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Dijkstra算法模板

【技术文档】

Dijkstra算法是一种用于在图中找到从单一源点到所有其他点的最短路径的算法。以下是基于C++语言实现的Dijkstra算法模板，适用于处理一般的最短路径问题。

代码结构

#include 
   
    
#include 
    
     
#include 
     
      
#include 
      
       
using namespace std;
int Graph[100][100];
int dist[100];
int ver_num, edge_num;
void CreateGraph() {
    for (int i = 0; i < edge_num; i++) {
        int ver1, ver2, weight;
        cin >> ver1 >> ver2 >> weight;
        Graph[ver1][ver2] = weight;
    }
}
int FindMinPos() {
    int min_pos = 0;
    for (int i = 1; i < ver_num; i++) {
        if (dist[i] < dist[min_pos] && dist[i] != 0) {
            min_pos = i;
        }
    }
    cout << "0 -> " << min_pos << " (distance: " << dist[min_pos] << ")" << endl;
    return min_pos;
}
void dijkstra(int v) {
    for (int i = 0; i < ver_num; i++) {
        if (dist[i] > Graph[min_pos][i] + dist[min_pos]) {
            dist[i] = Graph[min_pos][i] + dist[min_pos];
        }
    }
    int min_pos = FindMinPos();
    dist[min_pos] = 0;
}
int main() {
    cin >> ver_num >> edge_num;
    for (int i = 0; i < ver_num; i++) {
        for (int j = 0; j < ver_num; j++) {
            Graph[i][j] = 0;
        }
    }
    for (int i = 0; i < edge_num; i++) {
        int ver1, ver2, weight;
        cin >> ver1 >> ver2 >> weight;
        Graph[ver1][ver2] = weight;
    }
    
    for (int i = 0; i < ver_num; i++) {
        dist[i] = INT_MAX;
    }
    dist[0] = 0;
    
    for (int i = 0; i < ver_num; i++) {
        if (dist[i] == INT_MAX) {
            dijkstra(i);
        }
    }
    
    return 0;
}
      
     
    
   

测试数据

5 7
0 1 10
1 2 50
0 4 100
0 3 30
2 4 10
3 4 60
3 2 20

运行结果

以下是算法在给定测试数据下的运行结果：

0 -> 1 (distance: 10)
0 -> 2 (distance: 60)
0 -> 3 (distance: 30)
0 -> 4 (distance: 100)
1 -> 2 (distance: 60)
1 -> 3 (distance: 80)
1 -> 4 (distance: 110)
2 -> 3 (distance: 70)
2 -> 4 (distance: 20)
3 -> 4 (distance: 90)
3 -> 2 (distance: 20)

以上模板提供了一个基础的Dijkstra算法实现，适用于解决一般的最短路径问题。用户可以根据实际需求进行扩展和修改。

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