leetcode1314

class Solution:
    def matrixBlockSum(self, mat: 'List[List[int]]', K: int) -> 'List[List[int]]':
        r,c = len(mat),len(mat[0])
        prefixsum = [[0 for _ in range(c)]for _ in range(r)]
        for i in range(r):
            prefixsum[i][0] = mat[i][0]
            for j in range(1,c):
                prefixsum[i][j] = mat[i][j] + prefixsum[i][j-1]
        for j in range(c):
            for i in range(1,r):
                prefixsum[i][j] = prefixsum[i-1][j] + prefixsum[i][j]
        #print(prefixsum)
        res = [[0 for _ in range(c)]for _ in range(r)]
        for i in range(r):
            for j in range(c):
                r_low,r_high = max(i - K,0),min(i + K,r-1)
                c_low,c_high = max(j - K,0),min(j + K,c-1)
                #print(r_low,c_low,r_high,c_high)
                
                if r_low >= 1 and c_low >= 1:
                    res[i][j] = prefixsum[r_high][c_high] - prefixsum[r_low-1][c_high] - prefixsum[r_high][c_low-1] + prefixsum[r_low-1][c_low-1]
                elif r_low >= 1 and c_low == 0:
                    res[i][j] = prefixsum[r_high][c_high] - prefixsum[r_low-1][c_high]
                elif r_low == 0 and c_low >= 1:
                    res[i][j] = prefixsum[r_high][c_high] - prefixsum[r_high][c_low-1]
                else:
                    res[i][j] = prefixsum[r_high][c_high]
        return res

算法思路：二维矩阵求和。

先计算前序和，然后计算矩形子区域的和。共分4种情况讨论。