poj1191

 1 #include <iostream>
 2 #include <cmath>
 3 #include <cstring>
 4 #include <cstdio>
 5 using namespace std;
 6 
 7 const int nMax = 15;
 8 const int size = 9;
 9 const int INF = 100000000;
10 
11 int dp[nMax][size][size][size][size];
12 int sum[size][size];   //左上角为(1,1)的矩形的和
13 
14 int getSum(int x1, int y1, int x2, int y2)
15 {
16     return sum[x2][y2] - sum[x1-1][y2] - sum[x2][y1-1] + sum[x1-1][y1-1];
17 }
18 
19 int cut(int k, int x1, int y1, int x2, int y2)
20 {
21     if(dp[k][x1][y1][x2][y2] != -1)
22     {
23         return dp[k][x1][y1][x2][y2];
24     }
25 
26     if(k == 1)
27     {
28         int t1 = getSum(x1, y1, x2, y2);
29         return (dp[k][x1][y1][x2][y2] = t1*t1);
30     }
31 
32     int minVal = INF, tmp;
33     for(int i = x1; i < x2; ++i)      //纵向切割
34     {
35         int t1 = getSum(x1, y1, i, y2);
36         int t2 = getSum(i+1, y1, x2, y2);
37         tmp = min(cut(k-1, i+1, y1, x2, y2) + t1*t1, cut(k-1, x1, y1, i, y2) + t2*t2);
38         if(minVal > tmp)
39         {
40             minVal = tmp;
41         }
42     }
43 
44     for(int i = y1; i < y2; ++i) //横向切割
45     {
46         int t1 = getSum(x1, y1, x2, i);
47         int t2 = getSum(x1, i+1, x2, y2);
48         tmp = min(cut(k-1, x1, i+1, x2, y2) + t1*t1, cut(k-1, x1, y1, x2, i) + t2*t2);
49         if(minVal > tmp)
50         {
51             minVal = tmp;
52         }
53     }
54 
55     return (dp[k][x1][y1][x2][y2] = minVal);
56 }
57 
58 int main()
59 {
60     int n;
61 
62     memset(dp, -1, sizeof(dp));
63     memset(sum, 0, sizeof(sum));
64 
65     cin>>n;
66     int tot = 0;
67     for(int i = 1; i <= 8; ++i)
68     {
69         for(int j = 1; j <= 8; ++j)
70         {
71             int val;
72             cin>>val;
73             tot += val;
74             sum[i][j] = sum[i-1][j] + sum[i][j-1] - sum[i-1][j-1] + val;
75         }
76     }
77 
78     int res = cut(n, 1, 1, size-1, size-1);
79 
80     double avrg = tot*1.0/n;
81     double ans = sqrt(res*1.0/n-avrg*avrg);
82     printf("%.3f\n", ans);
83 
84     return 0;
85 }