Corn Fields +POJ+dp+状态压缩
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Description
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
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
Sample Input
2 31 1 10 1 0
Sample Output
9
Hint
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.
code:
#include<iostream>#include<cstdio>#include<cstring>using namespace std;const int maxn=1<<13;int M,N,top;int state[maxn];///每行能种的状态int cur[maxn];///土地每行的状态int dp[14][maxn];///每行的状态void init(){ int s=1<<N; top=0; for(int i=0; i<s; i++) { if(!(i&(i<<1))) state[++top]=i; }}int main(){ while(~scanf("%d%d",&M,&N)) { init();///求出行内符合的状态 for(int i=1; i<=M; i++) { cur[i]=0; for(int j=1; j<=N; j++) { int num; scanf("%d",&num); if(num==0) { cur[i]+=1<<(N-j);///能种的位置标1,不能种的是0 } } } memset(dp,0,sizeof(dp)); for(int i=1; i<=top; i++) { if(!(state[i]&cur[1])) dp[1][i]=1;///初始化第一行 } for(int i=2; i<=M; i++) for(int j=1; j<=top; j++) { if(!(state[j]&cur[i])) { for(int k=1; k<=top; k++) { if(!(state[j]&state[k])) { if(!(cur[i-1]&state[k])) { dp[i][j]=(dp[i][j]+dp[i-1][k])%100000000; } } } } } int ans=0; for(int j=1; j<=top; j++) { ans=(ans+dp[M][j])%100000000; } printf("%d\n",ans); } return 0;}
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