图论专题 F(差分约束)

关于差分约束的介绍可以直接看wikioi

链接在这里：差分约束 - OI Wiki (oi-wiki.org)

算法学习笔记(11): 差分约束 - 知乎 (zhihu.com)

 

#include "bits/stdc++.h"
using namespace std;
typedef long long LL;
const int MAX=1e5+5;
int n,m,ans;
int tot,head[MAX],adj[MAX<<1],nxt[MAX<<1],wei[MAX<<1],dis[MAX],cnt[MAX];
queue <int> q;
bool t[MAX];
struct Edge{int u,v,w1,w2;bool operator <(const Edge &tt) const {return w1<tt.w1;}}edge[MAX];
inline int read(){
    int an=0,x=1;char c=getchar();
    while (c<'0' || c>'9') {if (c=='-') x=-1;c=getchar();}
    while (c>='0' && c<='9') {an=an*10+c-'0';c=getchar();}
    return an*x;
}
void addedge(int u,int v,int w){
    tot++;
    adj[tot]=v;wei[tot]=w;
    nxt[tot]=head[u];
    head[u]=tot;
}
bool spfa(){
    int i,j,u,v;
    for (i=1;i<=n;i++) cnt[i]=0;
    while (!q.empty()){
        u=q.front();q.pop();t[u]=false;
        if (cnt[u]>n) return false;
        for (i=head[u];i;i=nxt[i]){
            v=adj[i];
            if (dis[v]>dis[u]+wei[i]){
                dis[v]=dis[u]+wei[i];
                if (!t[v]){
                    q.push(v),t[v]=true;
                    cnt[v]++;
                }
            }
        }
    }
    return true;
}
int main(){
    freopen ("f.in","r",stdin);
    freopen ("f.out","w",stdout);
    int i,j;
    n=read();m=read();
    for (i=1;i<=m;i++){
        edge[i].u=read();
        edge[i].v=read();
        edge[i].w1=read();
        addedge(edge[i].v,edge[i].u,edge[i].w1);
    }
    for (i=1;i<=n;i++) addedge(n+1,i,0);
    memset(t,false,sizeof(t));
    for (i=1;i<=n+1;i++) dis[i]=1e9;
    q.push(n+1);t[n+1]=true;dis[n+1]=0;
    if (spfa()) printf("YES");
    else printf("NO");
    return 0;
}