HDU 2544 最短

链接：http://acm.hdu.edu.cn/showproblem.php?

pid=2544

解析：

首先数据量为V<=100

那么这里使用不论什么基础的最短路的算法都不会超时！

常见数据：

 5 6
 1 2 10
 1 3 4
 2 4 2
 3 4 3
 2 5 5
 4 5 100
// 答案：14 

 2 4
 1 2 10
 1 3 4
 2 4 2
 3 4 3
// 答案：9

Bellman-Ford算法：

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
using namespace std;
#define MAX_E 10010
#define MAX_V 105
#define INF 1e8

struct edge{int from, to, cost; };
edge es[2*MAX_E];
int d[MAX_V];
int V, E;

void shortest_path(int s){
    for(int i=1; i<=V; ++i) d[i] = INF;
    d[s] = 0;
    while(true){
        bool update = false;
        for(int i=0; i<2*E; ++i){
            edge e = es[i];
            if(d[e.from] != INF&&d[e.to]>d[e.from]+e.cost){
                d[e.to] = d[e.from] + e.cost;
                update = true;
            }
        }
        if(!update) break;

    }
}

int main(){
    while(~scanf("%d%d", &V, &E), V||E){
        int i;
        int a,b,c;

        for(i=0; i<E; ++i){
            scanf("%d%d%d", &a, &b, &c);
            es[i].from = a; es[i].to = b; es[i].cost = c;
            es[i+E].from = b; es[i+E].to = a; es[i+E].cost = c;
        }
        shortest_path(1);
        printf("%d\n", d[V]);
    }
}

Dijkstra算法：

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <string>
using namespace std;
#define MAX_V 105
#define MAX_X 105
#define INF 1e8

int cost[MAX_V][MAX_V];
int d[MAX_X];
bool used[MAX_X];
int n,m;

void dijkstra(int s){
    for(int i=1; i<=n; ++i){
        d[i] = INF;
        used[i] = false;
    }
    d[s] = 0;

    while(true){
        int v = -1;
        for(int u=1; u<=n; ++u){
            if(!used[u]&&(v==-1||d[u]<d[v])) v = u;
        }
        if(v == -1) break;
        used[v] = true;
        for(int u=1; u<=n; ++u){
            d[u] = min(d[u], d[v]+cost[v][u]);
        }
    }
}

int main(){
    while(~scanf("%d%d", &n, &m), m||n){
        int i;
        int a,b,c;

        for(i=1; i<=n; ++i)
            for(int j=1; j<=n; ++j)
                cost[i][j] = INF;

        for(i=0; i<m; ++i){
            scanf("%d%d%d", &a, &b, &c);
            cost[a][b] = c;
            cost[b][a] = c;
        }
        dijkstra(1);
        printf("%d\n", d[n]);
    }
}

Floyd算法：

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
using namespace std;
#define MAX_V 105
#define MAX_X 105
#define INF 1e8

int d[MAX_V][MAX_V];
bool used[MAX_X];
int n,m;

void floyd(){
    for(int k=1; k<=n; ++k){
        for(int i=1; i<=n; ++i){
            for(int j=1; j<=n; ++j){
                d[i][j] = min(d[i][j], d[i][k]+d[k][j]);
            }
        }
    }
}

int main(){
    while(~scanf("%d%d", &n, &m), m||n){
        int i;
        int a,b,c;

        for(i=1; i<=n; ++i)
            for(int j=1; j<=n; ++j)
                d[i][j] = INF;
        for(i=1; i<=n; ++i) d[i][i] = 0;

        for(i=0; i<m; ++i){
            scanf("%d%d%d", &a, &b, &c);
            d[a][b] = c;
            d[b][a] = c;
        }
        floyd();
        printf("%d\n", d[1][n]);
    }
}

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