[状态压缩DP/递推/位运算] Pku/Poj Corn Fields 状态DP入门题详细注释。

 

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.

 

http://poj.org/problem?id=3254

 

直接DFS肯定超时的，记忆化搜索可解，但是状态难以表示。

所以直接用状态DP。转移方程就是  dp[i]=dp[i]+dp[i-1]; 简单递推。

 

 

#include<iostream> #include<cstdio> #include<cstdlib> #include<cstring> using namespace std; const int M = 1<<12; const int MOD = 100000000; int dp[13][M]; int mat[13]; int st[M]; int main() { int n,m,t,idx; while(cin >> n >> m) { idx=0; for(int i=1;i<=n;++i) { int mask=0; for(int j=0;j<m;++j) { scanf("%d",&t); mask|=(t<<j);//地图状态压缩成二进制数1,可种，2不可。 } mat[i]=mask; //cout<<mat[i]<<endl; } for(int i=0;i<=M;++i)//遍历每一种状态2^12。可以表示每一行所有的可能性。 { if(!((i>>1)&i)||!((i<<1)&i))//排除非法状态 比如101和010 ---> 5&2=0 st[++idx]=i;//合法状态 } memset(dp,0,sizeof(dp)); for(int i=1;i<=idx;++i) { if(!(st[i]&(~mat[1])))//表示当前状态合法。 dp[1][st[i]]=1;//自底而上。先解决第一层，按层更新 } for(int i=2;i<=n;++i)//从第二层开始 { for(int j=1;j<=idx;++j)//例举每个状态。 { if(!(st[j]&(~mat[i])))//第i层前状态是否符合地图。 { for(int k=1;k<=idx;++k)//符合则例举和这层相邻的层 { if(!(st[j]&st[k]) && !(st[k]&(~mat[i-1])))//i和i-1层符合 且第i-1层 和第i-1层的地图符合。 { dp[i][st[j]]+=dp[i-1][st[k]];//递推 dp[i][st[j]]%=MOD; } } } } } int ans=0; for(int i=0;i<=M;++i) { ans+=dp[n][i];//将每个状态的终点加起来就是所得答案。 ans%=MOD; } cout<<ans<<endl; } return 0; }  

Accepted

932K

16MS

G++

1589B