304.二维区域和检索 - 矩阵不可变.py

# 给定一个二维矩阵，计算其子矩形范围内元素的总和，该子矩阵的左上角为 (row1, col1) ，右下角为 (row2, col2)。
#
#
# 上图子矩阵左上角 (row1, col1) = (2, 1) ，右下角(row2, col2) = (4, 3)，该子矩形内元素的总和为 8。
#
# 示例:
#
# 给定 matrix = [
#   [3, 0, 1, 4, 2],
#   [5, 6, 3, 2, 1],
#   [1, 2, 0, 1, 5],
#   [4, 1, 0, 1, 7],
#   [1, 0, 3, 0, 5]
# ]
#
# sumRegion(2, 1, 4, 3) -> 8
# sumRegion(1, 1, 2, 2) -> 11
# sumRegion(1, 2, 2, 4) -> 12


class NumMatrix:

    def __init__(self, matrix: List[List[int]]):
        if (not matrix):
            return
        m = len(matrix)
        n = len(matrix[0])
        self.dp = [[0] * (n + 1) for _ in range(m + 1)]
        for i in range(1, m + 1):
            for j in range(1, n + 1):
                self.dp[i][j] = self.dp[i - 1][j] + self.dp[i][j - 1] + matrix[i - 1][j - 1] - self.dp[i - 1][j - 1]

    def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:
        return self.dp[row2 + 1][col2 + 1] - self.dp[row2 + 1][col1] - self.dp[row1][col2 + 1] + self.dp[row1][col1]