最短路径

 算法一 ：迪杰斯特拉

算法详情：贪心 维护一个 dis 数组 进行 松弛操作

适用： 单源最短路

#include<bits/stdc++.h>
using namespace std;
#define LOACL  freopen("in","r",stdin);\
            freopen("out","w",stdout); 

#define add(u,v,w) (e[++tot]=(edge){v,head[u],1},head[u]=tot;) 
#define f(i,l,r) for(int i=l;i<=r;++i)
#define g(i,l,r) for(int i=l;i>=r;--i)
#define CLR(arr,val) memset(arr,val,sizeof(arr))

typedef long long ll;
const int inf = 0x3f3f3f; 
int n,m,s,t,u,v,w;
int g[10005][10005];
int dis[10005];
bool vis[10005] ;
void dij(int s )
{
    f(i,1,n)dis[i]=g[s][i];
    vis[s] =1;
    dis[s] =0;

    f(i,1,n-1)
    {
        int mm = inf,pos;
        f(j,1,n)
        {
            if(!vis[j] && dis[j]<mm)
            {
                mm =dis[j];
                pos =j;
            }
        }
        if(mm==inf ) break;
        vis[pos] =1;
        f(j,1,n)
        {
            if(!vis[j] && dis[pos]+g[pos][j]<dis[j])
                dis[j]=dis[pos]+g[pos][j];
        }
    }
}


void dijkstra(int s){
    for(int i = 1; i <= n; i++)
        dis[i] = g[s][i];
    vis[s] = 1;
    dis[s] = 0;

    for(int i = 1; i < n; i++){
        int min = inf, pos;
        for(int j = 1; j <= n; j++){
            if(!vis[j] && dis[j] < min){
                min = dis[j];
                pos = j;
            }
        }

        if(min == inf)
            break;

        vis[pos] = 1;
        for(int j = 1; j <= n; j++){
            if(!vis[j] && dis[pos] + g[pos][j] < dis[j]){
                dis[j] = dis[pos] + g[pos][j];
            }
        }
    }
}

int main()
{
    LOACL

    CLR(g,inf);
    CLR(vis,false);

    cin>>n>>m>>s>>t; 
    f(i,1,n)g[i][i]=0;
 
       
    f(i,1,m)
    {
        cin>>u>>v>>w;
        g[u][v]=min(g[u][v],w);
        g[v][u]=min(g[v][u],w);
    } 
    dijkstra(s);
    cout<<dis[t]<<endl;  
    return 0;
}

 算法二 ：Floyd

算法详情：dp 规划

适用：多源非负环，注意 初值别太大 ，会炸int

#include<bits/stdc++.h>
using namespace std;
#define LOACL  freopen("in","r",stdin);\
            freopen("out","w",stdout); 

#define add(u,v,w) (e[++tot]=(edge){v,head[u],1},head[u]=tot;) 
#define f(i,l,r) for(int i=l;i<=r;++i)
#define g(i,l,r) for(int i=l;i>=r;--i)
#define CLR(arr,val) memset(arr,val,sizeof(arr))

typedef long long ll; 
const int inf = 1e4+6;
const int sz = 1005;
int g[sz][sz];
int n,m,u,v,w;
 
void floyd()
{
    f(k,1,n)
    f(i,1,n)
    f(j,1,n)
    g[i][j]=min(g[i][j],g[i][k]+g[k][j]);
}
int main()
{
    LOACL
    CLR(g,inf);
    cin>>n>>m;
    f(i,1,n)g[i][i]=0;

     
    f(i,1,m)
    {
        cin>>u>>v>>w;
        if(w < g[u][v]) 
            g[u][v]=g[v][u]=w; 
    }

     
 
    floyd() ;
         
    f(i,1,n)
    {
        f(j,1,n)
        cout<<g[i][j]<<" ";
        cout<<endl;
    }
 
    return 0;
}

 算法二 ：spfa

算法详情： 优化的bfs

适用：边数少最短路，注意，回述时候的标记取消

#include<bits/stdc++.h>
using namespace std;
#define LOACL  freopen("in","r",stdin);\
            freopen("out","w",stdout); 

//#define add(u,v,w) (e[++tot]=(edge){v,head[u],w},head[u]=tot;) 
#define f(i,l,r) for(int i=l;i<=r;++i)
#define g(i,l,r) for(int i=l;i>=r;--i)
#define CLR(arr,val) memset(arr,val,sizeof(arr))

typedef long long ll; 
const int sz =1e6+5;
const int inf =0x3f3f3f;
int n,m,s,t,u,v,w;
 int dis[sz], vis[sz] ;
 struct  edge 
 {
     int v,nxt,w;
 }e[sz<<1];
 int head[sz],tot;
void add(int u,int v,int w )
{
    e[++tot]=(edge){v,head[u],w},head[u]=tot;
}
 void  spfa()
 {
     int pos ;
     queue<int >q;
     q.push(s);
     vis[s]=1;
     dis[s]=0;
     while(!q.empty())
     {
         int pos = q.front();
         q.pop();
         vis[pos]=0;
         for(int i = head[pos];i!=-1;i=e[i].nxt)
         {
             int v =e[i].v;
             if(dis[v]> dis[pos]+e[i].w)
             {
                 dis[v] = dis[pos]+e[i].w ;
                 if(!vis[v])
                 {
                     vis[v]=1;
                     q.push(v);
                 }
             }    
         
         }
     }




 }
int main()
{
    LOACL
    CLR(vis,0);
    CLR(dis,inf);
    CLR(head,-1);
    cin>>n>>m>>s>>t;
     f(i,1,m)
     {
         cin>>u>>v>>w;
         add(u,v,w);add(v,u,w);
     }
    spfa();  
    cout<<dis[t]<<endl;
    return 0;
}