UVA - 11090 Going in Cycle!!

Posted 2021-01-18 widsom

UVA - 11090

思路:

二分答案 + spfa判负环

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize(4)
#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pi acos(-1.0)
#define LL long long
//#define mp make_pair
#define pb push_back
#define ls rt<<1, l, m
#define rs rt<<1|1, m+1, r
#define ULL unsigned LL
#define pll pair<LL, LL>
#define pli pair<LL, int>
#define pii pair<int, int>
#define piii pair<pii, int>
#define mem(a, b) memset(a, b, sizeof(a))
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
//head

const int N = 55;
const double eps = 1e-4;
vector<pii> g[N];
bool vis[N];
double dis[N];
int n;
bool spfa(int u, double x) {
    vis[u] = true;
    for (pii e : g[u]) {
        int v = e.fi;
        if(dis[u] + (double)e.se - x < dis[v]) {
            dis[v] = dis[u] + e.se - x;
            if(vis[v]) return true;
            if(spfa(v, x)) return true;
        }
    }
    vis[u] = false;
    return false;
}
bool check(double x) {
    mem(vis, false);
    for (int i = 1; i <= n; i++) dis[i] = 0;
    for (int i = 1; i <= n; i++) if(spfa(i, x)) return true;
    return false;
}
int main() {
    int T, m, u, v, w;
    scanf("%d", &T);
    for (int cs = 1; cs <= T; cs++) {
        scanf("%d %d", &n, &m);
        for (int i = 1; i <= n; i++) g[i].clear();
        double sum = 0;
        for (int i = 0; i < m; i++) {
            scanf("%d %d %d", &u, &v, &w);
            g[u].pb(pii{v, w});
            sum += w;
        }
        double l = 0, r = sum+1, mid = (l+r)/2;
        while(l + eps < r) {
            if(check(mid)) r = mid;
            else l = mid;
            mid = (l+r)/2;
        }
        if(check(r)) printf("Case #%d: %.2f
", cs, mid);//检查右端点来判负环
        else printf("Case #%d: No cycle found.
", cs);
    }
    return 0;
}