First Solar Panel Placement in a Binary Grid

Given a 2-D binary grid and a solar panel height / width, return the first coordinate where the panel can fit. `0` means empty, `1` means blocked; the round asks for brute force, implementation, tests, and optimization. Requirements Input: a 2-D grid containing 0 and 1. 0 means empty; 1 means blocker. Input: panel height and width. Return the first coordinate where the rectangular panel can fit without covering blockers. Implement the code, write tests, and discuss optimization. Follow-up discussion may ask how to design a system around this placement computation. Notes Brute force checks every top-left coordinate and scans the height x width rectangle. The standard optimization is a 2-D prefix sum over blockers. Then each candidate rectangle can be checked in O(1) by asking whether blocker count is zero. Use an exclusive-prefix matrix of size (rows + 1) x (cols + 1) to avoid boundary branches in rectangle queries. Clarify ordering for 'first coordinate' before coding: row-major top-left is the usual assumption. Edge cases: panel larger than the grid, zero-sized panel, blockers on boundaries, and multiple valid placements. Preparation Implement brute force first, then replace the inner rectangle scan with a 2-D prefix-sum query and compare both outputs on random small grids. Memorize the rectangle formula sum = ps[r2][c2] - ps[r1][c2] - ps[r2][c1] + ps[r1][c1] using exclusive bottom/right indices. Add tests for 1x1 panels, full-grid panels, panel larger than grid, blockers on corners, and row-major tie-breaking.