POJ 2032 Square Carpets

最新推荐文章于 2019-09-11 19:34:19 发布

原创最新推荐文章于 2019-09-11 19:34:19 发布 · 695 阅读

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#IDA #不等式缩小剪枝

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博客介绍了如何解决POJ 2032编程题，涉及关键算法IDA和不等式缩小剪枝技术。通过题目链接可以查看详细题目，注释代码部分展示了具体的解题思路。

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题目大意：

题目链接

注释代码：

/*                                       
 * Problem ID : POJ 2032 Square Carpets
 * Author     : Lirx.t.Una                                       
 * Language   : C++                           
 * Run Time   : 0 ms                                       
 * Run Memory : 180 KB                                       
*/

#include <iostream>
#include <climits>
#include <cstring>
#include <cstdio>
#include <bitset>
#include <vector>

#define	MAXW	10

using namespace std;

bitset<MAXW + 1>			g[MAXW + 1];
char						dp_w[MAXW + 1][MAXW + 1];
vector<pair<char, char> >	cov;
vector<char>				to_cov[MAXW + 1][MAXW + 1];
bool						vis_cov[MAXW * MAXW];
bool						cp_vis_cov[MAXW * MAXW];

int		w, h;
int		hval;
int		bound;
int		stp;

inline int
min( int a, int b ) {

	return a < b ? a : b;
}

int
h_val(void) {

	int		i, j, k;
	int		lft;

	memcpy(cp_vis_cov, vis_cov, sizeof(vis_cov));

	lft = 0;
	for ( i = 1; i <= h; i++ )
		for ( j = 1; j <= w; j++ )
			if ( g[i][j] ) {
			
				for ( k = 0; k < to_cov[i][j].size(); k++ )
					if ( cp_vis_cov[ to_cov[i][j][k] ] )
						goto _h_val_CONT_;
				
				lft++;
				for ( k = 0; k < to_cov[i][j].size(); k++ )
					cp_vis_cov[ to_cov[i][j][k] ] = true;

_h_val_CONT_:	continue;
			}

	return lft;
}

int
dfs( int x, int y ) {

	int		k;
	int		tmp_bound;
	int		ret_bound;

	if ( !hval ) return -1;
	if ( hval + stp > bound ) return hval + stp;

	if ( y > w ) { y = 1; x++; }

	if ( !g[x][y] ) return dfs( x, y + 1 );
	for ( k = 0; k < to_cov[x][y].size(); k++ )
		if ( vis_cov[ to_cov[x][y][k] ] )
			return dfs( x, y + 1 );

	ret_bound = INT_MAX;
	for ( k = 0; k < to_cov[x][y].size(); k++ ) {
	
		vis_cov[ to_cov[x][y][k] ] = true; hval = h_val();
		stp++;
		if ( ( tmp_bound = dfs( x, y + 1 ) ) == -1 ) return -1;
		stp--;
		vis_cov[ to_cov[x][y][k] ] = false;

		ret_bound = min( ret_bound, tmp_bound );
	}

	return ret_bound;
}

int
main() {

	int		i, j, k;
	int		x, y;
	int		bit;

	while ( scanf("%d%d", &w, &h), w ) {
	
		memset(vis_cov, 0, sizeof(vis_cov));

		for ( i = 1; i <= h; i++ )
			for ( j = 1; j <= w; j++ ) {

				scanf("%d", &bit);
				g[i][j] = bit;
			}

		cov.clear();
		for ( i = 1; i <= w; i++ ) dp_w[h][i] = g[h][i];
		for ( i = 1; i <= h; i++ ) dp_w[i][w] = g[i][w];
		for ( i = h - 1; i > 0; i-- )
			for ( j = w - 1; j > 0; j-- )
				dp_w[i][j] = !g[i][j] ? 0 :
					1 + min( min( dp_w[i + 1][j], dp_w[i][j + 1] ),
						     dp_w[i + 1][j + 1] );

		for ( i = 1; i <= h; i++ )
			for ( j = 1; j <= w; j++ )
				if ( g[i][j] ) {
				
					for ( x = 1; x <= i; x++ )
						for ( y = 1; y <= j; y++ ) {

							if ( x == i && y == j ) continue;
							if ( x + dp_w[x][y] >= i + dp_w[i][j] &&
								 y + dp_w[x][y] >= j + dp_w[i][j] )
								goto _CONT_;
						}

					cov.push_back(make_pair(i, j));
_CONT_:				continue;
				}

		for ( i = 1; i <= h; i++ )
			for ( j = 1; j <= w; j++ )
				if ( g[i][j] ) {
				
					to_cov[i][j].clear();
					for ( k = 0; k < cov.size(); k++ ) {
					
						x = cov[k].first;
						y = cov[k].second;

						if ( x <= i && y <= j &&
							 x + dp_w[x][y] > i &&
							 y + dp_w[x][y] > j )
							to_cov[i][j].push_back(k);
					}
				}

		for ( stp = 0, bound = 0, hval = h_val(); bound != -1; bound = dfs( 1, 1 ) );
		printf("%d\n", stp);
	}

	return 0;
}

无注释代码：

#include <iostream>
#include <climits>
#include <cstring>
#include <cstdio>
#include <bitset>
#include <vector>

