小美的平衡矩阵

python解法如下：

def solve(i, j, m, sum_all):
    if m*m % 2 == 1:
        return False
    if i == 0 and j == 0 and i + m - 1 < n and j + m - 1 < n and sum_all[i + m - 1][j + m - 1] == m * m / 2:
        return True
    elif i == 0 and j > 0 and i + m - 1 < n and j + m - 1 < n and sum_all[i + m - 1][j + m - 1] - sum_all[i + m - 1][
        j - 1] == m * m / 2:
        return True
    elif j == 0 and i > 0 and i + m - 1 < n and j + m - 1 < n and sum_all[i + m - 1][j + m - 1] - sum_all[i - 1][
        j + m - 1] == m * m / 2:
        return True
    elif i >= 1 and j >= 1 and i + m - 1 < n and j + m - 1 < n and (
            sum_all[i + m - 1][j + m - 1] - sum_all[i + m - 1][j - 1] - sum_all[i - 1][j + m - 1] + sum_all[i - 1][
        j - 1]) == m * m / 2:
        return True
    return False


n = int(input())
a = [[0] * n for _ in range(n)]
for i in range(n):
    l = list(input())
    l = [int(j) for j in l]
    a[i] = l

# 二维前缀和sum_all[i][j]表示从(0, 0)到(i, j)的和
sum_all = [[0]*n for _ in range(n)]
sum_all[0][0] = a[0][0]
for j in range(1, n):
    sum_all[0][j] = sum_all[0][j-1] + a[0][j]
for i in range(1, n):
    sum_all[i][0] = sum_all[i-1][0] + a[i][0]
for i in range(1, n):
    for j in range(1, n):
        sum_all[i][j] = sum_all[i-1][j] + sum_all[i][j-1] - sum_all[i-1][j-1] + a[i][j]

res = [0] * n
for i in range(n):
    for j in range(n):
        for k in range(1, n + 1):
            if solve(i, j, k, sum_all):
                res[k-1] += 1

for i in range(n):
    print(res[i])