107 lines
2.5 KiB
C++
107 lines
2.5 KiB
C++
// Copyright (c) 2023 Xi Xu, All rights reserved.
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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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int tsp(); // TSP 算法，计算最短哈密顿回路
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void tsp_backtrack(int k, int *path, int *visited, int &min_path); // 回溯法
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int path_len(int *path, int k); // 计算路径长度
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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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}
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for (size_t i = 0; i < n; i++) {
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adj[i][i] = 0; // 对角线上的元素为0
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for (int j = i + 1; j < n; j++) {
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in >> adj[i][j]; // 读取邻接矩阵
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adj[j][i] = adj[i][j]; // 邻接矩阵是对称矩阵
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}
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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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int Graph::tsp() {
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int *path = new int[n]; // 存储当前的路径
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int *visited = new int[n]; // 存储已经访问过的顶点
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int min_path = INT_MAX; // 存储最短路径长度
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// 初始化
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for (int i = 0; i < n; i++) {
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visited[i] = 0;
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}
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visited[0] = 1;
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path[0] = 0;
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// 回溯
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tsp_backtrack(1, path, visited, min_path);
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// 释放内存
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delete[] path;
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delete[] visited;
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return min_path;
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}
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void Graph::tsp_backtrack(int k, int *path, int *visited, int &min_path) {
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if (k == n) // 所有的顶点都已经遍历完了
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{
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int path_len = 0;
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for (int i = 0; i < n - 1; i++) {
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path_len += adj[path[i]][path[i + 1]];
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}
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path_len += adj[path[n - 1]][0]; // 回到起点
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if (path_len < min_path) {
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min_path = path_len;
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}
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return;
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}
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for (int i = 0; i < n; i++) {
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if (!visited[i]) {
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path[k] = i;
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visited[i] = 1;
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if (path_len(path, k) < min_path) // 剪枝
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{
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tsp_backtrack(k + 1, path, visited, min_path);
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}
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visited[i] = 0;
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}
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}
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}
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int Graph::path_len(int *path, int k) {
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int len = 0;
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for (int i = 0; i < k - 1; i++) {
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len += adj[path[i]][path[i + 1]];
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}
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len += adj[path[k - 1]][0]; // 回到起点
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return len;
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}
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int main() {
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ifstream fin("adj.txt"); // 打开输入文件
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Graph g(fin); // 创建图
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fin.close(); // 关闭输入文件
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cout << g.tsp() << endl; // 计算最短哈密顿回路并输出
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return 0;
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}
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