POJ 1191 DP+DFS棋盘分割问题

 1 #include <cstdio>
 2 #include <cstring>
 3 #include <cmath>
 4 #include <algorithm>
 5 using namespace std;
 6 #define INF 0x3f3f3f3f
 7 int dp[15][9][9][9][9],val[9][9],n;
 8 
 9 int sum(int x1,int y1,int x2,int y2)
10 {
11     int ans=val[x2][y2]-val[x1-1][y2]-val[x2][y1-1]+val[x1-1][y1-1];
12     return ans*ans;
13 }
14 
15 int dfs(int k,int x1,int y1,int x2,int y2)
16 {
17     if(dp[k][x1][y1][x2][y2]) return dp[k][x1][y1][x2][y2];
18     if(k==1||x1==x2||y1==y2){
19         dp[k][x1][y1][x2][y2]= sum(x1,y1,x2,y2);
20         return dp[k][x1][y1][x2][y2];
21     }
22     int nowstate=INF;
23     for(int i=x1;i<x2;i++){
24         nowstate=min(nowstate,dfs(k-1,i+1,y1,x2,y2)+sum(x1,y1,i,y2));
25         nowstate=min(nowstate,dfs(k-1,x1,y1,i,y2)+sum(i+1,y1,x2,y2));
26     }
27     for(int i=y1;i<y2;i++){
28         nowstate=min(nowstate,dfs(k-1,x1,i+1,x2,y2)+sum(x1,y1,x2,i));
29         nowstate=min(nowstate,dfs(k-1,x1,y1,x2,i)+sum(x1,i+1,x2,y2));
30     }
31     dp[k][x1][y1][x2][y2]=nowstate;
32     return nowstate;
33 }
34 
35 void change()
36 {
37     for(int i=0;i<=8;i++)
38         val[i][0]=0,val[0][i]=0;
39 
40     for(int i=1;i<=8;i++)
41         for(int j=1;j<=8;j++)
42             val[i][j]+=val[i-1][j]+val[i][j-1]-val[i-1][j-1];
43 }
44 
45 int main()
46 {
47     while(~scanf("%d",&n)){
48 
49         memset(dp,0,sizeof(dp));
50 
51         for(int i=1;i<=8;i++)
52             for(int j=1;j<=8;j++)
53                 scanf("%d",&val[i][j]);
54 
55         change();
56 
57         double res;
58         double ave=1.0*val[8][8]/n;
59         res=sqrt((double)dfs(n,1,1,8,8)/n-ave*ave);
60         printf("%.3f\n", res);
61     }
62     return 0;
63 }