Dijstra算法：

//POJ 2378
#include <bits/stdc++.h>
using namespace std;
#define MAXN 1005
const int INF = (1 << 30);
int t,V,d[MAXN],costs[MAXN][MAXN];
bool used[MAXN];
void dijkstra(int s){
    fill(used,used + V + 1,false);
    fill(d,d + V + 1,INF);
    d[s]=0;
    while(true){
        int v = -1;
        for(int i=1;i<=V;i++){
            if(!used[i]&&(v==-1||d[i]<d[v])) v=i;
        }
        if(v==-1) break;
        used[v]=true;
        for(int i = 1;i <= V;i ++){
            d[i]=min(d[i],d[v]+costs[v][i]);
        }
    }
}
int main(void)
{
    int x,y,c;
    scanf("%d%d",&t,&V);
    fill(costs[0],costs[0] + MAXN * MAXN,INF);
    for(int i = 0;i < t;i ++){
        scanf("%d%d%d",&x,&y,&c);
        costs[x][y] = costs[y][x] = min(costs[x][y],c);
    }
    dijkstra(1);
    cout << d[V] << endl;
    return 0;
}

//POJ 2378 堆优化版本
#include <iostream>
#include <queue>
#define MAX_V 1005
#define INF (1 << 28)
using namespace std;
struct edge{int to,cost;edge(int a,int b):to(a),cost(b){}};
typedef pair<int,int> P;
int V,E,d[MAX_V];
vector <edge> G[MAX_V];
struct cmp{
    bool operator () (P p1,P p2){
        return p1.first > p2.first;
    }
};
void dijkstra(int s){
    priority_queue <P,vector<P>,cmp>que;
    fill(d,d + V,INF);
    d[s] = 0;
    que.push(P(0,s));
    while(!que.empty()){
        P p = que.top();que.pop();
        int v = p.second;
        if(d[v] < p.first) continue;
        for(int i = 0;i < G[v].size();i ++){
            edge e = G[v][i];
            if(d[e.to] > d[v] + e.cost){
                d[e.to] = d[v] + e.cost;
                que.push(P(d[e.to],e.to));
            }
        }
    }
}
int main(void)
{
    cin >> E >> V;
    for(int i = 0;i < E;i ++){
        int f,t,c;
        cin >> f >> t >> c;
        f --,t --;
        G[f].push_back(edge(t,c));
        G[t].push_back(edge(f,c));
    }
    dijkstra(0);
    cout << d[V - 1] << endl;
    return 0;
}

Bellman-Ford 算法：

struct edge { int from,to,cost; };
edge es[MAX_E];
int V,E,d[MAX_V];
void bellman_ford(int s){
    fill(d,d + MAX_V,INF);
    d[s] = 0;
    while(true){
        bool update = false;
        for(int i = 0;i < 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;
    }
}

Bellman-Ford 判断有无负权环：

bool find_negative_loop(){
    fill(d,d + MAX_V,0);
    for(int i = 0;i < V;i ++){
        for(int j = 0;j < E;j ++){
            edge e = es[i];
            if(d[e.to] > d[e.from] + e.cost){
                d[e.to] = d[e.from] + e.cost;
                if(i == V - 1) return true;//或者可以在 for 循环外测试一轮松弛
            }
        }
    }
    return false;
}

Floyd-Warshall 算法：

long long d[MAX_V][MAX_V];
long long V;
void floyd(){
        for(long long k = 0;k < V;k ++){
                for(long long i = 0;i < V;i ++){
                        for(long long j = 0;j < V;j ++){
                                d[i][j] = min(d[i][j],d[i][k] + d[k][j]);
                        }
                }
        }
}

SPFA 算法：

// From ACM Template of kuangbin
struct Edge{
    int v,cost;
    Edge(int _v=0,int _cost=0):v(_v),cost(_cost){}
};
vector<Edge>E[MAXN];
void addedge(int u,int v,int w){
    E[u].push_back(Edge(v,w));
}
bool vis[MAXN];//在队列标志
int cnt[MAXN];//每个点的入队列次数
int d[MAXN];
bool SPFA(int s,int n){
    memset(vis,false,sizeof(vis));
    for(int i=1;i<=n;i++)d[i]=INF;
    vis[s]=true;
    d[s]=0;
    queue<int>que;
    while(!que.empty())que.pop();
    que.push(s);
    memset(cnt,0,sizeof(cnt));
    cnt[s]=1;
    while(!que.empty()){
        int u=que.front();
        que.pop();
        vis[u]=false;
        for(int i=0;i<E[u].size();i++){
            int v=E[u][i].v;
            if(d[v]>d[u]+E[u][i].cost){
                d[v]=d[u]+E[u][i].cost;
                if(!vis[v]){
                    vis[v]=true;
                    que.push(v);
                    if(++cnt[v]>n)return false;
                }
            }
        }
    }
    return true;
}