{"id":2013,"date":"2021-09-06T18:58:27","date_gmt":"2021-09-06T10:58:27","guid":{"rendered":"http:\/\/47.101.202.111\/?p=2013"},"modified":"2023-04-07T12:56:39","modified_gmt":"2023-04-07T04:56:39","slug":"pat-advanced-graph","status":"publish","type":"post","link":"http:\/\/139.196.114.170\/?p=2013","title":{"rendered":"PAT – ADVANCED – \u56fe\u7b97\u6cd5\u7cbe\u8bb2"},"content":{"rendered":"

\u672c\u6587\u4e3b\u8981\u8bb2\u89e3\u56fe\u7684\u8868\u793a\u4e0e\u7ecf\u5178\u7b97\u6cd5\u5728PAT\u89e3\u9898\u4e2d\u7684\u7b97\u6cd5\u9009\u578b\u3001\u5e94\u7528\u601d\u8def<\/p>\n

<\/p>\n

\u8054\u901a\u5206\u91cf\u95ee\u9898<\/h2>\n

A1013 \u8fde\u901a\u5206\u91cf\u8ba1\u6570<\/h3>\n

\u6570\u636e\u7ed3\u6784\uff1a\u7531\u4e8e\u4ec5\u6d89\u53ca\u8282\u70b9\u7f16\u53f7\uff0c\u65e0\u5176\u4ed6\u4fe1\u606f\uff0c\u65e0\u5411\u56fe\u7684\u90bb\u63a5\u8868\u793a\u7528vector\u6570\u7ec4\u3002
\n\u9898\u610f\u89e3\u6790\uff1a\u654c\u4eba\u5360\u9886\u4e00\u4e2a\u57ce\u5e02\u540e\uff0c\u8be5\u57ce\u5e02\u4e0e\u5176\u4ed6\u57ce\u5e02\u7684\u9053\u8def\u5747\u5c01\u95ed\uff0c\u6b64\u65f6\u81f3\u5c11\u5efa\u51e0\u6761\u8def\u624d\u80fd\u4fdd\u8bc1\u9664\u8be5\u57ce\u5e02\u7684\u6240\u6709\u57ce\u5e02\u4fdd\u6301\u8054\u901a\u3002\u56fe\u4e2d\u5220\u53bb\u8282\u70b9\u53ca\u90bb\u8def\u540e\uff0c\u6700\u5c11\u7684\u5efa\u8def\u65b9\u6848\u662f\u5728\u5269\u4f59\u7684n\u4e2a\u8fde\u901a\u5206\u91cf\u4e4b\u95f4\u5efan-1\u6761\u8def<\/strong>\uff0c\u53ef\u4ee5\u7528DFS\u6216\u5e76\u67e5\u96c6\u7edf\u8ba1\u8fde\u901a\u5206\u91cf\u4e2a\u6570\uff0c\u4e0d\u8fc7\u5e76\u67e5\u96c6\u4ee3\u7801\u91cf\u7565\u5927\u4e00\u4e9b<\/p>\n

\n

\u4e40(\u02c9\u03b5\u02c9\u4e40)<\/strong> Q\uff1a\u57ce\u5e02\u9053\u8def\u5c01\u95ed\u662f\u600e\u4e48\u8003\u8651\u7684\u5462\uff1f<\/p>\n

(\u033f\u2580\u033f\u2009\u033f\u0139\u032f\u033f\u033f\u2580\u033f \u033f)<\/strong> A\uff1a\u6309\u7406\u6765\u8bf4\u5e94\u8be5\u5728\u56fe\u4e2d\u5220\u9664\u8be5\u8282\u70b9\u53ca\u6240\u6709\u90bb\u8fb9\u518d\u53bb\u7edf\u8ba1\u8fde\u901a\u5206\u91cf\uff0c\u4f46\u662f\u4fee\u6539\u4e86\u56fe\u7ed3\u6784\u3002\u4e0d\u5220\u9664\u7684\u65b9\u6cd5\u662f\u7edf\u8ba1\u8fde\u901a\u5206\u91cf\u65f6\u4e0d\u7edf\u8ba1\u8fd9\u4e2a\u8282\u70b9\uff0c\u4e14DFS\u8fc7\u7a0b\u4e2d\u65e0\u8bba\u54ea\u4e2a\u8282\u70b9\u5230\u8fbe\u8fd9\u4e2a\u8282\u70b9\u90fd\u8fd4\u56de\uff0c\u5373\u6ca1\u6709\u8fd9\u6761\u90bb\u8fb9\uff0c\u76f8\u5f53\u4e8e\u89c6\u5176\u4e0d\u5b58\u5728<\/p>\n

