80 lines
2.0 KiB
C++
80 lines
2.0 KiB
C++
// Copyright (c) 2023 Xi Xu
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// SPDX-License-Identifier: GPL-3.0-or-later
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#include <bits/stdc++.h>
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using namespace std;
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class Graph {
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private:
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int n; // 图的顶点数
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int **adj; // 邻接矩阵
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public:
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Graph(istream &in); // 构造函数，从输入流in中读取邻接矩阵
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~Graph(); // 析构函数，释放邻接矩阵的内存
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void floyd() const; // Floyd算法，计算任意两点之间的最短路径
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};
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Graph::Graph(istream &in) {
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in >> n; // 读取顶点数
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adj = new int *[n]; // 动态分配二维数组
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for (size_t i = 0; i < n; i++) {
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adj[i] = new int[n];
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for (size_t j = 0; j < n; j++)
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in >> adj[i][j]; // 读取邻接矩阵
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}
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}
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Graph::~Graph() {
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for (size_t i = 0; i < n; i++)
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delete[] adj[i]; // 释放每一行的内存
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delete[] adj; // 释放二维数组的内存
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}
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void Graph::floyd() const {
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int dist[n][n]; // 存储任意两点之间的最短距离
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int path[n][n]; // 存储任意两点之间的最短路径
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for (size_t i = 0; i < n; i++)
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for (size_t j = 0; j < n; j++) {
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dist[i][j] = adj[i][j]; // 初始化最短距离
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path[i][j] = j; // 初始化最短路径
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}
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for (size_t k = 0; k < n; k++)
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for (size_t i = 0; i < n; i++)
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for (size_t j = 0; j < n; j++)
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if (dist[i][k] + dist[k][j] < dist[i][j]) // 如果经过k点的路径更短
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{
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dist[i][j] = dist[i][k] + dist[k][j]; // 更新最短距离
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path[i][j] = path[i][k]; // 更新最短路径
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}
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for (size_t i = 0; i < n; i++) {
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cout << "From " << i + 1 << ":" << endl; // 输出起点
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for (size_t j = 0; j < n; j++) {
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if (i == j)
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continue;
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cout << "To " << j + 1 << ": ";
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cout << i + 1 << " "; // 输出起点
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int k = path[i][j];
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while (k != j) // 输出路径上的中间点
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{
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cout << k + 1 << " ";
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k = path[k][j];
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}
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cout << j + 1 << endl; // 输出终点
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}
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cout << endl;
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}
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}
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int main() {
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// 打开输入文件
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ifstream fin("adj.txt");
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// 创建图
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Graph g(fin);
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// 关闭输入文件
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fin.close();
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// 计算任意两点之间的最短路径
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g.floyd();
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return 0;
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} |