【Part 1】最短路问题

Floyd算法：【佛楼医德】

// luogu-judger-enable-o2
#include<cstdio>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
using namespace std;
const int N=205;
int f[N][N];
int n;
int main(){
    //freopen("1359.in","r",stdin);
    //freopen("1359.out","w",stdout);
    scanf("%d",&n);
    for (int i=1; i<=n; i++){
        for (int j=i+1; j<=n; j++){
            scanf("%d",&f[i][j]);
            f[j][i]=2133333333;
        }
    }
    for(int k=1;k<=n;k++)
        for(int i=1;i<=n;i++)
            for(int j=1;j<=n;j++)
                f[i][j]=min(f[i][j],f[i][k]+f[k][j]);
    printf("%d\n",f[1][n]);
    return 0;
}

dijkstra算法：【DJ撕他】

#include<cstdio>
#include<iostream>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
typedef long long ll;
using namespace std;
const int oo=2147483647;
int n,m,dis[5005],vis[5005],a[5005][5005];
int main(){
    freopen("dijs.in","r",stdin);
    freopen("dijs.out","w",stdout);
    scanf("%d %d",&n,&m);
    int x,y,z;
    memset(a,-1,sizeof(a));
    for(int i=1;i<=m;i++){
        cin>>x>>y>>z;
        a[x][y]=z;
        a[y][x]=z;
    }
    for(int i=1;i<=n;i++){
        dis[i]=oo;
        vis[i]=0;
    }
    dis[1]=0;
    for(int i=1;i<=n;i++){
        int now=oo,ii;
        for(int j=1;j<=n;j++)
            if(vis[j]==0 && dis[j]<now){
                ii=j; now=dis[j];
            }
        vis[ii]=1;
        for(int j=1;j<=n;j++)
            if(a[ii][j]!=-1 && vis[j]==0 &&dis[ii]+a[ii][j]<dis[j])
               dis[j]=dis[ii]+a[ii][j];
    }
    for(int i=1;i<=n;i++)
        cout<<dis[i]<<endl;
    return 0;
}

Bellman_Ford算法【贝尔曼福特】

#include<cstdio>
#include<iostream>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
typedef long long ll;
using namespace std;
const int oo=214748364;
int n,m,dis[5005],vis[5005];
struct node{
    int x,y,z;
}a[10004];
int main(){
    freopen("bell.in","r",stdin);
    freopen("bell.out","w",stdout);
    scanf("%d %d",&n,&m);
    //int x,y,z;
    //memset(a,-1,sizeof(a));
    for(int i=1;i<=m;i++){
        cin>>a[i].x>>a[i].y>>a[i].z;
        /*a[m+i].x=a[i].y;
        a[m+i].y=a[i].x;
        a[m+i].z=a[i].z;*/
    }
    for(int i=1;i<=n;i++){
        dis[i]=oo;
    //    vis[i]=0;
    }
    dis[1]=0;
    int ans=0;
    for(int i=1;i<=n;i++){
        int flag=0;
        for(int j=1;j<=m;j++){
            int xx=a[j].x;
            int yy=a[j].y;
            int zz=a[j].z;
            if(dis[xx]+zz<dis[yy]){
                dis[yy]=dis[xx]+zz;
                flag=1;
            }
        }
        if(flag==0){
            ans=2;
            break;
        }
    }
    if(ans==0) cout<<-1;//判断负环
    else{
        for(int i=1;i<=n;i++)
            cout<<dis[i]<<endl;
    }
    return 0;
}

SPFA算法

#include<cstdio>
#include<iostream>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<queue>
typedef long long ll;
using namespace std;
const int oo=21474836;
int n,m,k,cnt,x,y,dis[10005],vis[10005];
struct node{
    int to;
    int val;
    int next;
}e[10005];
int head[10004];
void add(int a,int b,int c){
    cnt++;
    e[cnt].to=b;
    e[cnt].val=c;
    e[cnt].next=head[a];
    head[a]=cnt;
}
queue<int>q;
int main(){
    freopen("spfa.in","r",stdin);
    freopen("spfa.out","w",stdout);
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%d",&k);
        for(int j=1;j<=k;j++){
            scanf("%d %d",&x,&y);
            add(i,x,y);
        }
    }
    for(int i=1;i<=n;i++)
        dis[i]=oo;
    q.push(1);
    dis[1]=0;
    vis[1]=1;
    while(!q.empty()){
        x=q.front();
        q.pop();
        vis[x]=0;
        for(int i=head[x];i!=0;i=e[i].next){
            int too=e[i].to;
            if(dis[too]>dis[x]+e[i].val)
            { 
               dis[too]=dis[x]+e[i].val;
                if(vis[too]==0){
                    vis[too]=1; q.push(too);
                }
            } 
        }
    }
    for(int i=1;i<=n;i++)
        cout<<dis[i]<<endl;
    return 0;
}