Range Sum Query 2D - Immutable — LeetCode 304 Python Solution

The problem

Given a 2D matrix matrix, handle multiple queries of the following type: Calculate the sum of the elements of matrix inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2). Implement the NumMatrix class: NumMatrix(int[][] matrix) Initializes the object with the integer matrix matrix.

Example

Input

["NumMatrix", "sumRegion", "sumRegion", "sumRegion"]

Output

[null, 8, 11, 12]

Explanation

NumMatrix numMatrix = new NumMatrix([[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]]);

Python solution

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]
        )


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

Complexity

Pattern: Prefix Sum

Precompute running totals once so any range query becomes a single subtraction. LeetCode 304. Range Sum Query 2D - Immutable is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Prefix Sum.

The prefix sum guide has the Python template for the pattern and the 157 LeetCode problems that use it.

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