*=\u035f\u035f\u035e\u035e(\ua4aa\u2313\ua4aa<\/em>)** Q\uff1a\u6211\u60f3\u7684\u662f\u65b0\u4fee\u8def\u6570=\u88ab\u5360\u8282\u70b9\u7684\u76f8\u90bb\u8282\u70b9\u6570-\u76f8\u90bb\u8282\u70b9\u4e4b\u95f4\u7684\u8fde\u901a\u4e2a\u6570\u3002\u800c\u4e14\u89c9\u5f97\u53ea\u770b\u8fd9K\u4e2a\u8282\u70b9\u5c31OK\uff0c\u6ca1\u5fc5\u8981\u7ba1\u5168\u56fe\u3002\u6655\u6655\u7684~<\/p>\n

(\u0e07 \u02d9o\u02d9)\u0e27<\/strong> A\uff1a\u4f60\u8fd9\u4e2a\u4ec5\u9002\u7528\u4e8e\u8fd9K\u4e2a\u8282\u70b9\u5c31\u662f\u5168\u56fe\u7684\u60c5\u51b5\uff0c\u7406\u7531\u5982\u4e0b\uff1a\u5982\u679c\u53bb\u6389K\u56fe\u4e2d\u7684\u8282\u70b9\u5f97\u5230\u56feK’\u4ecd\u7136\u8054\u901a\uff0c\u8fd9\u6837\u770b\u6765\u5c31\u4e0d\u9700\u8981\u5efa\u8def\u4e86\uff0c\u4f46\u662f\u4f60\u6709\u6ca1\u6709\u60f3\u8fc7\uff0c\u603b\u4f53N\u9664\u53bbK\u7684\u5b50\u56fe\u672c\u8eab\u4e5f\u53ef\u80fd\u662f\u4e0d\u8fde\u901a\u7684\u5462\uff1f\u5b50\u56fe\u7684\u4e0d\u8fde\u901a\u5206\u91cf\u4e5f\u8981\u5efa\u7684\u5440\u4eb2~\u6240\u4ee5\u6bcf\u68c0\u67e5\u4e00\u4e2a\u8282\u70b9\u90fd\u8981\u91cd\u65b0\u8ba1\u7b97\u5168\u56fe\u7684\u8fde\u901a\u5206\u91cf\u4e2a\u6570\u3002\u5176\u6b21\u68c0\u6d4b\u8fde\u63a5\u6027\u7528\u5e76\u67e5\u96c6\u5427\uff0c\u4e24\u4e24\u68c0\u6d4bM\u4e2a\u76f8\u90bb\u8282\u70b9\u4e4b\u95f4\u7684\u8fde\u63a5\u6027\u8981 $\\scriptsize O(M^2)$\uff0c\u5982\u679c\u7528DFS\u592a\u6162\u4e86\u3002\u54e6\u5bf9\u4e86\uff0c\u6ce8\u610f\u4e00\u4e0b\u8fd9\u9053\u9898\u76ee\u7684\u8282\u70b9\u9ed8\u8ba4\u6807\u53f7\u662f1-N\uff0c\u4e0d\u8981\u641e\u9519<\/p>\n

(\u2449\uff65\u0306-\uff65\u0306\u2449)<\/strong> Q\uff1a\u600e\u4e48\u6c42\u8fde\u901a\u5206\u91cf\u4e2a\u6570\uff1f<\/p>\n

\u2727*\u3002\u0669(\u02ca\u03c9\u02cb)\u0648\u2727\\<\/em>\u3002<\/strong> A\uff1a\u6bcf\u6b21DFS\u90fd\u8bbf\u95ee\u4e00\u6574\u4e2a\u8054\u901a\u5206\u91cf\uff0c\u8fd9\u6837\u904d\u5386\u56fe\u4e2d\u6bcf\u4e2a\u8282\u70b9\uff0c\u4f9d\u6b21\u68c0\u67e5\u56fe\u7684\u6bcf\u4e00\u4e2a\u8fde\u901a\u5206\u91cf\u8ba1\u6570\u5373\u53ef\u3002\u8bbf\u95ee\u8fc7\u7684\u8282\u70b9\u90fd\u662f\u5df2\u77e5\u8fde\u901a\u5206\u91cf\u4e2d\u7684\uff0c\u672a\u8bbf\u95ee\u7684\u8282\u70b9\u8fdb\u884cDFS\u6807\u8bb0\u5c31\u662f\u5c06\u8981\u6807\u8bb0\u7684\u4e00\u4e2a\u65b0\u7684\u8fde\u901a\u5206\u91cf<\/p>\n

