poj 2411 Mondriaan's Dream(状态压缩dP)

题目:http://poj.org/problem?id=2411

Input

The input contains several test cases. Each test case is made up of two integer numbers: the height h and the width w of the large rectangle. Input is terminated by h=w=0. Otherwise, 1<=h,w<=11.

Output

For each test case, output the number of different ways the given rectangle can be filled with small rectangles of size 2 times 1. Assume the given large rectangle is oriented, i.e. count symmetrical tilings multiple times.

题意:一个矩阵,只能放1*2的木块,问将这个矩阵完全覆盖的不同放法有多少种。

思路:一道很经典的状态dp,但是还是很难想,横着放定义为11,竖着放定义为01.

 #include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
using namespace std;
__int64 d[][<<], f[<<];//用———int64,因为有可能数很大
int h, w, full; bool ok(int x) //判断一行里是否出现连续奇数个1,第一行的话不允许
{
int sum = ;
while(x>)
{
if((x&)==)
sum++;
else
{
if((sum&)==)
return false;
sum = ;
}
x = (x>>);
}
if((sum&)==)
return false;
return true;
}
bool check(int x1, int x2)
{
int xx = (<<w)-;
if((x1|x2)==xx&&f[x1&x2])//去掉竖着00和竖着单独11的情况,一定不要忘了单独11的情况
return true;
return false;
}
int main()
{
int i, j, k;
memset(f, , sizeof(f));
full = (<<); for(i = ; i < full; i++)
if(ok(i))
f[i] = ; //记录连续的奇数个1
while(~scanf("%d%d", &h, &w))
{
if(h==&&w==)
break;
full = (<<w);
memset(d, , sizeof(d));
for(i = ; i < full; i++)
if(f[i])
d[][i] = ; for(k = ; k < h; k++)
for(i = ; i < full; i++)
for(j = ; j < full; j++)
{
if(check(i, j))
d[k][i] += d[k-][j];
}
printf("%I64d\n", d[h-][full-]); //最后一行,而且满1
}
return ;
}
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