题目链接:https://onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=0&problem=2031&mosmsg=Submission+received+with+ID+26584370
求有向图平均权最小的回路
二分答案 (x),将所有边都减去 (x),看图中是否有负环即可
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 105;
const double eps = 1e-3;
int T, n, m;
int h[maxn], cnt = 0;
struct E{
int to, next;
double cost;
}e[maxn * maxn];
void add(int u, int v, double w){
e[++cnt].to = v;
e[cnt].cost = w;
e[cnt].next = h[u];
h[u] = cnt;
}
int in[maxn], tot[maxn]; double d[maxn];
bool spfa(double mid){
queue<int> q;
memset(tot, 0, sizeof(tot));
memset(in, 0, sizeof(in));
for(int i = 1 ; i <= n ; ++i) {
d[i] = 0;
in[i] = 1;
q.push(i);
}
while(!q.empty()){
int u = q.front(); q.pop(); in[u] = 0;
for(int i = h[u] ; i != -1 ; i = e[i].next){
int v = e[i].to;
if(d[u] + e[i].cost - mid - d[v] < 0){
d[v] = d[u] + e[i].cost - mid;
if(!in[v]){
in[v] = 1;
q.push(v);
++tot[v];
if(tot[v] > n) return false;
}
}
}
}
return true;
}
bool check(double x){
return !spfa(x);
}
ll read(){ ll s = 0, f = 1; char ch = getchar(); while(ch < '0' || ch > '9'){ if(ch == '-') f = -1; ch = getchar(); } while(ch >= '0' && ch <= '9'){ s = s * 10 + ch - '0'; ch = getchar(); } return s * f; }
int main(){
scanf("%d", &T);
int kase = 0;
while(T--){
memset(h, -1, sizeof(h)); cnt = 0;
scanf("%d%d", &n, &m);
int u, v; double w;
double L = 0, R = 0;
for(int i = 1 ; i <= m ; ++i){
scanf("%d%d%lf", &u, &v, &w);
add(u, v, w);
R = max(R, w * 1.0);
}
printf("Case #%d: ", ++kase);
if(!check(R + 1.0)) printf("No cycle found.
");
else {
double ans = 0;
while(R - L > eps){
double mid = (R + L) / 2;
if(check(mid)){
R = mid;
} else{
L = mid;
}
}
printf("%.2lf
", L);
}
}
return 0;
}