\n
#include <iostream>\n#include <vector>\n#include <bits\/stdc++.h>\nusing namespace std;\n\nconst int maxn = 1001;\nvector<int> g[maxn];\nbool isVisited[maxn];\nint cur;\n\nvoid DFS(int s) {\n    if (s == cur) return;\n    isVisited[s] = true;\n    for (int &x : g[s])\n        if (!isVisited[x])\n            DFS(x);\n}\n\nint main() {\n    int N, M, K;\n    int s, t, cnt;\n    scanf("%d %d %d", &N, &M, &K);\n    for (int i = 0; i < M; i++) {\n        scanf("%d %d", &s, &t);\n        g[s].push_back(t);\n        g[t].push_back(s);\n    }\n\n    for (int i = 0; i < K; i++) {\n        cnt = 0;\n        scanf("%d", &cur);\n        memset(isVisited, 0, sizeof(isVisited));\n        for (int i = 1; i <= N; i++) {\n            if (!isVisited[i] && i != cur) {\n                DFS(i);\n                cnt++;\n            }\n        }\n        printf("%d\\n", cnt - 1);\n    }\n\n    return 0;\n}<\/code><\/pre>\n
\u6700\u77ed\u8def\u5f84\u95ee\u9898<\/h2>\n
\u6700\u77ed\u8def\u5f84\u95ee\u9898\u7684\u7406\u8bba\u8bb2\u89e3\u8be6\u89c1 \u2708\u6700\u77ed\u8def\u5f84\u7ecf\u5178\u7b97\u6cd5<\/a><\/p>\n
A1003 \u6700\u77ed\u8def\u5f84\u8ba1\u6570\u3001\u53cc\u5c3a\u5ea6\u70b9\u6743\u6700\u4f18<\/h3>\n
\u5806\u4f18\u5316\u7684Dijkstra<\/h4>\n
\u7b97\u6cd5\u9009\u578b\uff1a\u8282\u70b9\u4e2a\u6570\u591a\u4e8e200\uff0c\u6392\u9664 $\\scriptsize O(n^3)$ \u7684Floyd\u3002\u8def\u5f84\u957f\u5ea6\u65e0\u8d1f\u6743\u503c\uff0c\u4f18\u9009\u961f\u5217\u4f18\u5316\u7684Dijkstra\uff0c\u91c7\u7528\u94fe\u5f0f\u524d\u5411\u661f\u5b9e\u73b0<\/p>\n
\u601d\u8def\u89e3\u6790\uff1a\u9898\u610f\u4e3a\u4e09\u4e2a\u76ee\u6807\uff1a
\n\u2460\u5bfb\u627e\u6700\u77ed\u8def\u5f84\uff1aDijkstra\u7b56\u7565\u4ece\u6e90\u8282\u70b9s\u9010\u6b65\u677e\u5f1b\u5404\u8fb9\u5373\u53ef
\n\u2461\u8bb0\u5f55\u6700\u77ed\u8def\u5f84\u6761\u6570\uff1arNum\u8bb0\u5f55\u6e90\u8282\u70b9\u5230\u5f53\u524d\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u6761\u6570\u3002\u4ece\u6e90\u8282\u70b9\u51fa\u53d1\u8bb0\u6761\u6570\u4e3a1\u5f00\u59cb\u6269\u6563\u3002
