Day4-A-最短路 HDU2544

在每年的校赛里，所有进入决赛的同学都会获得一件很漂亮的t-shirt。但是每当我们的工作人员把上百件的衣服从商店运回到赛场的时候，却是非常累的！所以现在他们想要寻找最短的从商店到赛场的路线，你可以帮助他们吗？ 

Input输入包括多组数据。每组数据第一行是两个整数N、M（N<=100，M<=10000），N表示成都的大街上有几个路口，标号为1的路口是商店所在地，标号为N的路口是赛场所在地，M则表示在成都有几条路。N=M=0表示输入结束。接下来M行，每行包括3个整数A，B，C（1<=A,B<=N,1<=C<=1000）,表示在路口A与路口B之间有一条路，我们的工作人员需要C分钟的时间走过这条路。 
输入保证至少存在1条商店到赛场的路线。 
Output对于每组输入，输出一行，表示工作人员从商店走到赛场的最短时间Sample Input

2 1
1 2 3
3 3
1 2 5
2 3 5
3 1 2
0 0

Sample Output

3
2

简单的最短路板子题，用来练习各种算法，代码如下：
dijkstra：

const int maxm = 110;
const int INF = 0x7fffffff;

int N, M, G[maxm][maxm], d[maxm], vis[maxm];

struct Node {
    int sum, i;
    Node(int _sum, int _i) : sum(_sum), i(_i){}

    bool operator<(const Node &a) const {
        return a.sum < sum;
    }
};

void init() {
    for (int i = 2; i <= N; ++i) {
        d[i] = INF;
    }
    memset(G, 0, sizeof(G)), memset(vis, 0, sizeof(vis));
}

int main() {
    while(scanf("%d%d",&N,&M) && N + M) {
        init();
        for (int i = 0; i < M; ++i) {
            int t1, t2, t3;
            scanf("%d%d%d", &t1, &t2, &t3);
            G[t1][t2] = G[t2][t1] = t3;
        }
        priority_queue<Node>q;
        q.push(Node(0, 1));
        while(!q.empty()) {
            Node p = q.top();
            q.pop();
            if(vis[p.i]++)
                continue;
            for (int i = 1; i <= N; ++i) {
                if(G[p.i][i] && G[p.i][i] + d[p.i] < d[i]) {
                    d[i] = G[p.i][i] + d[p.i];
                    q.push(Node(d[i],i));
                }
            }
        }
        printf("%d\n", d[N]);
    }
    return 0;
}

　Bellman_Ford:

const int maxm = 110;
const int maxn = 20010;
const int INF = 0x7fffffff;

int N, M, v[maxn], u[maxn], cost[maxn], d[maxm];

void init() {
    memset(v, 0, sizeof(v)), memset(u, 0, sizeof(u)), memset(cost, 0, sizeof(cost));
    for (int i = 2; i <= N; ++i)
        d[i] = INF;
}

int main() {
    while(scanf("%d%d",&N,&M) && N + M) {
        init();
        for (int i = 0; i < M; ++i) {
            int t1, t2, t3;
            scanf("%d%d%d", &t1, &t2, &t3);
            v[i * 2] = t1, u[i * 2] = t2, cost[i * 2] = t3;
            v[i * 2 + 1] = t2, u[i * 2 + 1] = t1, cost[i * 2 + 1] = t3;
        }
        for (int j = 0; j < N-1; ++j) {
            for (int i = 0; i < M * 2; ++i) {
                int x = v[i], y = u[i], c = cost[i];
                if(d[x] < INF)
                    d[y] = min(d[y], d[x] + c);
            }
        }
    
        printf("%d\n", d[N]);
    }
    return 0;
}

    SPFA:

const int maxm = 110;
const int INF = 0x7fffffff;

int N, M, G[maxm][maxm], d[maxm], inq[maxm];

struct Node {
    int sum, i;
    Node(int _sum, int _i) : sum(_sum), i(_i){}
};

void init() {
    for (int i = 2; i <= N; ++i) {
        d[i] = INF;
    }
    memset(G, 0, sizeof(G)), memset(inq, 0, sizeof(inq));
}

int main() {
    while(scanf("%d%d",&N,&M) && N + M) {
        init();
        for (int i = 0; i < M; ++i) {
            int t1, t2, t3;
            scanf("%d%d%d", &t1, &t2, &t3);
            G[t1][t2] = G[t2][t1] = t3;
        }
        queue<int>q;
        q.push(1);
        inq[1] = 1;
        while(!q.empty()) {
            int u = q.front();
            q.pop();
            inq[u] = 0;
            for (int i = 1; i <= N; ++i) {
                if(G[u][i] && G[u][i] + d[u] < d[i]) {
                    d[i] = G[u][i] + d[u];
                    if(!inq[i])
                        q.push(i);
                }
            }
        }
        printf("%d\n", d[N]);
    }
    return 0;
}

　Floyd:

const int maxm = 110;
const int INF = 0x7fffffff;

int N, M, G[maxm][maxm];

void init() {
    for(int i = 1; i <= N; ++i) {
        for (int j = 1; j <= N; ++j) {
            if(i == j)
                G[i][i] = 0;
            else 
                G[i][j] = INF;
        }
    }
}

int main() {
    while(scanf("%d%d",&N,&M) && N + M) {
        init();
        for (int i = 0; i < M; ++i) {
            int t1, t2, t3;
            scanf("%d%d%d", &t1, &t2, &t3);
            G[t1][t2] = G[t2][t1] = t3;
        }
        for (int k = 1; k <= N; ++k)
            for(int i = 1; i <= N; ++i)
                for (int j = 1; j <= N; ++j) {
                    if(G[i][k] < INF && G[k][j] < INF)
                        G[i][j] = min(G[i][j], G[i][k] + G[k][j]);
                }
        printf("%d\n", G[1][N]);
    }
    return 0;
}