DFS(剪枝条件下的)TSP问题

lwming1227

于 2022-02-05 12:04:21 发布

阅读量403

点赞数

文章标签：深度优先剪枝图论

本文链接：https://blog.youkuaiyun.com/ab459548764/article/details/122789250

版权

该博客介绍了如何使用深度优先搜索（DFS）策略解决带有剪枝条件的旅行商问题（TSP）。通过输入节点数和边数，程序构建邻接矩阵并初始化，接着利用DFS进行遍历，同时检查路径总距离以实现剪枝，以找到最短路径。最终，程序输出最短路径的总距离和路径本身。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

DFS(剪枝条件下的)TSP问题


#include <iostream>
#include <vector>
using namespace std;

const int INF = 100000;
int graph[100][100];
int visited[100];
int node;
int edge;
int path_distance = INF;
vector<int> path;

int get_forward_loop_sum(vector<int> path)
{
    int sum = 0;
    for(int i = 0;i < path.size() - 1;i++){
        sum += graph[path[i]][path[i+1]];
    }
    return sum;
}

int get_backward_loop_sum(vector<int> path)
{
    int start = path[0];
    int end = path[path.size()-1];
    return graph[start][end];
}

void print(vector<int> array)
{
    for(int i = 0;i < array.size();i++){
        cout << array[i] << " ";
    }
    cout << endl;
}

void dfs(vector<int> x_path, int pre)
{
    if(x_path.size() == node){
        int x_distance = 0;
        x_distance += get_forward_loop_sum(x_path);
        x_distance += get_backward_loop_sum(x_path);
        path_distance = min(path_distance, x_distance);
        path = x_path;
        return;
    }
    else if(get_forward_loop_sum(x_path) < path_distance){
        for(int i = 0;i < node;i++){
            if(visited[i] == 0 and graph[pre][i] < INF){
                visited[i] = 1;
                x_path.push_back(i);
                dfs(x_path, i);
                x_path.pop_back();
                visited[i] = 0;
            }
        }
    }
}

void init()
{
    for(int i = 0;i < node;i++){
        for(int j = 0;j < node;j++){
            graph[i][j] = INF;
        }
    }
}

int main()
{
    cin >> node >> edge;
    init();

    for(int i = 0;i < edge; i++){
        int p_x, p_y, p_dis;
        cin >> p_x >> p_y >> p_dis;
        graph[p_x][p_y] = p_dis;
        graph[p_y][p_x] = p_dis;
    }

    vector<int> x_path;
    visited[0] = 1;
    x_path.push_back(0);
    dfs(x_path, 0);

    system("pause");
    return 0;
}

/*
5 9
0 1 3
0 3 8
0 4 9
1 2 3
1 3 10
1 4 5
2 3 4
2 4 3
3 4 20
*/