\n\u6bcf\u6b21\u6267\u884c\u677e\u5f1b\u4ee3\u8868\u627e\u5230\u4eces\u2192from\u2192to\u7684\u552f\u4e00\u4e00\u6761\u6700\u77ed\u8def\u5f84<\/strong>\uff0c\u800cs\u2192from\u53ef\u80fd\u6709\u591a\u6761\u76f8\u540c\u957f\u5ea6\u7684\u6700\u77ed\u8def\u5f84\uff0c\u6240\u4ee5s\u2192from\u2192to\u7684\u6700\u77ed\u8def\u5f84\u6570\u5c31\u662fs\u2192from\u7684\u6700\u77ed\u8def\u5f84\u6570\u3002
\ndis[from]+length=dis[to]\u8868\u793a\u627e\u5230s\u2192from\u2192to\u7684\u53e6\u4e00\u6761\u4e0d\u540c\u7684\u6700\u77ed\u8def\u5f84<\/strong>\uff0c\u6b64\u65f6\u5728\u539f\u6709\u57fa\u7840\u4e0a\u53c8\u591a\u4e86rNum[from]\u6761\u6700\u77ed\u8def\u5f84
\n\u2462\u8bb0\u5f55\u6700\u77ed\u8def\u5f84\u4e2d\u7684\u6700\u5927\u70b9\u6743\u548c\uff1a\u6bcf\u627e\u5230\u4e00\u6761\u6700\u77ed\u8def\u5f84\uff0c\u90fd\u66f4\u65b0\u4e3a\u8be5\u6761\u6700\u77ed\u8def\u5f84\u7684\u70b9\u6743\u548c\uff0c\u6700\u77ed\u8def\u5f84\u957f\u5ea6\u76f8\u540c\u65f6\uff0c\u66f4\u65b0\u4e3a\u66f4\u5c0f\u7684\u70b9\u6743\u548c\uff0c\u66f4\u65b0\u516c\u5f0f\u4e3a $\\scriptsize \\sum \\limits_{i=s}^{to}Wi = \\sum \\limits<\/em>{i=s}^{from}Wi + W<\/em>{to}$<\/p>\n
\n
(\u256f>\u0434<)\u256f<\/strong> Q\uff1a\u94fe\u5f0f\u524d\u5411\u661f\u662f\u4ec0\u4e48\u795e\u79d8\u7684\u6570\u636e\u7ed3\u6784\uff1f<\/p>\n
(:3\u2593\u2592<\/strong> A\uff1a\u94fe\u5f0f\u524d\u5411\u661f\u7531\u4e00\u4e2a\u6570\u7ec4(\u8868\u793a\u8282\u70b9)\u548c\u4e00\u4e2a\u7ed3\u6784\u4f53\u6570\u7ec4(\u8868\u793a\u8fb9)\u548c\u4e00\u4e2a\u8fb9\u5730\u5740\u7d2f\u8ba1\u7d22\u5f15(\u8868\u793a\u65b0\u8fb9\u63d2\u5165\u7ed3\u6784\u4f53\u6570\u7ec4\u7684\u7d22\u5f15)\u7ec4\u6210\u3002\u8282\u70b9\u6570\u7ec4\uff1a\u5bf9\u5e94\u4e0b\u6807\u8868\u793a\u8282\u70b9\u7f16\u53f7\uff0c\u503c\u6307\u5411\u6700\u540e\u4e00\u6b21\u63d2\u5165\u7684\u8fb9\u5730\u5740\u3002\u7ed3\u6784\u4f53\u6570\u7ec4\uff1a\u4fdd\u5b58\u8fb9\u6743\u3001\u8be5\u6761\u6709\u5411\u8fb9\u6307\u5411\u7684\u8282\u70b9\u3001\u540c\u9876\u70b9\u5176\u4ed6\u51fa\u8fb9\u7684\u7d22\u5f15\u3002\u6dfb\u52a0\u7684\u65b0\u8fb9\u4f9d\u6b21\u4fdd\u5b58\u5728\u8fb9\u6570\u7ec4[\u7d22\u5f15]\u3001\u8fb9\u6570\u7ec4[\u7d22\u5f15+1]\u2026\u8fb9\u6570\u7ec4[\u7d22\u5f15+i]\u4e2d\u3002\u6bcf\u63d2\u5165\u4e00\u6761\u65b0\u8fb9\u4f7f\u5176\u6307\u5411\u4e0a\u4e00\u6b21\u63d2\u5165\u7684\u8fb9old\uff0c\u518d\u8ba9\u8be5\u51fa\u8fb9\u7684\u8282\u70b9\u6307\u5411\u65b0\u8fb9new\uff0