Maximum Square Area by Removing Fences From a Field — Algorithm Visualization & Coding Challenge

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Understanding Maximum Square Area by Removing Fences From a Field

Detailed explanation and reference materials

Problem Overview

🟦 Maximum Square Area by Removing Fences From a Field

Difficulty: Medium
Topics: Geometry, Math, Sets

🌾 Problem Overview

You are given a large rectangular field of size (m − 1) × (n − 1) with corners at:

(1, 1)
(m, n)

Inside the field, there are:

Horizontal fences → provided in hFences
Vertical fences → provided in vFences

Your task is to remove some fences (possibly none) and determine the maximum possible area of a square field that can be formed.

If it’s impossible to form a square, return -1.

⚠️ Since the result can be very large, return the answer (10^9 + 7).

🧱 Fence Details

Horizontal Fences

Each horizontal fence is located at:

(hFences[i], 1) → (hFences[i], n)

Vertical Fences

Each vertical fence is located at:

(1, vFences[i]) → (m, vFences[i])

🚧 Boundary Fences (Cannot Be Removed)

The field is permanently surrounded by 4 fences:

Top: (1, 1) → (1, n)
Bottom: (m, 1) → (m, n)
Left: (1, 1) → (m, 1)
Right: (1, n) → (m, n)

These fences cannot be removed.

🎯 Objective

Find the largest square area that can be formed by removing some internal fences.

✅ Return the maximum square area
❌ Return -1 if no square can be formed

🧪 Examples

✅ Example 1

Input

m = 4, n = 3
hFences = [2, 3]
vFences = [2]

Output

Explanation
Removing:

Horizontal fence at 2
Vertical fence at 2

Creates a 2 × 2 square, so area = 4.

❌ Example 2

Input

m = 6, n = 7
hFences = [2]
vFences = [4]

Output

-1

Explanation
No possible way to remove fences to form a square.

📌 Constraints

\begin{aligned} &3 \le m, n \le 10^9 \\ &1 \le |hFences|, |vFences| \le 600 \\ &1 < hFences[i] < m \\ &1 < vFences[i] < n \end{aligned}

All fence positions are unique
Boundary fences cannot be removed

— Written by Saurabh Patil • B.Tech CSE • Software Developer

Reference Link

https://leetcode.com/problems/maximum-square-area-by-removing-fences-from-a-field/

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