What is the time complexity of Maximize Area of Square Hole in Grid?

The optimal solution has a time complexity of O(n log n + m log m).

What data structures are used to solve Maximize Area of Square Hole in Grid?

This problem uses Array, Sorting. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Maximize Area of Square Hole in Grid?

Insight 1: The problem requires finding the longest consecutive sequence of bars that are *not* removed in both horizontal and vertical directions. The length of these sequences determines the size of the hole. Insight 2: Sorting the removable bars allows efficient identification of consecutive gaps, which correspond to the lengths of the continuous 'not removed' bars.

Which companies ask LeetCode 2943. Maximize Area of Square Hole in Grid in interviews?

This problem is frequently asked at Swiggy.

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Maximize Area of Square Hole in Grid - LeetCode 2943 Solution

Maximize Area of Square Hole in Grid - Complete Solution Guide

Maximize Area of Square Hole in Grid is LeetCode problem 2943, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given the two integers, n and m and two integer arrays, hBars and vBars . The grid has n + 2 horizontal and m + 2 vertical bars, creating 1 x 1 unit cells. The bars are indexed starting from 1 . You can remove some of the bars in hBars from horizontal bars and some of the bars in vBars from vertical bars. Note that other bars are fixed and cannot be removed. Return an integer denoting the maximum area of a square-shaped hole in the grid, after removing some bars (possibly none). Example

Detailed Explanation

The problem asks us to find the maximum area of a square-shaped hole that can be created in a grid by removing some horizontal and vertical bars. We are given the dimensions of the grid (n and m, implying n+2 horizontal bars and m+2 vertical bars), as well as two arrays, hBars and vBars, containing the indices of horizontal and vertical bars that we *can* remove. The goal is to remove bars such that the largest possible square hole is formed, and we return the area of that square.

Solution Approach

The solution first finds the maximum consecutive length of 'not removed' bars in both horizontal and vertical directions. It achieves this by sorting the removable bars (hBars and vBars) and then iterating through them to identify consecutive sequences. The length of the longest consecutive sequence plus one gives the length of the hole that can be made. Finally, it takes the minimum of these two lengths (horizontal and vertical) to find the side length of the largest possible *square* hole, and returns the area (side * side).

Step-by-Step Algorithm

Step 1: Define a helper function `get_max_len` that takes an array of bar indices as input.
Step 2: Inside `get_max_len`, sort the input array of bar indices.
Step 3: Iterate through the sorted array, keeping track of the current consecutive sequence length and the maximum consecutive sequence length encountered so far.
Step 4: If two consecutive bars are adjacent (differ by 1), increment the current consecutive sequence length. Otherwise, reset it to 1.
Step 5: Update the maximum consecutive sequence length if the current one is larger.
Step 6: Return the maximum consecutive sequence length plus 1 (this represents the number of *unremoved* bars, thus the hole's side length).
Step 7: Call `get_max_len` for both hBars and vBars to get the maximum hole length in the horizontal and vertical directions, respectively.
Step 8: Determine the side length of the largest possible square hole by taking the minimum of the two lengths obtained in the previous step.
Step 9: Calculate and return the area of the square hole by squaring the side length.

Key Insights

Insight 1: The problem requires finding the longest consecutive sequence of bars that are *not* removed in both horizontal and vertical directions. The length of these sequences determines the size of the hole.
Insight 2: Sorting the removable bars allows efficient identification of consecutive gaps, which correspond to the lengths of the continuous 'not removed' bars.
Insight 3: The side length of the largest possible square hole is limited by the smaller of the longest horizontal and vertical consecutive bars not removed.

Complexity Analysis

Time Complexity: O(n log n + m log m)

Space Complexity: O(1)

Topics

This problem involves: Array, Sorting.

Companies

Asked at: Swiggy.

Maximize Area of Square Hole in Grid | LeetCode 2943

Medium

Array Sorting

Time: O(n log n + m log m)Space: O(1)

Solution Code

Available in:

import java.util.Arrays;

class Solution {
    public int maximizeSquareHoleArea(int n, int m, int[] hBars, int[] vBars) {
        
        int max_height = get_max_len(hBars);
        int max_width = get_max_len(vBars);
        
        int side = Math.min(max_height, max_width);
        
        return side * side;
    }

    private int get_max_len(int[] bars) {
        if (bars == null || bars.length == 0) {
            return 1;
        }
        
        Arrays.sort(bars);
        
        int max_consecutive = 1;
        int current_consecutive = 1;
        for (int i = 1; i < bars.length; i++) {
            if (bars[i] == bars[i-1] + 1) {
                current_consecutive += 1;
            } else {
                current_consecutive = 1;
            }
            max_consecutive = Math.max(max_consecutive, current_consecutive);
        }
        
        return max_consecutive + 1;
    }
}

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Problem Info

Description

Problem 2943: Maximize Area of Square Hole in Grid - Detailed explanation and solution approaches.

