leetcode304

class NumMatrix:
    def __init__(self, matrix: 'List[List[int]]'):
        self.matrix = matrix
        m,n = 0,0
        m = len(matrix)
        if m > 0:
            n = len(matrix[0])
        self.prefix = [[0 for _ in range(n)]for _ in range(m)]
        for i in range(m):
            for j in range(n):
                if j == 0:
                    self.prefix[i][j] = matrix[i][j]
                else:
                    self.prefix[i][j] = self.prefix[i][j-1] + matrix[i][j]
        #print(self.prefix)
        for j in range(n):
            for i in range(1,m):
                self.prefix[i][j] = self.prefix[i-1][j] + self.prefix[i][j]
        #print(self.prefix)

    def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:
        if row1 == row2  and col1 == col2:
            return self.matrix[row1][col1]
        botton_right = self.prefix[row2][col2]
        botton_left = 0
        if col1 > 0:
            botton_left = self.prefix[row2][col1-1]
        top_right = 0
        if row1 > 0:
            top_right = self.prefix[row1-1][col2]
        top_left = 0
        if row1 > 0 and col1 > 0:
            top_left = self.prefix[row1-1][col1-1]

        return botton_right - botton_left - top_right + top_left

算法思路：二维数组。

这道题目是二维数组区域求和的常见题型，先计算从(0,0)点到(i,j)点的累加和。

然后再用四个矩形区域的加减运算，求出局部矩形的和。