Date: 2026-06-06
Time: 18:20
number-of-rectangles-that-can-form-the-largest-square/solution.pyThis file solves LeetCode 1725 — given a list of rectangles, determine how many can produce a square with the maximum possible side length. Each rectangle [l, w] can form a square with side min(l, w). The file owns the complete solution logic and exposes it via the standard Solution class.
Solution.numberOfSets(rectangles: List[List[int]]) -> int — the single method. Note the method name numberOfSets doesn't match LeetCode's canonical countGoodRectangles, but the contract is identical: accept a list of [length, width] pairs, return the count of rectangles whose inscribed square side equals the global maximum.
Single-pass max-tracking: Rather than computing all square sides, finding the max, then counting matches (two passes), this does both in one loop. When a new maximum is found, the count resets to 1; when a tie is found, the count increments. This is a common idiom across this repo's solutions — avoid materializing intermediate lists when a running accumulator suffices.
LeetCode Solution class convention: Every problem directory exposes a Solution class with the solving method, matching the structure LeetCode expects. The test files import from this module.
Imports: Only typing.List — no external libraries. The solution is self-contained.
Imported by: number-of-rectangles-that-can-form-the-largest-square/test_solution.py is the direct consumer. The massive "Imported By" list in the prompt is misleading — those are unrelated test files that each import their own local solution.py, not this one.
1. Initialize max_len = 0 and count = 0.
2. For each rectangle [l, w], compute side = min(l, w) — the largest square that fits.
3. If side > maxlen: new global max found, reset count = 1 and update maxlen.
4. Elif side == max_len: another rectangle ties the max, increment count.
5. Return count.
This is O(n) time, O(1) space.
i, max_len equals the maximum min(l, w) seen so far, and count equals exactly how many rectangles achieved that maximum.count is always >= 1 after the first iteration (assuming non-empty input), since the first rectangle always sets a new max.rectangles is non-empty — with an empty list it returns 0, which is arguably correct but undocumented.None. The method trusts its input matches the LeetCode contract (non-empty list of two-element integer lists). No validation, no exceptions. This is consistent with the repo's convention — solutions assume valid input per problem constraints.
number-of-rectangles-that-can-form-the-largest-square/test_solution.py — See what edge cases are tested (empty input, single rectangle, all-equal sides)number-of-rectangles-that-can-form-the-largest-square/review.md — May document the method-name discrepancy (numberOfSets vs countGoodRectangles)construct-the-rectangle/solution.py:Solution — Related geometry problem that goes the other direction (area → optimal rectangle dimensions)single-pass-max-tracking — This pattern (track max + count simultaneously) appears in many solutions; compare with largest-number-at-least-twice-of-others and element-appearing-more-than-25-in-sorted-arraysingle-pass-rectangle-counting — numberOfSets computes the result in O(n) time and O(1) space using a single pass with a running max and countmethod-name-diverges-from-leetcode — The method is named numberOfSets rather than LeetCode's canonical countGoodRectangles, which would break direct LeetCode submission without renaminginscribed-square-side-is-min-dimension — The largest square inscribable in a rectangle [l, w] has side min(l, w), which is the core geometric insight the solution relies onno-input-validation — The method performs no validation on rectangles and will return 0 on empty input rather than raising an error