0304.Range Sum Query 2D - Immutable

from typing import List

class NumMatrix:
    def __init__(self, matrix: List[List[int]]):
        m, n = len(matrix), len(matrix[0])
        self.s = [[0] * (n + 1) for _ in range(m + 1)]
        for i, row in enumerate(matrix):
            for j, v in enumerate(row):
                self.s[i + 1][j + 1] = (
                    self.s[i][j + 1] + self.s[i + 1][j] - self.s[i][j] + v
                )

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


if __name__ == "__main__":
    mat = [
        [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]
    ]
    obj = NumMatrix(mat)
    print(obj.sumRegion(2,1,4,3)) # 8
    print(obj.sumRegion(1,1,2,2)) # 11
    print(obj.sumRegion(1,2,2,4)) # 12