loj2308 「APIO2017」商旅

ref

#include <iostream>
#include <cstring>
#include <cstdio>
#include <queue>
using namespace std;
typedef long long ll;
int n, m, k, uu, vv, hea[105], cnt, tot[105];
ll b[105][1005], s[105][1005], w[105][105], bst[105][105], dis[105], ww;
bool ins[105];
const ll oo=0x3f3f3f3f3f3f3f3f;
queue<int> d;
struct Edge{
    int too, nxt;
    ll val;
}edge[20005];
void add_edge(int fro, int too, ll val){
    edge[++cnt].nxt = hea[fro];
    edge[cnt].too = too;
    edge[cnt].val = val;
    hea[fro] = cnt;
}
bool chk(ll lim){
    memset(hea, 0, sizeof(hea));
    memset(dis, 0, sizeof(dis));
    while(!d.empty())   d.pop();
    cnt = 0;
    for(int i=1; i<=n; i++)
        for(int j=1; j<=n; j++)
            if(bst[i][j]!=-1 && w[i][j]<oo)
                add_edge(i, j, bst[i][j]-lim*w[i][j]);
    for(int i=1; i<=n; i++){
        d.push(i);
        tot[i] = ins[i] = 1;
    }
    while(!d.empty()){
        int x=d.front();
        d.pop();
        ins[x] = false;
        for(int i=hea[x]; i; i=edge[i].nxt){
            int t=edge[i].too;
            if(dis[t]<=dis[x]+edge[i].val){//这里是大于等于，零环也合法
                tot[t] = tot[x] + 1;
                if(tot[t]>n)    return true;
                dis[t] = dis[x] + edge[i].val;
                if(!ins[t]){
                    ins[t] = true;
                    d.push(t);
                }
            }
        }
    }
    return false;
}
int main(){
    memset(w, 0x3f, sizeof(w));
    memset(bst, -1, sizeof(bst));
    cin>>n>>m>>k;
    for(int i=1; i<=n; i++)
        for(int j=1; j<=k; j++)
            scanf("%lld %lld", &b[i][j], &s[i][j]);
    for(int i=1; i<=n; i++)
        w[i][i] = 0;
    for(int i=1; i<=m; i++){
        scanf("%d %d %lld", &uu, &vv, &ww);
        w[uu][vv] = min(w[uu][vv], ww);
    }
    for(int l=1; l<=n; l++)
        for(int i=1; i<=n; i++)
            for(int j=1; j<=n; j++)
                w[i][j] = min(w[i][j], w[i][l]+w[l][j]); 

    ll l=0, r=0, mid, re;
    for(int i=1; i<=n; i++)
        for(int j=1; j<=n; j++){
            if(i!=j && w[i][j]<oo){
                bst[i][j] = 0;
                for(int l=1; l<=k; l++)
                    if(s[j][l]!=-1 && b[i][l]!=-1)
                        bst[i][j] = max(bst[i][j], s[j][l]-b[i][l]);
                r = max(r, bst[i][j]);
            }
        }
    while(l<=r){
        mid = (l + r) >> 1;
        if(chk(mid))    re = mid, l = mid + 1;
        else    r = mid - 1;
    }
    cout<<re<<endl;
    return 0;
}