c\u8fd9\u6837\u5c31\u5b9e\u73b0\u4e86vertex\u2192new\u2192old\uff0c\u4e32\u8d77\u4e86\u8282\u70b9\u51fa\u53d1\u7684\u6240\u6709\u90bb\u8fb9\uff0c\u6240\u4ee5\u672c\u8d28\u4e0a\u662f\u56fe\u7684\u90bb\u63a5\u8868\u8868\u793a<\/strong>\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\u672c\u9898\u662f\u65e0\u5411\u56fe\uff0c\u5efa\u56fe\u7684\u65f6\u5019\u4e00\u5b9a\u8981\u5206\u522b\u6dfb\u52a0\u4e24\u4e2a\u65b9\u5411\u7684\u8fb9\u3002<\/p>\n
(\u02d8\u2022\u03c9\u2022\u02d8)\u0e07<\/strong> Q\uff1a\u4e3a\u4ec0\u4e48\u6211\u7684Dijkstra\u7b97\u6cd5\u6ca1\u5199\u9519\uff0c\u4f46\u662f\u8fd0\u884c\u4e00\u6b21\u5c31\u9000\u51fa\u4e86\uff0c\u6709\u65f6\u5019\u8fd8\u8fd0\u884c\u4e0d\u5bf9\uff1f<\/p>\n
\u207d\u207d\u0b18( \u02ca\u1d55\u02cb )\u0b13\u207e\u207e<\/strong> A\uff1a\u5728\u5efa\u56fe\u540e\u3001\u677e\u5f1b\u64cd\u4f5c\u65f6\u3001\u7b2c\u4e8c\u5c3a\u5ea6\u5224\u65ad\u65f6\u57cb\u6253\u5370\u70b9\uff0c\u62ff\u8f93\u51fa\u7ed3\u679c\u548c\u5b9e\u4f8b\u6bd4\u5bf9\u4e00\u4e0b\uff0c\u65b9\u4fbf\u8c03\u8bd5\u627e\u5230\u95ee\u9898\u3002\u5f88\u53ef\u80fd\u7684\u539f\u56e0\u662f\u8fd0\u884c\u7b97\u6cd5\u524d\u521d\u59cb\u5316\u51fa\u9519\u4e86\u3002\u4e00\u5b9a\u4e0d\u8981\u5fd8\u8bb0\u521d\u59cb\u6761\u4ef6\u4e0b\uff1a\u6e90\u8282\u70b9\u5230\u81ea\u8eab\u8ddd\u79bb0\u3001\u6e90\u8282\u70b9\u51fa\u53d1\u7684\u6700\u77ed\u8def\u5f84\u6761\u65701\u3001\u6e90\u8282\u70b9\u672c\u8eab\u5373\u662f\u6700\u5927\u70b9\u6743\u548c<\/p>\n
\n
#include <iostream>\n#include <queue>\n#include <vector>\n#include <bits\/stdc++.h>\nusing namespace std;\n\nconst int maxV = 500;\nconst int maxE = 1e5;\nconst int inf = 1e6;\nint vertex[maxV], dis[maxV], done[maxV], inq[maxV];\nint tSum[maxV], rNum[maxV], tNum[maxV];\nint p = 0;\n\nstruct e {\n    int next;\n    int to;\n    int w;\n} edge[maxE];\n\nstruct Cmp {\n    bool operator()(int a, int b) {\n        return dis[a] > dis[b];\n    }\n};\n\npriority_queue<int, vector<int>, Cmp> q;\n\nvoid addEdge(int u, int v, int w) {\n    edge[p].to = v;\n    edge[p].w = w;\n    edge[p].next = vertex[u];\n    vertex[u] = p++;\n}\n\nvoid dijkstra(int s) {\n    q.push(s);\n    dis[s] = 0;\n    rNum[s] = 1;\n    tSum[s] = tNum[s];\n    while (!q.empty()) {\n        int v = q.top();\n        q.pop();\n        done[v] = 1;\n        inq[v] = 