Codeforces Testing Round #4 B. Smile House 倍增+Floyd

输入:

结点u, v, 两点之前边权 d(u-v), d(v-u);

题意:

给定有向图,带边权,问最小的正环(环的权值和为正数)包含结点个数;

思路:

倍增想法+Floyd判正环

d[p][i][j] 表示 最大间隔为(2^p)的两个点i , j 之间的最长距离; 利用的倍增的思想;

这里的Floyd不是真正的,只是利用那个思想,用来更新当前长度两点间的最大权值;

然后枚举上述的 p ,如果当前新图能形成的正环则继续,如果不能形成正环,那就使用这个图,跟后面的图继续进行floyd操作;


#include<bits/stdc++.h>
using namespace std;
const int maxn = 300 + 7, INF = 1e9;//0x7f7f7f7f;
int n, m;
int d[10][maxn][maxn];
int t[maxn][maxn];
int nd[maxn][maxn];

void work(int c[][maxn], int a[][maxn], int b[][maxn]) {
    for(int i = 1; i <= n; ++i) {
        for(int j = 1; j <= n; ++j) {
            c[i][j] = -INF;
        }
    }
    for(int k = 1; k <= n; ++k) {
        for(int i = 1; i <= n; ++i) {
            for(int j = 1; j <= n; ++j) {
                c[i][j] = max(c[i][j], a[i][k]+b[k][j]);
            }
        }
    }
}
bool is_ok(int a[][maxn]) {
    for(int i = 1; i <= n; ++i) {
        if(a[i][i] > 0) return true;
    }
    return false;
}
void print(int t[][maxn]) {
    for(int i = 1; i <= n; ++i) {
        for(int j = 1; j <= n; ++j) {
            cout << t[i][j] << ' ';
        } cout << endl;
    }
    cout << endl << endl;
}

int main() {
    ios::sync_with_stdio(0); cin.tie(0);
    cin >> n >> m;
    for(int i = 1; i <= n; ++i) {
        for(int j = 1; j <= n; ++j) {
            if(i == j) d[0][i][j] = 0;
            else d[0][i][j] = -INF;
        }
    }
    for(int i = 1; i <= m; ++i) {
        int u, v; cin >> u >> v;
        cin >> d[0][u][v] >> d[0][v][u];
    }
    for(int i = 1; i <= n; ++i) {
        for(int j = 1; j <= n; ++j) {
            t[i][j] = d[0][i][j];
        }
    }
    for(int i = 0; i < 9; ++i) {
        work(d[i+1], d[i], d[i]);
    }
    if(!is_ok(d[9])) {
        cout << 0 << endl; return 0;
    }
    int ans = 1;
    for(int i = 8; i >= 0; --i) {
        work(nd, d[i], t);
        if(!is_ok(nd)) {

            for(int i = 1; i <= n; ++i) {
                for(int j = 1; j <= n; ++j) {
                    t[i][j] = nd[i][j];
                }
            }
            ans += (1<<i);
        }
    }
    cout << ans+1 << endl;
    return 0;
}


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转载自blog.csdn.net/xiang_6/article/details/80488642