u56fe\u4e2d\uff0c\u5982\u679c\u7231\u4e3d\u4e1d\u6307\u5411\u9c8d\u52c3\uff0c\u8bf7\u60f3\u8c61\u7231\u4e3d\u4e1d\u8bf4\uff1a\u201c\u563f\u9c8d\u52c3\uff0c\u6211\u5173\u6ce8\u4f60\uff0c\u4f46\u4f60\u4e0d\u5173\u6ce8\u6211\u3002\u201d 2. \u56fe\u7684\u7c7b\u578b 2.1. \u65e0\u5411\u56fe\u4e0e\u6709\u5411\u56fe \u65e0\u5411\u56fe\uff1a\u8282\u70b9\u4e4b\u95f4\u7684\u5173\u7cfb\u662f\u53cc\u5411\u7684\u3002\u5982\u679c a \u548c b \u4e4b\u95f4\u6709\u8fb9\uff0c\u60a8\u53ef\u4ee5\u4ece a \u5230 b\uff0c\u518d\u4ece b \u5230 a\u3002 \u6709\u5411\u56fe\uff08digraph\uff09\uff1a\u8fb9\u6709\u65b9\u5411\u3002\u5982\u679c\u4ece a \u5230 b \u6709\u4e00\u6761\u8fb9\uff0c\u4f60\u53ef\u4ee5\u4ece a \u5230 b\uff0c\u4f46\u4e0d\u4e00\u5b9a\u80fd\u8fd4\u56de\u3002 2.2. \u52a0\u6743\u4e0e\u672a\u52a0\u6743\u56fe\u8868 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-65165","post","type-post","status-publish","format-standard","hentry","category-16"],"_links":{"self":[{"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/posts\/65165","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/comments?post=65165"}],"version-history":[{"count":0,"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/posts\/65165\/revisions"}],"wp:attachment":[{"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/media?parent=65165"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/categories?post=65165"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/tags?post=65165"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}