Dynamic Programming21 sections · 916 units
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LeetCode 304 Range Sum Query 2D - Problem Statement

2D prefix sum queries

This is Range Sum Query 2D (two-dimensional) from LeetCode. Given a 2D matrix, handle multiple queries that each ask for the sum of elements in a rectangle defined by its upper-left (row1,col1)(row1, col1) and lower-right (row2,col2)(row2, col2) corners.

The 1D (one-dimensional) formula was pref[r]pref[l1]pref[r] - pref[l-1]. For 2D, you need something more sophisticated. The 2D version needs 44 prefix sum lookups per query using inclusion-exclusion on the rectangle corners.