What is the time complexity of Largest Local Values in a Matrix?

The optimal solution has a time complexity of O(n^2).

What is the space complexity of Largest Local Values in a Matrix?

The space complexity is O(n^2).

What data structures are used to solve Largest Local Values in a Matrix?

This problem uses Array, Matrix. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Largest Local Values in a Matrix?

The problem can be solved efficiently using nested loops to iterate through all possible 3x3 submatrices. No sophisticated data structures are needed; simple nested loops and a `max` function are sufficient.

Which companies ask LeetCode 2373. Largest Local Values in a Matrix in interviews?

This problem is frequently asked at OpenAI.

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Largest Local Values in a Matrix - LeetCode 2373 Solution

Largest Local Values in a Matrix - Complete Solution Guide

Largest Local Values in a Matrix is LeetCode problem 2373, a Easy 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 an n x n integer matrix grid . Generate an integer matrix maxLocal of size (n - 2) x (n - 2) such that: maxLocal[i][j] is equal to the largest value of the 3 x 3 matrix in grid centered around row i + 1 and column j + 1 . In other words, we want to find the largest value in every contiguous 3 x 3 matrix in grid . Return the generated matrix . Example 1: Input: grid = [[9,9,8,1],[5,6,2,6],[8,2,6,4],[6,2,2,2]] Output: [[9,9],[8,6]] Explanation: The diagram above shows the original ma

Detailed Explanation

The problem asks you to find the largest value within each 3x3 submatrix of a given square matrix (n x n). The input is an n x n integer matrix `grid`. The output is an (n-2) x (n-2) matrix `maxLocal`, where each element `maxLocal[i][j]` represents the maximum value found in the 3x3 submatrix centered at `grid[i+1][j+1]`. The problem emphasizes that the submatrices are always 3x3 and contiguous within the larger matrix. Constraints limit the size of the input matrix (3 ≤ n ≤ 100) and the range of values within the matrix (1 ≤ grid[i][j] ≤ 100).

Solution Approach

The provided solutions use a brute-force approach. They iterate through each possible 3x3 submatrix within the input grid. For each submatrix, they find the maximum value among its nine elements and store this maximum value in the corresponding position in the output matrix `maxLocal`. This approach is straightforward and easy to understand.

Step-by-Step Algorithm

Initialize an (n-2) x (n-2) matrix `maxLocal` to store the results.
Iterate through each possible starting row index `i` from 0 to n-3.
For each `i`, iterate through each possible starting column index `j` from 0 to n-3.
For each `(i, j)` pair, iterate through the 3x3 submatrix centered at `grid[i+1][j+1]`, finding the maximum value.
Store the maximum value found in step 4 at `maxLocal[i][j]`.
Return the `maxLocal` matrix.

Key Insights

The problem can be solved efficiently using nested loops to iterate through all possible 3x3 submatrices.
No sophisticated data structures are needed; simple nested loops and a `max` function are sufficient.
The output matrix will always be smaller than the input matrix by a border of one row and one column on each side, because 3x3 submatrices can't be formed at the edges.

Complexity Analysis

Time Complexity: O(n^2)

Space Complexity: O(n^2)

Topics

This problem involves: Array, Matrix.

Companies

Asked at: OpenAI.

Largest Local Values in a Matrix | LeetCode 2373

Easy

Array Matrix

Time: O(n^2)Space: O(n^2)

Solution Code

Available in:

class Solution {
    public int[][] largestLocal(int[][] grid) {
        int n = grid.length;
        int[][] maxLocal = new int[n - 2][n - 2];

        for (int i = 0; i < n - 2; i++) {
            for (int j = 0; j < n - 2; j++) {
                int maxVal = 0;
                for (int row = i; row < i + 3; row++) {
                    for (int col = j; col < j + 3; col++) {
                        maxVal = Math.max(maxVal, grid[row][col]);
                    }
                }
                maxLocal[i][j] = maxVal;
            }
        }

        return maxLocal;
    }
}

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Problem Info

Description

Problem 2373: Largest Local Values in a Matrix - Detailed explanation and solution approaches.

Topics

Array Matrix

Companies

OpenAI

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2373

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

6 steps

1
Initialize an (n-2) x (n-2) matrix `maxLocal` to store the results.
2
Iterate through each possible starting row index `i` from 0 to n-3.
3
For each `i`, iterate through each possible starting column index `j` from 0 to n-3.
4
For each `(i, j)` pair, iterate through the 3x3 submatrix centered at `grid[i+1][j+1]`, finding the maximum value.
5
Store the maximum value found in step 4 at `maxLocal[i][j]`.
6
Return the `maxLocal` matrix.

💡

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^2)

🐢 Quadratic - Gets slow with large inputs. Consider optimization!

💾

Space Complexity

O(n^2)

📚 Quadratic space - Uses lots of memory!

📝

Why?

The nested loops iterate approximately n-2 times each, giving a time complexity of O((n-2)^2), which simplifies to O(n^2). The output matrix `maxLocal` requires O((n-2)^2) or O(n^2) space to store the results. The additional space used for temporary variables is negligible compared to the size of the output matrix.

📖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

✨

Key Insights

1The problem can be solved efficiently using nested loops to iterate through all possible 3x3 submatrices.
2No sophisticated data structures are needed; simple nested loops and a `max` function are sufficient.
3The output matrix will always be smaller than the input matrix by a border of one row and one column on each side, because 3x3 submatrices can't be formed at the edges.

📚

Key Terms Explained

For Students

Array

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

Edge Cases

Empty input matrix (n=0): The code handles this implicitly by the condition `(n-2)` that results in an empty `maxLocal` being created. This is a correct handling. The problem statement specifically prevents this scenario (3 <= n).
Small input matrix (n=3): The output `maxLocal` will be a 1x1 matrix containing the maximum value of the entire input matrix. The code handles this correctly.

⚠️

Common Mistakes to Avoid

✗Off-by-one errors in loop indices: Incorrectly calculating the starting and ending indices of the 3x3 submatrices. Pay close attention to the boundary conditions when iterating through the `grid`.

✗Forgetting to handle the case where n < 3: The provided code doesn't explicitly check for this, as the problem statement ensures n >= 3. However, robust code should always include such checks for handling unexpected inputs.

✅

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?

💼Image processing: Finding local maxima in images for feature detection or segmentation.

🏦Data analysis: Identifying regions of high values in a dataset representing geographical data, sensor readings, or other spatial data.

💡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

Even for easy problems, discuss time and space complexity. Interviewers want to see you think analytically.

⚠️ 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: July 4, 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 14

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

@TechLeadJul 7

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

@DevExpert92Jun 30

❓

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.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

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 "Largest Local Values in a Matrix"?

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

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