BZOJ 1486: [HNOI2009]最小圈( 二分答案 + dfs判负圈 )

二分答案m, 然后全部边权减掉m, 假如存在负圈, 那么说明有平均值更小的圈存在. 负圈用dfs判断.

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#include<bits/stdc++.h>

 

#define rep(i, n) for(int i = 0; i < n; ++i)

#define clr(x, c) memset(x, c, sizeof(x))

#define foreach(i, x) for(__typeof(x.begin()) i = x.begin(); i != x.end(); i++)

 

using namespace std;

 

const int maxn = 3009;

const double eps = 1e-9;

 

struct edge {

int to;

double dist, w;

};

vector<edge> G[maxn];

 

int n;

double d[maxn];

bool vis[maxn], F;

 

void dfs(int x) {

vis[x] = true;

foreach(e, G[x]) if(d[e->to] > d[x] + e->w) {

if(!vis[e->to]) {

   d[e->to] = d[x] + e->w;

   dfs(e->to);

} else

   F = true;

if(F) break;

}

vis[x] = false;

}

 

bool check(double m) {

rep(i, n) {

   foreach(it, G[i]) it->w = it->dist - m;

   vis[i] = false, d[i] = 0;

}

F = false;

rep(i, n) {

dfs(i);

if(F) return true;

}

return false;

}

 

int main() {

freopen("test.in", "r", stdin);

int m;

cin >> n >> m;

rep(i, n) G[i].clear();

while(m--) {

int u, v;

double d;

scanf("%d%d%lf", &u, &v, &d); u--, v--;

G[u].push_back( (edge) {v, d, 0} );

}

double L = -1e7, R = 1e7;

while(R - L > eps) {

double m = (L + R) / 2;

check(m) ? R = m : L = m;

}

printf("%.8lf\n", L);

return 0;

}

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1486: [HNOI2009]最小圈

Time Limit: 10 Sec  Memory Limit: 64 MB
Submit: 1447  Solved: 679
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