最短路 模板 【bellman-ford,dijkstra,floyd-warshall】

Bellman-ford:

/*
bellman ford
*/
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int INF = 0x3f3f3f3f;
const int Max = 9999;
typedef struct edge{
    int from,to;
    int ed;
}Edge;
Edge edge[100];
int v[Max];
int d[Max];
int V,E;
void bellman_ford(int s)
{
    memset(d,0x3f,sizeof(d));
    d[s]=0;
    while(true){//如果不存在负圈，最多执行|V|-1次
        bool update = false;
        for(int i=0;i<E;i++){
            Edge e = edge[i];
            if(d[e.from]!=INF&&d[e.to]>d[e.from]+e.ed){
                d[e.to]=d[e.from]+e.ed;
                update = true;
            }
        }
        if(!update) break;
    }
}
bool find_negative_loop()
{
    memset(d,0,sizeof(d));
    for(int i=0;i<V;i++)
        for(int j=0;j<E;j++){
            Edge e = edge[j];
            if(d[e.to]>d[e.from]+e.ed){
                d[e.to] = d[e.from]+e.ed;
                if(i==V-1) return true;
            }
        }
    return false;
}
int main()
{
    int s,e;
    scanf("%d%d",&V,&E);
    for(int i=0;i<V;i++)
        scanf("%d",&v[i]);
    for(int i=0;i<E;i++)
        scanf("%d%d%d",&edge[i].from,&edge[i].to,&edge[i].ed);
    if(find_negative_loop()) printf("yes\n");
    else printf("no\n");
    return 0;
}

floyd-warshall：

/*
floyd-warshall
*/
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int INF = 0x3f3f3f3f;
const int Max = 200;

int d[Max][Max];
int V,E;
bool floyd_warshall()
{
    for(int k=1;k<=V;k++){
        for(int i=1;i<=V;i++){
            for(int j=1;j<=V;j++){
                d[i][j]=min(d[i][j],d[i][k]+d[k][j]);
            }
        }
    }
    for(int i=1;i<=V;i++)
    if(d[i][i]<0){
        return false;
    }
    return true;
}
int main()
{
    freopen("input.txt","r",stdin);
    scanf("%d%d",&V,&E);
    for(int i=1;i<=V;i++)
        for(int j=1;j<=V;j++)
            d[i][j]=d[j][i] = (i==j?0:INF);
    for(int i=0;i<E;i++)
    {
        int from,to,cost;
        scanf("%d%d%d",&from,&to,&cost);
        d[from][to]=d[to][from]=cost;
    }

    if(floyd_warshall()) printf("%d\n",d[1][V]);
    else printf("负圈\n");
    return 0;
}

dijkstra:

邻接矩阵实现

/*
dijkstra1
*/
#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;

const int Max = 200;
const int INF = 0x3f3f3f3f;
int d[Max];
int vis[Max];
int cost[Max][Max];
int V,E;

void dijkstra(int s)
{
    memset(d,0x3f,sizeof(d));
    memset(vis,0,sizeof(vis));
    d[s]=0;
    while(1){
        int v = -1;
        for(int u=1;u<=V;u++){
            if(!vis[u]&&(v==-1||d[u]<d[v]))
                v = u;
        }
        if(v==-1) break;
        vis[v]=1;
        for(int u=1;u<=V;u++){
            d[u]=min(d[u],d[v]+cost[v][u]);
        }
    }
}
int main()
{
    //freopen("input.txt","r",stdin);
    int from,to,co;
    cin>>V>>E;
    for(int i=1;i<=V;i++)
        for(int j=1;j<=V;j++)
        cost[i][j]=INF;

    for(int i=0;i<E;i++)
    {
        cin>>from>>to;
        cin>>cost[from][to];
    }
    int s,en;
    cin>>s>>en;
    dijkstra(s);
    cout<<d[en]<<endl;
    return 0;
}

void dijkstra()
{
    memset(dis,0x3f,sizeof(dis));
    memset(vis,0,sizeof(vis));
    dis[1]=0;
    for(int i=1;i<=V;i++)
    {
        int mi = INF,k;
        for(int j=1;j<=V;j++){
            if(vis[j]==0&&dis[j]<mi){
                mi = dis[j];
                k = j;
            }
        }//找最小
        vis[k]=1;
        for(int j=1;j<=V;j++)
            dis[j]=min(dis[j],dis[k]+mp[k][j]);
    }
}

优先队列实现：

/*
dijkstra2
*/
#include <iostream>
#include <cstdio>
#include <vector>
#include <queue>
#include <cstring>
using namespace std;
const int INF = 0x3f3f3f3f;
const int Max = 200;
typedef pair<int,int> P;
typedef struct Edge{
    int v,cost;
};
Edge edge[Max];
vector<Edge> G[Max];
int d[Max];
int V,E;

void dijkstra(int s)
{
    memset(d,0x3f,sizeof(d));
    d[s]=0;
    priority_queue<P ,vector<P>,greater<P> > que;
    que.push(P(0,s));
    while(!que.empty()){
        P top = que.top();que.pop();
        int u = top.second;
        if(d[u]<top.first) continue;

        for(int i=0;i<G[u].size();i++){
            Edge e = G[u][i];
            if(d[e.v]>d[u]+e.cost){
                d[e.v]=d[u]+e.cost;
                que.push(P(d[e.v],e.v));
            }
        }
    }

}
int main()
{
    cin>>V>>E;
    for(int i=0;i<E;i++){
        int u;
        cin>>u>>edge[i].v>>edge[i].cost;
        G[u].push_back(edge[i]);
    }
    int s,e;
    cin>>s>>e;
    dijkstra(s);
    printf("s->e:%d\n",d[e]);
    return 0;
}

路径还原：

            memset(pre,-1,sizeof(pre));
        …………………………
            pre[v]=now;
        …………………………
            vector<int> path;
            int tmp = t;
            while(tmp!=-1){
                path.push_back(tmp);
                tmp = pre[tmp];
            }
            for(int i=path.size()-1;i>=0;i--)
                if(i==0) printf("%d ",path[i]);
                else printf("%d -> ",path[i]);