[POJ 3254]Corn Fields（狀壓DP）

Description

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Farmer John has purchased a lush new rectangular pasture composed of M by N (1 ≤ M ≤ 12; 1 ≤ N ≤ 12) square parcels. He wants to grow some yummy corn for the cows on a number of squares. Regrettably, some of the squares are infertile and can’t be planted. Canny FJ knows that the cows dislike eating close to each other, so when choosing which squares to plant, he avoids choosing squares that are adjacent; no two chosen squares share an edge. He has not yet made the final choice as to which squares to plant.

Being a very open-minded man, Farmer John wants to consider all possible options for how to choose the squares for planting. He is so open-minded that he considers choosing no squares as a valid option! Please help Farmer John determine the number of ways he can choose the squares to plant.

Input

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Line 1: Two space-separated integers: M and N
Lines 2..M+1: Line i+1 describes row i of the pasture with N space-separated integers indicating whether a square is fertile (1 for fertile, 0 for infertile)

Output

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Line 1: One integer: the number of ways that FJ can choose the squares modulo 100,000,000.

Sample Input

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2 3
1 1 1
0 1 0

Sample Output

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9

Hint

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Number the squares as follows:

1 2 3
4

There are four ways to plant only on one squares (1, 2, 3, or 4), three ways to plant on two squares (13, 14, or 34), 1 way to plant on three squares (134), and one way to plant on no squares. 4+3+1+1=9.

Solution

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一塊矩形要種玉米，有些地方不可以種，而可種的地方也不能有兩塊玉米挨在一起，求方案數

狀壓DP
用i&(i<<1)來判斷一行有沒有相鄰的1
用state[j]&state[k]來判斷有沒有上下相鄰的1
(state[j]&a[1])==state[j]表示state[j]在a[i]上可放

#include<cstring>
#include<cstdlib>
#include<iostream>
#include<cstdio>
#include<string>
#define Mod 100000000
using namespace std;
int m,n;
int f[13][4100],cnt;
int a[13],state[4100];
void init()
{
    memset(f,0,sizeof(f));
    memset(a,0,sizeof(a));
    cnt=0;
    for(int i=0;i<=(1<<n);i++)
    {
        if(!(i&(i<<1)))state[++cnt]=i;
    }
}
int main()
{
    while(~scanf("%d%d",&m,&n))
    {
        init();
        for(int i=1;i<=m;i++)
        {
            int x;
            for(int j=1;j<=n;j++)
            {
                scanf("%d",&x);
                a[i]<<=1;
                a[i]+=x;
            }
        }
        for(int j=1;j<=cnt;j++)
        {
            if((state[j]&a[1])==state[j])f[1][j]=1;
        }
        for(int i=2;i<=m;i++)
        {
            for(int j=1;j<=cnt;j++)
            {
                if((state[j]&a[i])!=state[j])continue;
                for(int k=1;k<=cnt;k++)
                {
                    if(state[j]&state[k])continue;
                    f[i][j]+=f[i-1][k];
                    f[i][j]%=Mod;
                }
            }
        }
        int ans=0;
        for(int i=1;i<=cnt;i++)
        {
            ans+=f[m][i];
            ans%=Mod;
        }
        printf("%d\n",ans);
    }
    return 0;
}