poj1681-Painter's-Problem （ 高斯消元）

題目鏈鎖 ： http://poj.org/problem?id=1681

#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;


#define inf 0x3f3f3f3f
#define eps 1e-9
#define mod 100007
#define FOR(i,s,t) for(int i = s; i < t; ++i )
#define REP(i,s,t) for( int i = s; i <= t; ++i )
#define LL long long
#define ULL unsigned long long
#define pii pair
#define MP make_pair
#define lson id << 1 , l , m
#define rson id << 1 | 1 , m + 1 , r 
#define maxn ( 100000+10 )
#define maxe ( 20000+10 )

int a[333][333];
int x[333];
int free_x[333], free_num;
int gauss ( int var, int equ ) {
	int max_r, col, k;
	free_num = 0;
	for( k = 0, col = 0; k < equ && col < var; ++col, ++k ) {
		max_r = k;
		for( int i = k+1; i < equ; ++i ) {
			if( a[i][col] > a[max_r][col] ) 
				max_r = i;
		}
		if( a[max_r][col] == 0 ) {
			free_x[free_num++] = col;
			--k;
			continue;
		}
		if( max_r != k ) {
			for( int j = col; j < var+1; ++j ) 
				swap( a[k][j], a[max_r][j] );
		}
		for( int i = k+1; i < equ ; ++i ) {
			if( a[i][col] )
				for( int j = col;j < var+1; ++j ) 
					a[i][j] ^= a[k][j] ;
		}
	}

	for( int i = k; i < equ; ++i ) {
		if( a[i][col] != 0 ) return -1;
	}

	if( var > k ) return var - k;

	for( int i = var - 1; i >= 0; -- i ) {
		x[i] = a[i][var];
		for( int j = i+1; j < var; ++j ) {
			x[i] ^= ( a[i][j] && x[j] );
		}
	}

	return 0;
}

char  G[33][33];


int main () {
	int T;
	int cas = 1;
	scanf("%d", &T ) ;
	while( T-- ) {
		int n;
		scanf("%d", &n );
		for( int i = 0; i < n; ++i )
			scanf("%s", G[i] );
		memset( a, 0, sizeof( a ) );
		memset( x, 0, sizeof( x ) );
		int m = n * n;
		for( int i = 0; i < n; ++i ) 
			for( int j = 0; j < n; ++j ) 
				if( G[i][j] == 'y' )
					a[i * n + j][m] = 0;
				else a[i* n + j][m] = 1;
		
		for( int i = 0; i < n; ++i ) 
			for( int j = 0; j < n; ++j ) {
				int t = i * n + j;
				a[t][t] = 1;
				if( i > 0 ) a[t-n][t] = 1;
				if( i < n-1 ) a[t+n][t] = 1;
				if( j > 0 ) a[t-1][t] = 1;
				if( j < n-1 ) a[t+1][t] = 1;
			}


		int ans = gauss( m, m );
		if( ans == -1 ) {
			puts("inf" );
		}
		else if( ans == 0 ) {
			int res = 0;
			for( int i = 0; i < m; ++i )
				res += x[i];
			printf("%d\n", res );
		}
		else {
		//枚舉自由變元
			int tot = ( 1 << ans );
			int res = inf;
			for( int i = 0; i < tot; ++i ) {
				int cnt = 0;
				for( int j = 0; j < ans; ++j ) {
					if( ( 1 << j ) & i ) 
						x[free_x[j]] = 1, ++cnt;
					else x[free_x[j]] = 0;
				}
			//how ?
				for( int j = m - 1 - ans; j >= 0; --j ) {
					int id;
					for( id = j; id < m; ++id )
						if( a[j][id] ) break;
					x[id] = a[j][m];
					for( int k = id + 1; k < m; ++k )
						if( a[j][k] ) x[id] ^= x[k];
					cnt += x[id];
				}
				res = min ( res, cnt );
			}
			printf("%d\n", res );
		}
	}
}