Tiling 分类： POJ 2015-06-17 15:15 8人阅读 评论(0) 收藏

Tiling

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 8091		Accepted: 3918

Description

In how many ways can you tile a 2xn rectangle by 2x1 or 2x2 tiles?
Here is a sample tiling of a 2x17 rectangle.

Input

Input is a sequence of lines, each line containing an integer number 0 <= n <= 250.

Output

For each line of input, output one integer number in a separate line giving the number of possible tilings of a 2xn rectangle.

Sample Input

2
8
12
100
200

Sample Output

3
171
2731
845100400152152934331135470251
1071292029505993517027974728227441735014801995855195223534251
这个题是一个递推，a[i]=a[i-1]+2*a[i-2],不过要注意零a[0]=1.
#include <cstdio>
#include <string.h>
#include <cmath>
#include <stack>
#include <iostream>
#include <algorithm>
#define WW freopen("output.txt","w",stdout)
using namespace std;
const int Mod=10;
const int Max=200;
int num[300][Max];
int main()
{
    memset(num,0,sizeof(num));
    num[0][0]=0;
    num[1][0]=1;
    num[2][0]=3;
    for(int i=3;i<300;i++)//模拟大数
    {
        for(int j=0;j<Max;j++)
        {
            num[i][j]+=(num[i-1][j]+num[i-2][j]+num[i-2][j]);
            if(num[i][j]>=Mod)
            {
                num[i][j+1]=num[i][j+1]+(num[i][j]/Mod);
                num[i][j]=num[i][j]%Mod;
            }
        }
    }
    int n;
    while(~scanf("%d",&n))
    {
        if(n==0)
        {
            printf("1\n");
            continue;
        }
        bool flag=false;
        for(int i=Max-1;i>=0;i--)
        {
            if(flag)//去前导零
            {
                printf("%d",num[n][i]);
            }
            else
            {
                if(num[n][i])
                {
                    flag=true;
                    printf("%d",num[n][i]);
                }
            }
        }
        printf("\n");
    }
    return 0;
}

 

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