0;\n\n        for (int i = vertex[v]; ~i; i = edge[i].next) {\n            int w = edge[i].w;\n            int to = edge[i].to;\n            if (done[to]) continue;\n            if (dis[v] + w < dis[to]) {\n                dis[to] = dis[v] + w;\n                tSum[to] = tSum[v] + tNum[to];\n                rNum[to] = rNum[v];\n                if (!inq[to]) {\n                    q.push(to);\n                    inq[to] = 1;\n                }\n            }\n            else if (dis[v] + w == dis[to]) {\n                if (tSum[v] + tNum[to] > tSum[to])\n                    tSum[to] = tSum[v] + tNum[to];\n                rNum[to] += rNum[v];\n            }\n        }\n    }\n}\n\nint main() {\n    int N, M, C1, C2;\n    int u, v, w;\n    scanf("%d %d %d %d", &N, &M, &C1, &C2);\n    for (int i = 0; i < N; i++)\n        scanf("%d", &tNum[i]);\n\n    fill(dis, dis + N, inf);\n    memset(vertex, -1, sizeof(vertex));\n    memset(done, 0, sizeof(done));\n    memset(inq, 0, sizeof(inq));\n    memset(tSum, 0, sizeof(tSum));\n    memset(rNum, 0, sizeof(rNum));\n\n    for (int i = 0; i < M; i++) {\n        scanf("%d %d %d", &u, &v, &w);\n        addEdge(u, v, w);\n        addEdge(v, u, w);\n    }\n\n    dijkstra(C1);\n    printf("%d %d\\n", rNum[C2], tSum[C2]);\n\n    return 0;\n}<\/code><\/pre>\n
Dijkstra+DFS<\/h4>\n
\u6765\u81ea\u6674\u795e\u300a\u7b97\u6cd5\u7b14\u8bb0\u300b\u7684\u89e3\u6cd5<\/p>\n
A1030 \u4fdd\u5b58\u6700\u77ed\u8def\u5f84+\u53cc\u5c3a\u5ea6\u8fb9\u6743<\/h3>\n
\u7b97\u6cd5\u9009\u578b\uff1a\u8282\u70b9\u4e2a\u6570\u591a\u4e8e200\uff0c\u8fb9\u957f\u4e3a\u57ce\u5e02\u8ddd\u79bb\u65e0\u8d1f\u6743\u503c\uff0c\u4f18\u9009\u961f\u5217\u4f18\u5316\u7684Dijkstra\uff0c\u91c7\u7528\u94fe\u5f0f\u524d\u5411\u661f\u5b9e\u73b0<\/p>\n
\u601d\u8def\u89e3\u6790\uff1a\u9898\u610f\u4e3a\u4e24\u4e2a\u76ee\u6807\uff1a
\n\u2460\u627e\u5230\u6700\u77ed\u8def\u5f84\u4e2d\u4ee3\u4ef7\u6700\u5c0f\u7684\u90a3\u6761\u3002\u53cc\u5c3a\u5ea6\u95ee\u9898\u5728A1003\u4e2d\u8be6\u7ec6\u89e3\u6790\u8fc7\uff0c\u6309\u7b2c\u4e00\u5c3a\u5ea6\u627e\u6700\u77ed\u8def\u5f84\uff0c\u6309\u7b2c\u4e8c\u5c3a\u5ea6\u8bb0\u5f55\u66f4\u65b0\u6700\u77ed\u8def\u5f84\u7684\u4ee3\u4ef7\u6700\u5c0f\u503c\u3002\u672c\u9898\u7684\u7b2c\u4e8c\u5c3a\u5ea6\u4ec5\u4ec5\u662f\u5c06\u70b9\u6743\u4fee\u6539\u4e3a\u8fb9\u6743\u3002
