稠密图

dijkstra

#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=1e4+10;
int dist[N];
int g[501][501];
int n,m;
bool st[501];
int dijk()
{
    memset(dist, 0x3f,sizeof dist);
    dist[1]=0;
   for(int i=0;i<n;i++)
    {
        int t=-1;
        for(int j=1;j<=n;j++)
        {
             if(!st[j]&&(t==-1||dist[t]>dist[j]))
             t=j;
        }
        st[t]=true;
       for(int j=1;j<=n;j++)
       {
           dist[j]=min(dist[j],dist[t]+g[t][j]);
       }


    }
   if(dist[n]==0x3f3f3f3f) return -1;
    return dist[n];
}
int main()
{
    cin>>n>>m;
    memset(g,0x3f,sizeof g);
    while(m--)
    {
        int x,y,z;
        cin>>x>>y>>z;
        g[x][y]=min(g[x][y],z);
    }
    printf("%d",dijk());
    return 0;
}

bellman-ford

#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;
const int N = 1e5+10;
struct Node
{
    int a,b,w;
};
int dist[510];
int main()
{
    int n,m;
    cin>>n>>m;

    vector<Node> q;
    for(int i=0;i<m;i++)
    {
        int x,y,z;
        cin>>x>>y>>z;
        q.push_back({x,y,z});
    }

    memset(dist,0x3f,sizeof dist);
    dist[1]=0;

    for(int i=0;i<n;i++)
        for(int j=0;j<q.size();j++)
            dist[q[j].b]=min(dist[q[j].b],dist[q[j].a]+q[j].w);

    if(dist[n]>0x3f3f3f3f/2) cout<<-1;
    else
    cout<<dist[n];
    return 0;
}

稀疏图

dijkstra邻接表写法

#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
const int N = 3e6+10;
typedef pair<int, int> PII;

int h[N],e[N],ne[N],idx,w[N];
int n,m;
int dist[N];
bool st[N];

void insert(int a,int b,int c)
{
    e[idx]=b;w[idx]=c;ne[idx]=h[a];h[a]=idx++;
}
int djs()
{
    memset(dist,0x3f,sizeof dist);
    priority_queue<PII,vector<PII>,greater<PII>> q;
    dist[1]=0;
    q.push({0,1});

    while(q.size())
    {
        auto t=q.top();
        q.pop();
        int ver=t.second,distance=t.first;

        if(st[ver]) continue;
        st[ver]=true;

        for(int i=h[ver];i!=-1;i=ne[i])
        {
            int j=e[i];
            if(dist[j]>dist[ver]+w[i])
            {
                dist[j]=dist[ver]+w[i];//注意是起点加权重,参考迪阶斯特拉I
                q.push({dist[j],j});
            }
        }
    }
    if(dist[n]==0x3f3f3f3f) return -1;//注意精度问题
    return dist[n];
}
int main()
{
    memset(h, -1, sizeof h);
    cin>>n>>m;
    while (m -- )
    {
        int x,y,z;
        cin>>x>>y>>z;
        insert(x,y,z);
    }
    cout<<djs()<<endl;
    return 0;
}

dijkstra二维vector代替邻接表

#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
const int N = 2e5+10;
typedef pair<int, int> PII;
vector<PII> h[N];
int dist[N];
int n,m;
bool st[N];
int dijkstra()
{
    memset(dist,0x3f,sizeof dist);
    dist[1]=0;
    priority_queue<PII,vector<PII>,greater<PII>> q;
    q.push({0,1});
    while(q.size())
    {
        auto t=q.top();
        q.pop();

        int v=t.second;
        if(st[v]) continue;
        st[v]=true;
        for(auto i:h[v])
        {
            int j=i.first,w=i.second;
            if(dist[j]>dist[v]+w)
            {
                dist[j]=dist[v]+w;
                q.push({dist[j],j});
            }
        }
    }
    if(dist[n]==0x3f3f3f3f) return -1;
    return dist[n];
}
int main()
{
    cin>>n>>m;
    while (m -- )
    {
        int a,b,c;
        cin>>a>>b>>c;
        h[a].push_back({b,c});
    }
    cout<<dijkstra()<<endl;
    return 0;
}

存在负权边

spfa

#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;
const int N = 1e5+10;
typedef pair<int, int> PII;
vector<PII> h[N];
int dist[N];
int q[N];
int hh=0,tt=-1;
int main()
{
    int n,m;
    cin>>n>>m;
    for(int i=0;i<m;i++)
    {
        int x,y,z;
        cin>>x>>y>>z;
        h[x].push_back({y,z});
    }

    memset(dist,0x3f,sizeof dist);
    dist[1]=0;
    q[++tt]=1;

    while(hh<=tt)
    {
        int t=q[hh++];
        for(auto j:h[t])
            if(dist[j.first]>dist[t]+j.second)
            {
                dist[j.first]=dist[t]+j.second;
                q[++tt]=j.first;
            }
    }
    if(dist[n]>0x3f3f3f3f/2) puts("impossible");
    else
    cout<<dist[n]<<endl;
    return 0;
}