UVA 11090Going in Cycle!! （spfa + 二分）

题意:

在一个有向图中找一个平均距离最小的环

分析:

−−这种东西记得要往二分上想啊！
二分枚举平均最小距离，每次每条边减去这个距离，然后spfa找负环
如果找到，说明平均最小距离比这个值要小，如果没找到，则说明平均最小距离比这个值大。

代码:

////  Created by TaoSama on 2015-11-04//  Copyright (c) 2015 TaoSama. All rights reserved.////#pragma comment(linker, "/STACK:1024000000,1024000000")#include <algorithm>#include <cctype>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iomanip>#include <iostream>#include <map>#include <queue>#include <string>#include <set>#include <vector>using namespace std;#define pr(x) cout << #x << " = " << x << "  "#define prln(x) cout << #x << " = " << x << endlconst int N = 1e5 + 10, INF = 0x3f3f3f3f, MOD = 1e9 + 7;int n, m;struct Edge {    int v, nxt;    double c;};vector<Edge> edge;int head[N];void add_edge(int u, int v, double c) {    edge.push_back((Edge) {v, head[u], c});    head[u] = edge.size() - 1;}double dp[N];int in[N], cnt[N];bool spfa() {    queue<int> q;    for(int i = 1; i <= n; ++i) {        dp[i] = 0;        in[i] = cnt[i] = 1;        q.push(i);    }    while(q.size()) {        int u = q.front(); q.pop();        in[u] = false;        for(int i = head[u]; ~i; i = edge[i].nxt) {            int v = edge[i].v;            if(dp[v] > dp[u] + edge[i].c) {                dp[v] = dp[u] + edge[i].c;                if(!in[v]) {                    in[v] = true;                    q.push(v);                    if(++cnt[v] > n) return true;                }            }        }    }    return false;}bool check(double x) {    for(auto &e : edge) e.c -= x;    bool ret = spfa();    for(auto &e : edge) e.c += x;    return ret;}int main() {#ifdef LOCAL    freopen("C:\\Users\\TaoSama\\Desktop\\in.txt", "r", stdin);//  freopen("C:\\Users\\TaoSama\\Desktop\\out.txt","w",stdout);#endif    ios_base::sync_with_stdio(0);    int t; scanf("%d", &t);    int kase = 0;    while(t--) {        scanf("%d%d", &n, &m);        edge.clear(); memset(head, -1, sizeof head);        double l = 1e18, r = -1e18;        for(int i = 1; i <= m; ++i) {            int u, v; double c; scanf("%d%d%lf", &u, &v, &c);            add_edge(u, v, c);            l = min(l, c);            r = max(r, c);        }        double maxv = (r += 5);        for(int i = 1; i <= 100; ++i) {            double mid = (l + r) / 2;            if(check(mid)) r = mid;            else l = mid;        }        if(l == maxv) printf("Case #%d: No cycle found.\n", ++kase);        else printf("Case #%d: %.2f\n", ++kase, l);    }    return 0;}