Leetcode #2975: Maximum Square Area by Removing Fences From a Field
In this guide, we solve Leetcode #2975 Maximum Square Area by Removing Fences From a Field 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
There is a large (m - 1) x (n - 1) rectangular field with corners at (1, 1) and (m, n) containing some horizontal and vertical fences given in arrays hFences and vFences respectively. Horizontal fences are from the coordinates (hFences[i], 1) to (hFences[i], n) and vertical fences are from the coordinates (1, vFences[i]) to (m, vFences[i]).
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Hash Table, Enumeration
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: m = 4, n = 3, hFences = [2,3], vFences = [2]
Output: 4
Explanation: Removing the horizontal fence at 2 and the vertical fence at 2 will give a square field of area 4.
Python Solution
class Solution:
def maximizeSquareArea(
self, m: int, n: int, hFences: List[int], vFences: List[int]
) -> int:
def f(nums: List[int], k: int) -> Set[int]:
nums.extend([1, k])
nums.sort()
return {b - a for a, b in combinations(nums, 2)}
mod = 10**9 + 7
hs = f(hFences, m)
vs = f(vFences, n)
ans = max(hs & vs, default=0)
return ans**2 % mod if ans else -1
Complexity
The time complexity is , and the space complexity is . 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.