#define	MAXW	10

using namespace std;

bitset<MAXW + 1>			g[MAXW + 1];
char						dp_w[MAXW + 1][MAXW + 1];
vector<pair<char, char> >	cov;
vector<char>				to_cov[MAXW + 1][MAXW + 1];
bool						vis_cov[MAXW * MAXW];
bool						cp_vis_cov[MAXW * MAXW];

int		w, h;
int		hval;
int		bound;
int		stp;

inline int
min( int a, int b ) {

	return a < b ? a : b;
}

int
h_val(void) {

	int		i, j, k;
	int		lft;

	memcpy(cp_vis_cov, vis_cov, sizeof(vis_cov));

	lft = 0;
	for ( i = 1; i <= h; i++ )
		for ( j = 1; j <= w; j++ )
			if ( g[i][j] ) {
			
				for ( k = 0; k < to_cov[i][j].size(); k++ )
					if ( cp_vis_cov[ to_cov[i][j][k] ] )
						goto _h_val_CONT_;
				
				lft++;
				for ( k = 0; k < to_cov[i][j].size(); k++ )
					cp_vis_cov[ to_cov[i][j][k] ] = true;

_h_val_CONT_:	continue;
			}

	return lft;
}

int
dfs( int x, int y ) {

	int		k;
	int		tmp_bound;
	int		ret_bound;

	if ( !hval ) return -1;
	if ( hval + stp > bound ) return hval + stp;

	if ( y > w ) { y = 1; x++; }

	if ( !g[x][y] ) return dfs( x, y + 1 );
	for ( k = 0; k < to_cov[x][y].size(); k++ )
		if ( vis_cov[ to_cov[x][y][k] ] )
			return dfs( x, y + 1 );

	ret_bound = INT_MAX;
	for ( k = 0; k < to_cov[x][y].size(); k++ ) {
	
		vis_cov[ to_cov[x][y][k] ] = true; hval = h_val();
		stp++;
		if ( ( tmp_bound = dfs( x, y + 1 ) ) == -1 ) return -1;
		stp--;
		vis_cov[ to_cov[x][y][k] ] = false;

		ret_bound = min( ret_bound, tmp_bound );
	}

	return ret_bound;
}

int
main() {

	int		i, j, k;
	int		x, y;
	int		bit;

	while ( scanf("%d%d", &w, &h), w ) {
	
		memset(vis_cov, 0, sizeof(vis_cov));

		for ( i = 1; i <= h; i++ )
			for ( j = 1; j <= w; j++ ) {

				scanf("%d", &bit);
				g[i][j] = bit;
			}

		cov.clear();
		for ( i = 1; i <= w; i++ ) dp_w[h][i] = g[h][i];
		for ( i = 1; i <= h; i++ ) dp_w[i][w] = g[i][w];
		for ( i = h - 1; i > 0; i-- )
			for ( j = w - 1; j > 0; j-- )
				dp_w[i][j] = !g[i][j] ? 0 :
					1 + min( min( dp_w[i + 1][j], dp_w[i][j + 1] ),
						     dp_w[i + 1][j + 1] );

		for ( i = 1; i <= h; i++ )
			for ( j = 1; j <= w; j++ )
				if ( g[i][j] ) {
				
					for ( x = 1; x <= i; x++ )
						for ( y = 1; y <= j; y++ ) {

							if ( x == i && y == j ) continue;
							if ( x + dp_w[x][y] >= i + dp_w[i][j] &&
								 y + dp_w[x][y] >= j + dp_w[i][j] )
								goto _CONT_;
						}

					cov.push_back(make_pair(i, j));
_CONT_:				continue;
				}

		for ( i = 1; i <= h; i++ )
			for ( j = 1; j <= w; j++ )
				if ( g[i][j] ) {
				
					to_cov[i][j].clear();
					for ( k = 0; k < cov.size(); k++ ) {
					
						x = cov[k].first;
						y = cov[k].second;

						if ( x <= i && y <= j &&
							 x + dp_w[x][y] > i &&
							 y + dp_w[x][y] > j )
							to_cov[i][j].push_back(k);
					}
				}

		for ( stp = 0, bound = 0, hval = h_val(); bound != -1; bound = dfs( 1, 1 ) );
		printf("%d\n", stp);
	}

	return 0;
}