POJ 2411 Mondriaan’s Dream

题目链接：POJ 2411 Mondriaan’s Dream

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Problem Description

Squares and rectangles fascinated the famous Dutch painter Piet Mondriaan. One night, after producing the drawings in his ‘toilet series’ (where he had to use his toilet paper to draw on, for all of his paper was filled with squares and rectangles), he dreamt of filling a large rectangle with small rectangles of width 2 and height 1 in varying ways.

Expert as he was in this material, he saw at a glance that he’ll need a computer to calculate the number of ways to fill the large rectangle whose dimensions were integer values, as well. Help him, so that his dream won’t turn into a nightmare!

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.

Sample Input

1 2
1 3
1 4
2 2
2 3
2 4
2 11
4 11
0 0

Sample Output

1
0
1
2
3
5
144
51205

题意：

给你n∗m（1<=n,m<=11）的方格矩阵，要求用1∗2的多米诺骨牌去填充，问有多少种填充方法。

AC代码：

#include <stdio.h>#include <string.h>#include <math.h>#include <stdlib.h>#include <algorithm>#include <iostream>#include <locale>#include <vector>#include <string>#include <iomanip>#include <cstdio>#include <cstring>#include <stack>#include <queue>#include <map>#include <set>#include <functional>using namespace std;int h,w;int way;long long dp[15][1<<15];int path[4200000][2];void get(int c,int pre,int now){    if(c>w)        return;    else if(c==w)    {        path[way][0]=pre;        path[way++][1]=now;        return;    }    get(c+1,(pre<<1)|1,(now<<1));    get(c+1,(pre<<1),(now<<1)|1);    get(c+2,(pre<<2)|3,(now<<2)|3);}int main(){    while(~scanf("%d%d",&h,&w),h+w)    {        way=0;        if(h<w)            swap(h,w);        get(0,0,0);        memset(dp,0,sizeof dp);        dp[0][(1<<w)-1]=1;        for(int i=0;i<h;i++)            for(int j=0;j<way;j++)                dp[i+1][path[j][1]]+=dp[i][path[j][0]];        printf("%lld\n",dp[h][(1<<w)-1]);    }    return 0;}