[JSOI2016]飞机调度 DAG最少路径覆盖

[JSOI2016]

• 题目

#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define MIN(a,b) (a>b? b:a)
using namespace std;
const int inf=1e9;
const int N=510;
struct node{int x,y,s,v,n;}e[N*N],r[N];
int t[N][N],g[N][N],lin[N*N],deep[N<<1],val[N],len=1,maxflow,cnt,S,T,n,m,x,y,s;
void LK(int x,int y,int v)
{e[++len].y=y,e[len].v=v,e[len].n=lin[x],lin[x]=len;}
void add(int x,int y,int v)
{LK(x,y,v),LK(y,x,0);}
inline int read(){
    int num=0;char ch=getchar();
    while(!isdigit(ch))ch=getchar();
    while(isdigit(ch))num=num*10+ch-'0',ch=getchar();
    return num;
}
bool bfs(){
    queue<int> q;
    memset(deep,0,sizeof(deep));
    deep[S]=1,q.push(S);
    while(q.size()){
        int x=q.front();q.pop();
        for(int i=lin[x];i;i=e[i].n){
            int y=e[i].y;
            if(deep[y]||!e[i].v)continue;
            deep[y]=deep[x]+1;
            q.push(y);
        }
    }return deep[T]>0;
}
int dfs(int x,int minf){
    if(x==T)return minf;
    int flow=0,sum=0;
    for(int i=lin[x];i;i=e[i].n){
        int y=e[i].y;
        if(!e[i].v||deep[y]!=deep[x]+1)continue;
        flow=dfs(y,min(e[i].v,minf));
        if(!flow)deep[y]=0;
        sum+=flow,minf-=flow,e[i].v-=flow,e[i^1].v+=flow;
        if(!minf)return sum;
    }return sum;
}
int main()
{
    n=read(),m=read(); S=2*m+1,T=S+1;
    rep(i,1,n)val[i]=read();
    rep(i,1,n)rep(j,1,n){
    	t[i][j]=read();
    	if(i!=j)t[i][j]+=val[j];
    	g[i][j]=t[i][j];
	}
    rep(i,1,m)r[i].x=read(),r[i].y=read(),r[i].s=read();

    rep(k,1,n)rep(i,1,n)rep(j,1,n)if(i!=j)t[i][j]=min(t[i][j],t[i][k]+t[k][j]);
    rep(i,1,m)add(S,i,1),add(i+m,T,1);
    rep(i,1,m){
        rep(j,1,m){
            if(i==j)continue;
            if(r[i].s+g[r[i].x][r[i].y]+t[r[i].y][r[j].x]<=r[j].s){
                add(i,j+m,1);
            }
        }
    }
    while(bfs())maxflow+=dfs(S,inf);
    cout<<m-maxflow;
    return 0;
}