Java 代码(记忆化搜索+区间DP)
import java.util.*;
public class Main {
static int N = 15;
static int n, m = 8;
static double X;
static int s[][] = new int[N][N];
static double f[][][][][] = new double[N][N][N][N][N];
static Scanner sc = new Scanner(System.in);
public static void main(String[] args) {
n = sc.nextInt();
for (int i = 1; i <= m; i++)
for (int j = 1; j <= m; j++) {
s[i][j] = sc.nextInt();
s[i][j] += s[i - 1][j] + s[i][j - 1] - s[i - 1][j - 1];
}
for (int i1 = 0; i1 < N; i1++)
for (int i2 = 0; i2 < N; i2++)
for (int i3 = 0; i3 < N; i3++)
for (int i4 = 0; i4 < N; i4++)
Arrays.fill(f[i1][i2][i3][i4], -1);
X = (double) s[m][m] / n;
System.out.printf("%.3f\n", Math.sqrt(dp(1, 1, 1, m, m) / n));
}
static double get(int x1, int y1, int x2, int y2) {
double sum = s[x2][y2] - s[x1 - 1][y2] - s[x2][y1 - 1] + s[x1 - 1][y1 - 1] - X;
return sum * sum;
}
static double dp(int k, int x1, int y1, int x2, int y2) {
if (f[k][x1][y1][x2][y2] >= 0) return f[k][x1][y1][x2][y2];
if (k == n) return f[k][x1][y1][x2][y2] = get(x1, y1, x2, y2);
double t = 1e9;
for (int i = x1; i < x2; i++) {
t = Math.min(t, dp(k + 1, x1, y1, i, y2) + get(i + 1, y1, x2, y2));
t = Math.min(t, dp(k + 1, i + 1, y1, x2, y2) + get(x1, y1, i, y2));
}
for (int i = y1; i < y2; i++) {
t = Math.min(t, dp(k + 1, x1, y1, x2, i) + get(x1, i + 1, x2, y2));
t = Math.min(t, dp(k + 1, x1, i + 1, x2, y2) + get(x1, y1, x2, i));
}
return f[k][x1][y1][x2][y2] = t;
}
}