\n\u2461\u8bb0\u5f55\u6700\u77ed\u8def\u5f84\u5e76\u6253\u5370\u3002\u5982\u679cu\u8282\u70b9\u7684\u51fa\u8fb9e\u4f7fu\u2192v\u677e\u5f1b\u8fbe\u5230\u6700\u77ed\u8def\u5f84\uff0c\u5c31\u5728v\u5904\u4fdd\u5b58\u524d\u5411\u7684\u8be5\u8282\u70b9<\/strong>\uff0c\u5982\u679c\u6700\u77ed\u8def\u5f84\u76f8\u540c\uff0c\u5c31\u66f4\u65b0\u4f7f\u7b2c\u4e8c\u5c3a\u5ea6\u66f4\u5c0f\u7684\u524d\u5411\u8282\u70b9u<\/strong>\uff0c\u5982\u6b64\u4ece\u76ee\u6807\u8282\u70b9\u56de\u6eaf\u5230\u6e90\u8282\u70b9\u5373\u53ef\u627e\u5230\u8be5\u6700\u77ed\u8def\u5f84\uff0c\u5012\u5e8f\u6253\u5370\u5373\u53ef\u3002<\/p>\n
\n
\u0669(*\u00b4\u25d2`*)\u06f6<\/strong> Q\uff1apath\u4fdd\u5b58\u7684\u662f\u5012\u5e8f\u7ed3\u679c\uff0c\u90a3\u600e\u4e48\u6b63\u5411\u6253\u5370\u8282\u70b9\u5462\uff1f<\/p>\n
<\uff0dbiubiu\uff0d\u2282(`\u03c9\u00b4\u2229)<\/strong> A\uff1a\u6808\u6216\u8005\u9012\u5f52\u54af\uff01\u9012\u5f52\u5199\u8d77\u6765\u7b80\u5355\uff0c\u6211\u4eec\u5c06\u9012\u5f52\u7f6e\u4e8e\u64cd\u4f5c\u4e4b\u524d\uff0c\u5c31\u80fd\u5b9e\u73b0\u5012\u5e8f\u64cd\u4f5c\u7684\u6548\u679c<\/strong>\u3002\u9012\u5f52\u8fb9\u754c\u662f\u5230\u8fbe\u6e90\u8282\u70b9\uff0c\u6b64\u65f6\u53ef\u4ee5\u7528path[s]=-1\u6765\u5224\u65ad\u3002\u6ce8\u610f\u6211\u4eec\u5224\u65ad\u7684\u662f\u524d\u5e8f\u8282\u70b9\u503cpath[i]\uff0c\u8f93\u51fa\u7684\u662f\u672c\u5c42\u8282\u70b9i<\/p>\n
\n
#include <iostream>\n#include <queue>\n#include <vector>\n#include <bits\/stdc++.h>\nusing namespace std;\n\nconst int maxV = 500;\nconst int maxE = 1e5;\nconst int inf = 1e6;\nint dis[maxV], done[maxV], path[maxV], inq[maxV], cost[maxV];\nint p = 0;\n\nint Vertex[maxV];\nstruct Edge {\n    int next;\n    int to;\n    int w;\n    int c;\n} e[maxE];\n\nvoid addEdge(int from, int to, int w, int c) {\n    e[p].to = to;\n    e[p].w = w;\n    e[p].c = c;\n    e[p].next = Vertex[from];\n    Vertex[from] = p++;\n}\n\nstruct Cmp {\n    bool operator()(int a, int b) {\n        return dis[a] > dis[b];\n    }\n};\n\npriority_queue<int, vector<int>, Cmp> q;\n\nvoid dijkstra(int s) {\n    dis[s] = 0;\n    cost[s] = 0;\n    q.push(s);\n\n    while (!q.empty()) {\n        int from = q.top();\n        q.pop();\n        done[from] = 1;\n        inq[from] = 0;\n        for (int i = Vertex[from]; ~i; i = e[i].next) {\n            int to = e[i].to;\n            int w = e[i].w;\n            int c = e[i].c;\n            if (done[to]) continue;\n            if (dis[from] + w < dis[to]) {\n                dis[to] = dis[from] + w;\n                cost[to] = cost[from] + c;\n                path[to] = from;\n                if (!inq[to]) {\n                    q.push(to);\n                    inq[to] = 1;\n                }\n            }\n            else if (dis[from] + w == dis[to]) {\n                if (cost[from] + c < cost[to]) {\n                    cost[to] = cost[from] + c;\n                    path[to] = from;\n                }\n            }\n        }\n    }\n}\n\nvoid printPath(int d) {\n    int u = path[d];\n    if (~u) {\n        printPath(u);\n        printf(" %d", d);\n    }\n    else {\n        printf("%d", d);\n        return;\n    }\n}\n\nint main() {\n    int N, M, S, D;\n    int C1, C2, w, c;\n    scanf("%d %d %d %d", &N, &M, &S, &D);\n\n    fill(dis, dis + N, inf);\n    memset(Vertex, -1, sizeof(Vertex));\n    memset(path, -1, sizeof(path));\n    memset(done, 0, sizeof(done));\n    memset(cost, 0, sizeof(cost));\n    memset(inq, 0, sizeof(inq));\n\n    while (M--) {\n        scanf("%d %d %d %d", &C1, &C2, &w, &c);\n        addEdge(C1, C2, w, c);\n        addEdge(C2, C1, w, c);\n    }\n\n    dijkstra(S);\n    printPath(D);\n    printf(" %d %d", dis[D], cost[D]);\n    return 0;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u672c\u6587\u4e3b\u8981\u8bb2\u89e3\u56fe\u7684\u8868\u793a\u4e0e\u7ecf\u5178\u7b97\u6cd5\u5728PAT\u89e3\u9898\u4e2d\u7684\u7b97\u6cd5\u9009\u578b\u3001\u5e94\u7528\u601d\u8def<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[12],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/2013"}],"collection":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2013"}],"version-history":[{"count":9,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/2013\/revisions"}],"predecessor-version":[{"id":2737,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/2013\/revisions\/2737"}],"wp:attachment":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2013"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2013"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2013"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}