Topics

Array Sorting

Companies

Swiggy

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2943

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

9 steps

1
Step 1: Define a helper function `get_max_len` that takes an array of bar indices as input.
2
Step 2: Inside `get_max_len`, sort the input array of bar indices.
3
Step 3: Iterate through the sorted array, keeping track of the current consecutive sequence length and the maximum consecutive sequence length encountered so far.
4
Step 4: If two consecutive bars are adjacent (differ by 1), increment the current consecutive sequence length. Otherwise, reset it to 1.
5
Step 5: Update the maximum consecutive sequence length if the current one is larger.
6
Step 6: Return the maximum consecutive sequence length plus 1 (this represents the number of *unremoved* bars, thus the hole's side length).
7
Step 7: Call `get_max_len` for both hBars and vBars to get the maximum hole length in the horizontal and vertical directions, respectively.
8
Step 8: Determine the side length of the largest possible square hole by taking the minimum of the two lengths obtained in the previous step.
9
Step 9: Calculate and return the area of the square hole by squaring the side length.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n log n + m log m)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The dominant operations are the sorting of hBars and vBars. The iteration to find consecutive elements takes O(h) and O(v) time respectively, which are dominated by the sorting complexity. All other operations (min, multiplication) are constant time.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Using a HashSet

Instead of sorting, you could use a HashSet to store the removable bars. Then, iterate through possible hole sizes, checking if all required bars are removable for that size. This could potentially avoid the O(n log n) sorting cost if the number of possible hole sizes is small.

Time: O(N * K), where N is the max(n, m) and K is the number of elements in hBars/vBars. The actual complexity depends on how one implements the checking for each sizeSpace: O(K), where K is the number of elements in hBars/vBars used to create the HashSets

Trade-offs: This approach might be better if the number of removable bars is small, and the number of possible hole sizes to check is even smaller. However, the constant factors might make the sorting approach faster in practice for larger inputs.

✨

Key Insights

1Insight 1: The problem requires finding the longest consecutive sequence of bars that are *not* removed in both horizontal and vertical directions. The length of these sequences determines the size of the hole.
2Insight 2: Sorting the removable bars allows efficient identification of consecutive gaps, which correspond to the lengths of the continuous 'not removed' bars.
3Insight 3: The side length of the largest possible square hole is limited by the smaller of the longest horizontal and vertical consecutive bars not removed.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: Empty hBars or vBars. The `get_max_len` function handles this by returning 1, which correctly accounts for the fixed bars at the edges of the grid.
Edge case 2: n or m being very large. The algorithm's time and space complexity depend on the number of elements in hBars and vBars, not n and m, so large grid dimensions do not pose a problem.
Edge case 3: hBars or vBars containing duplicates. The problem states that all values in hBars and vBars are distinct, so this is not an edge case we need to explicitly handle. However, if duplicates were present, the current algorithm would still produce the correct result because duplicates would not break the consecutive sequence logic.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to add 1 to the longest consecutive sequence length. The longest consecutive sequence length represents the number of gaps between bars that can be removed, but the hole size also depends on the fixed bars which aren't removed.

✗Common mistake 2: Not considering the square shape requirement. It is crucial to take the minimum of the horizontal and vertical hole lengths to ensure the resulting hole is a square.

✗Common mistake 3: Assuming the grid dimensions n and m directly determine the complexity. The complexity depends on the number of removable bars, not the grid size.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Optimizing resource allocation where resources are discrete and contiguous. For example, scheduling tasks on a machine with contiguous time slots or allocating memory blocks.

🏦Real-world scenario 2: Finding the largest clear area in a sensor network or a geographic region where certain locations are blocked or unavailable. The algorithm helps to determine the largest contiguous area that can be used for a specific purpose.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: August 3, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 13

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 6

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jun 29

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Maximize Area of Square Hole in Grid"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether sorting techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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