迪杰斯特拉dijkstra算法的使用

前言：迪杰斯特拉dijkstra算法的作用是求解区域内最优解

def generate_matrix():
    M = 1E100
    matrix = [[0, 12, M, M, M, 16, 14],
              [12, 0, 10, M, M, 7, M],
              [M, 10, 0, 3, 5, 6, M],
              [M, M, 3, 0, 4, M, M],
              [M, M, 5, 4, 0, 2, 8],
              [16, 7, 6, M, 2, 0, 9],
              [14, M, M, M, 8, 9, 0]]
    return matrix

def dijkstra(matrix, source):
    M = 1E100
    n = len(matrix)
    m = len(matrix[0])
    if source >= n or n != m:
        print('Error!')
        return
    found = [source]        # 已找到最短路径的节点
    cost = [M] * n          # source到已找到最短路径的节点的最短距离
    cost[source] = 0
    path = [[]]*n           # source到其他节点的最短路径
    path[source] = [source]
    while len(found) < n:   # 当已找到最短路径的节点小于n时
        min_value = M+1
        col = -1
        row = -1
        for f in found:     # 以已找到最短路径的节点所在行为搜索对象
            for i in [x for x in range(n) if x not in found]:   # 只搜索没找出最短路径的列
                if matrix[f][i] + cost[f] < min_value:  # 找出最小值
                    min_value = matrix[f][i] + cost[f]  # 在某行找到最小值要加上source到该行的最短路径
                    row = f         # 记录所在行列
                    col = i
        if col == -1 or row == -1:  # 若没找出最小值且节点还未找完，说明图中存在不连通的节点
            break
        found.append(col)           # 在found中添加已找到的节点
        cost[col] = min_value       # source到该节点的最短距离即为min_value
        path[col] = path[row][:]    # 复制source到已找到节点的上一节点的路径
        path[col].append(col)       # 再其后添加已找到节点即为sorcer到该节点的最短路径
    return found, cost, path

def main():
    matrix = generate_matrix()
    found, cost, path = dijkstra(matrix, 3)
    print('found:')
    print(found)
    print('cost:')
    print(cost)
    print('path:')
    for p in path:
        print(p)

if __name__ == '__main__':
    main()

#include <stdio.h>
int main()
{
    int e[10][10],dis[10],book[10],i,j,n,m,t1,t2,t3,u,v,min;
    int inf=99999999; //用inf(infinity的缩写)存储一个我们认为的正无穷值
    //读入n和m，n表示顶点个数，m表示边的条数
    scanf("%d %d",&n,&m);
                                                                  
    //初始化
    for(i=1;i<=n;i++)
        for(j=1;j<=n;j++)
            if(i==j) e[i][j]=0;
              else e[i][j]=inf;
                                                                            
    //读入边
    for(i=1;i<=m;i++)
    {
        scanf("%d %d %d",&t1,&t2,&t3);
        e[t1][t2]=t3;
    }
    //初始化dis数组，这里是1号顶点到其余各个顶点的初始路程
    for(i=1;i<=n;i++)
        dis[i]=e[1][i];
    //book数组初始化
    for(i=1;i<=n;i++)
        book[i]=0;
    book[1]=1;
                                                                  
    //Dijkstra算法核心语句
    for(i=1;i<=n-1;i++)
    {
        //找到离1号顶点最近的顶点
        min=inf;
        for(j=1;j<=n;j++)
        {
            if(book[j]==0 && dis[j]<min)
            {
                min=dis[j];
                u=j;
            }
        }
        book[u]=1;
        for(v=1;v<=n;v++)
        {
            if(e[u][v]<inf)
            {
                if(dis[v]>dis[u]+e[u][v])
                    dis[v]=dis[u]+e[u][v];
            }
        }
    }
                                                                  
    //输出最终的结果
    for(i=1;i<=n;i++)
        printf("%d ",dis[i]);
                                                                      
    getchar();
    getchar();
    return 0;
}