POJ 1069 The Bermuda Triangle-优快云博客

本文探讨了一个利用斜坐标系表示点并解决特定数据结构问题的方法。通过使用复杂的代码实现，作者成功地将运行时间压缩到了32毫秒。文章详细介绍了通过递归深度优先搜索算法来尝试填充各种大小的三角形。

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一道考数据结构的好题

要利用好斜坐标系来表示各点，原理网上都有

自己闲着无聊用冗杂的代码压时间，居然压到32ms

#include <iostream>
#include <algorithm>
using namespace std;

#define CHOICE_R 0
#define CHOICE_C 1

int side_len, triangle_num, triangle[15],
 data_map[55][55][2]; //0 正 1 倒
int col_num[55][2];
bool isOK, num_map[26];

bool cmp(const int &a, const int &b)
{
	return a<b;
}

int DFS_ROW(int row, int col, int choice)
{
	int i, j, lenth, k, s, last_lenth;
	bool ok ;
	switch (choice)
	{
	case CHOICE_R:
		for (; col <= col_num[row][1]; col++)
		{
			if (data_map[row][col][0])
			{
				break;
			}
		}
		if (col > col_num[row][1])
		{
			return DFS_ROW(row, col_num[row][0], CHOICE_C);
		}
		last_lenth = col;
		for (i = 0; i< triangle_num; i++)
		{
			lenth = triangle[i];
			if (row+lenth > 2*side_len || col+lenth-1 > col_num[row][1])
			{
				return 0;
			}
			for (k = last_lenth; k < col+lenth; k++)
			{
				if (!data_map[row][k][0])  //已被填充
				{
					return 0;	//失败
				}
			}
			last_lenth = k;
			for (j = row; j< row+lenth; j++)
			{
				for (k = col; k < col+lenth-j+row; k++)
				{
					data_map[j][k][0] = 0;
					if (k != col)
					{
						data_map[j][k][1] = 0;
					}
				}
		
			}//寻找下个点
			ok = 1;
			for (j = col+lenth; j<= col_num[row][1]; j++)
			{
				if (data_map[row][j][0])
				{
					if (DFS_ROW(row, j, CHOICE_R))
					{
						return 1;
					}
					else
					{	
						ok = 0;
					}
					break;
				}
			}
			if (j > col_num[row][1])
			{			
				if (!DFS_ROW(row, col_num[row][0], CHOICE_C))
					ok = 0;
				else
					return 1;
			}
			//恢复点
			if (!ok)
			{
				for (s = row; s< row+lenth; s++)
				{
					for (k = col; k < col+lenth-s+row; k++)
					{
						data_map[s][k][0] = 1;
						if (k != col)
						{
							data_map[s][k][1] = 1;
						}
					}
				}
			}
		}
		break;
	case CHOICE_C:
		for (; col <= col_num[row][1]; col++)
		{
			if (data_map[row][col][1])
			{
				break;
			}
		}
		if (col > col_num[row][1])
		{
			if (row == 2*side_len-1)	//搜索完毕	
				return 1;
			else
				return DFS_ROW(row+1, col_num[row][0], CHOICE_R);
		}
		for (i = 0; i< triangle_num; i++)
		{
			lenth = triangle[i];
			if (row+lenth > 2*side_len || col > col_num[row+lenth-1][1] || col-lenth+1 < col_num[row+lenth-1][0])
			{
				return 0;
			}
			for (j = row, k = col; j< row+lenth && k > col-lenth; j++, k--)
			{
				if (!data_map[j][col][1] || !data_map[j][k][1])
				{
					return 0;
				}
			}
			for (j = row; j< row+lenth; j++)
			{
				for (k = col-j+row; k <= col ; k++)
				{
					data_map[j][k][1] = 0;
					if (k != col)
					{
						data_map[j][k][0] = 0;
					}
				}
				
			}//寻找下个点
			ok = 1;
			for (j = col+1; j<= col_num[row][1]; j++)
			{
				if (data_map[row][j][1])
				{
					if (DFS_ROW(row, j, CHOICE_C))
					{
						return 1;
					}
					else
					{	
						ok = 0;
					}
					break;
				}
			}
			if (j > col_num[row][1])
			{		
				if (row == 2*side_len-1)
					return 1;
				if (!DFS_ROW(row+1, col_num[row+1][0], CHOICE_R))
					ok = 0;
				else
					return 1;
			}
			//恢复点
			if (!ok)
			{
				for (j = row; j< row+lenth; j++)
				{
					for (k = col-j+row; k <= col ; k++)
					{
						data_map[j][k][1] = 1;
						if (k != col)
						{
							data_map[j][k][0] = 1;
						}
					}
				}
			}
		}
		break;
	}
	return 0;
}

inline void solve()
{
	memset(data_map, 0, sizeof(data_map));
	int i, j;
	for (i = 0; i<= side_len; i++)
	{
		for (j = side_len - i; j <= side_len*2; j++)
		{
			data_map[i][j][0] = data_map[i][j][1] = 1;
			if (j == side_len*2)
			{
				data_map[i][j][0] = 0;
			}
		}
		col_num[i][0] = side_len - i;
		col_num[i][1] = side_len*2;
	}
	for (i = side_len; i< 2*side_len; i++)
	{
		for (j = 0; j < 3*side_len-i; j++)
		{
			data_map[i][j][0] = data_map[i][j][1] = 1;
			if ( j == 0 )
			{
				data_map[i][j][1] = 0;
			}
		}
		col_num[i][0] = 0;
		col_num[i][1] = 3*side_len-i-1;
	}
	data_map[side_len][2*side_len][1] = 0;
	if (DFS_ROW(0, side_len, CHOICE_R))
	{
		isOK = 1;
	}
}

int main()
{
	int sum, i, j, k, tmp_triangle[15];
	cin>>sum;
	while (sum--)
	{
		cin>>side_len>>triangle_num;
		isOK = 0;
		k = 0;
		memset(num_map, 0, sizeof(num_map));
		for (i = 0; i< triangle_num; i++)
		{
			cin>>tmp_triangle[i];
			if (side_len % tmp_triangle[i] == 0)
			{
				isOK = 1;
				goto my_stop;
			}
			if (tmp_triangle[i] > side_len)
			{
				isOK = 0;
				goto my_stop;
			}
			if (!num_map[tmp_triangle[i]])
			{
				triangle[k++] = tmp_triangle[i];
				for (j = tmp_triangle[i]; j < 26; j += tmp_triangle[i])
				{
					num_map[j] = 1;
				}
			}
		}
		triangle_num = k;
		sort(triangle, triangle+triangle_num, cmp);
		solve();

my_stop:
		if (isOK)
		{
			printf("YES\n");
		}
		else
		{
			printf("NO\n");
		}
	}
    return 0;
}