Leetcode #1725: Number Of Rectangles That Can Form The Largest Square
In this guide, we solve Leetcode #1725 Number Of Rectangles That Can Form The Largest Square in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an array rectangles where rectangles[i] = [li, wi] represents the ith rectangle of length li and width wi. You can cut the ith rectangle to form a square with a side length of k if both k <= li and k <= wi.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Array
Intuition
The constraints allow a direct scan that keeps only the essential state.
By translating the requirements into a clean loop, the logic stays easy to reason about.
Approach
Iterate through the data once, updating the state needed to compute the answer.
Return the final state after the traversal is complete.
Steps:
- Parse the input.
- Iterate and update state.
- Return the computed answer.
Example
Input: rectangles = [[5,8],[3,9],[5,12],[16,5]]
Output: 3
Explanation: The largest squares you can get from each rectangle are of lengths [5,3,5,5].
The largest possible square is of length 5, and you can get it out of 3 rectangles.
Python Solution
class Solution:
def countGoodRectangles(self, rectangles: List[List[int]]) -> int:
ans = mx = 0
for l, w in rectangles:
x = min(l, w)
if mx < x:
ans = 1
mx = x
elif mx == x:
ans += 1
return ans
Complexity
The time complexity is , where is the length of the array . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.