BZOJ 2466: [中山市选2009]树 [高斯消元]

2466: [中山市选2009]树

题意：开关上树

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见到拿高斯消元胡就行了

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <bitset>
using namespace std;
typedef unsigned long long ll;
const int N=105;
inline int read() {
	char c=getchar(); int x=0, f=1;
	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, u, v;
bitset<N> a[N];
int now, pivot[N], li[N], val[N];
void gauss() {
	now=1;
	for(int i=1; i<=n; i++) {
		int j=now;
		while(j<=n && !a[j][i]) j++;
		if(j==n+1) {li[++li[0]] = i; continue;}
		if(j!=now) swap(a[now], a[j]);
		for(int j=1; j<=n; j++) if(a[j][i] && j!=now) a[j] ^= a[now];
		pivot[i] = now;
		now++;
	}
	now--;
}
int ans;
void dfs(int d, int tot) { //printf("dfs %d %d\n",d,tot);
	if(d==0) {ans = min(ans, tot); return;}
	if(tot >= ans) return;

	if(pivot[d]) {
		bitset<N> &t = a[pivot[d]];
		int x = t[n+1];
		for(int i=1; i<=li[0]; i++) if(t[li[i]]) x ^= val[li[i]];
		dfs(d-1, tot+x);
	} else {
		val[d]=0; dfs(d-1, tot);
		val[d]=1; dfs(d-1, tot+1);
	}
}

int main() {
	freopen("in","r",stdin);
	while(true) {
		n=read(); if(n==0) break;
		for(int i=1; i<=n; i++) a[i].reset();
		memset(pivot, 0, sizeof(pivot)); memset(li, 0, sizeof(li));
		ans=n;
		for(int i=1; i<n; i++) u=read(), v=read(), a[u][v]=a[v][u]=1;
		for(int i=1; i<=n; i++) a[i][i]=a[i][n+1]=1;
		gauss(); //printf("now %d\n",now); for(int i=1; i<=n; i++) printf("%d ", a[i][n+1]==1); puts("");
		dfs(n, 0);
		printf("%d\n", ans);
	}
}