BZOJ2337: [HNOI2011]XOR和路径(期望 高斯消元)

#include<bits/stdc++.h>
using namespace std;
const int MAXN = 1001;
inline int read() {
    int x = 0, f = 1; char c = getchar();
    while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
int N, M, deg[MAXN];
vector<int> a[MAXN][MAXN];
double f[MAXN][MAXN];
void Gauss() {
    for(int i = 1; i <= N - 1; i++) {
        int mx = i;
        for(int j = i + 1; j <= N; j++) if(f[j][i] > f[mx][i]) mx = j;
        if(mx != i) swap(f[i], f[mx]);
        for(int j = 1; j <= N; j++) {
            if(i == j) continue;
            double p = f[j][i] / f[i][i];
            for(int k = i; k <= N + 1; k++) f[j][k] -= f[i][k] * p;
        }
    }
    for(int i = 1; i <= N; i++) f[i][N + 1] /= f[i][i];
}
int main() {
    //freopen("2.in", "r", stdin);
    N = read(); M = read();
    for(int i = 1; i <= M; i++) {
        int x = read(), y = read(), z = read();
        a[x][y].push_back(z); 
        deg[x]++;
        if(x != y) deg[y]++, a[y][x].push_back(z);
    }
    double ans = 0;
    for(int B = 0; B <= 31; B++) {
        memset(f, 0, sizeof(f));
        for(int i = 1; i <= N - 1; i++) {
            f[i][i] = deg[i];
            for(int j = 1; j <= N; j++) {
                for(int k = 0; k < a[i][j].size(); k++) {
                    int w = a[i][j][k];
                    if(w & (1 << B)) {//
                        f[i][N + 1]++;
                        if(j != N) f[i][j]++;
                    } else {
                        if(j != N) f[i][j]--;
                    }
                }
            }
        }
        Gauss();
        ans += (1 << B) * f[1][N + 1];
    }
    printf("%.3lf", ans);
    return 0;
}
/*
3 3 
1 2 4 
1 3 5 
2 3 6
*/