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#include <bits/stdc++.h>
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using namespace std;
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// 原始文档：https://www.cnblogs.com/xzxl/p/7246918.html
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#pragma region SPFA算法模板
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// 最短路径——SPFA算法
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// 最大值
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// https://blog.csdn.net/jiange_zh/article/details/50198097
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/**
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如果我们想要将某个数组清零，我们通常会使用memset(a,0,sizeof(a))，方便又高效，但是当我们想将某个数组全部赋值为无穷大时，
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就不能使用memset函数而得自己写循环了，因为memset是按字节操作的，它能够对数组清零是因为0的每个字节都是0（一般我们只有赋值为-1
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和0的时候才使用它）。现在好了，如果我们将无穷大设为0x3f3f3f3f，那么奇迹就发生了，0x3f3f3f3f的每个字节都是0x3f！所以要把一段
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内存全部置为无穷大，我们只需要memset(a,0x3f,sizeof(a))。所以在通常的场合下，0x3f3f3f3f真的是一个非常棒的选择！
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*/
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const int INF = 0x3f3f3f3f;
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// https://www.cnblogs.com/xzxl/p/7246918.html
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int matrix[100][100]; //邻接矩阵
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bool visited[100]; //标记数组
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int dist[100]; //源点到顶点i的最短距离
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int path[100]; //记录最短路的路径
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int enqueue_num[100]; //记录入队次数
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int vertex_num; //顶点数
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int edge_num; //边数
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int source; //源点
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bool SPFA() {
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memset(visited, 0, sizeof(visited));
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memset(enqueue_num, 0, sizeof(enqueue_num));
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for (int i = 1; i <= vertex_num; i++) {
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dist[i] = INF;
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path[i] = source;
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}
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queue<int> Q;
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Q.push(source);
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dist[source] = 0;
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visited[source] = 1;
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enqueue_num[source]++;
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while (!Q.empty()) {
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int u = Q.front();
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Q.pop();
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visited[u] = 0;
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for (int v = 1; v <= vertex_num; v++) {
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if (matrix[u][v] != INF) //u与v直接邻接
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{
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if (dist[u] + matrix[u][v] < dist[v]) {
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dist[v] = dist[u] + matrix[u][v];
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path[v] = u;
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if (!visited[v]) {
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Q.push(v);
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enqueue_num[v]++;
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if (enqueue_num[v] >= vertex_num)
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return false;
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visited[v] = 1;
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}
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}
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}
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}
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}
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return true;
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}
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void Print() {
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for (int i = 1; i <= vertex_num; i++) {
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if (i != source) {
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int p = i;
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stack<int> s;
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cout << "顶点 " << source << " 到顶点 " << p << " 的最短路径是： ";
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while (source != p) //路径顺序是逆向的，所以先保存到栈
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{
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s.push(p);
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p = path[p];
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}
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cout << source;
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while (!s.empty()) //依次从栈中取出的才是正序路径
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{
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cout << "--" << s.top();
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s.pop();
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}
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cout << " 最短路径长度是：" << dist[i] << endl;
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}
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}
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}
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#pragma endregion SPFA算法模板
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int main() {
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//输入+输出重定向
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freopen("../MiniPath/SPFA.txt", "r", stdin);
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cout << "请输入图的顶点数，边数，源点：";
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cin >> vertex_num >> edge_num >> source;
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for (int i = 1; i <= vertex_num; i++)
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for (int j = 1; j <= vertex_num; j++)
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matrix[i][j] = INF; //初始化matrix数组
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cout << "请输入" << edge_num << "条边的信息：\n";
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int u, v, w;
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for (int i = 1; i <= edge_num; i++) {
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cin >> u >> v >> w;
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matrix[u][v] = w;
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}
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if (SPFA())
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Print();
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else
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cout << "对不起，存在负权图，不能使用本算法!" << endl;
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//关闭文件
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fclose(stdin);
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return 0;
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} |
