class NumMatrix:

    def __init__(self, matrix: List[List[int]]):
        if matrix is None or not matrix:
            return
        n, m = len(matrix), len(matrix[0])
        self.sums = [ [0 for j in range(m + 1)] for i in range(n + 1) ]
        for i in range(1, n + 1):
            for j in range(1, m + 1):
                self.sums[i][j] = matrix[i - 1][j - 1] + self.sums[i][j - 1] + self.sums[i - 1][j] - self.sums[i - 1][j - 1]

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

# Your NumMatrix object will be instantiated and called as such:
# obj = NumMatrix(matrix)
# param_1 = obj.sumRegion(row1,col1,row2,col2)

# The idea is simple, just precompute sums for all matrices with (0, 0) as top left corner and (i, j) as bottom right corner. There are O(n^2) of these matrices, so we store them in a 2D table. In order to make code simpler, I add an extra column and row, filled with 0.
"""
304. Range Sum Query 2D - Immutable
Medium

809

164

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Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

Range Sum Query 2D
The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, col2) = (4, 3), which contains sum = 8.

Example:
Given 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
Note:
You may assume that the matrix does not change.
There are many calls to sumRegion function.
You may assume that row1 ≤ row2 and col1 ≤ col2.
"""