What is the time complexity of Lucky Numbers in a Matrix?

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

What is the space complexity of Lucky Numbers in a Matrix?

The space complexity is O(m+n).

What data structures are used to solve Lucky Numbers 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 Lucky Numbers in a Matrix?

Insight 1: Finding the minimum value in each row and the maximum value in each column is crucial. This requires iterating through the matrix in two different ways. Insight 2: Efficiently checking if a row minimum is also a column maximum requires a way to quickly access column maximums (often using a separate array).

Which companies ask LeetCode 1380. Lucky Numbers in a Matrix in interviews?

This problem is frequently asked at Cisco.

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Lucky Numbers in a Matrix - LeetCode 1380 Solution

Lucky Numbers in a Matrix - Complete Solution Guide

Lucky Numbers in a Matrix is LeetCode problem 1380, 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

Given an m x n matrix of distinct numbers, return all lucky numbers in the matrix in any order . A lucky number is an element of the matrix such that it is the minimum element in its row and maximum in its column. Example 1: Input: matrix = [[3,7,8],[9,11,13],[15,16,17]] Output: [15] Explanation: 15 is the only lucky number since it is the minimum in its row and the maximum in its column. Example 2: Input: matrix = [[1,10,4,2],[9,3,8,7],[15,16,17,12]] Output: [12] Explanation: 12 is the only luc

Detailed Explanation

The problem asks you to find all "lucky numbers" within a given matrix. A lucky number is defined as an element that is simultaneously the minimum value in its row and the maximum value in its column. The input is a matrix (2D array) of distinct integers. The output is a list (or array) containing all the lucky numbers found in the matrix. The matrix contains only distinct numbers.

Solution Approach

The provided solutions use a two-pass approach. First, they find the minimum element in each row and store it in a list (or array). Then, they find the maximum element in each column and store it in another list (or array). Finally, they compare the two lists to identify elements that appear in both (the lucky numbers). The Python solution uses list comprehensions for conciseness; Java and C++ use explicit loops; C uses manual memory management.

Step-by-Step Algorithm

Step 1: Iterate through each row of the matrix and find the minimum element in that row. Store these minimums in a `row_min` list/array.
Step 2: Iterate through each column of the matrix and find the maximum element in that column. Store these maximums in a `col_max` list/array.
Step 3: Compare the `row_min` and `col_max` lists/arrays. Identify elements that exist in both lists/arrays. These are the lucky numbers.
Step 4: Return the list/array of lucky numbers.

Key Insights

Insight 1: Finding the minimum value in each row and the maximum value in each column is crucial. This requires iterating through the matrix in two different ways.
Insight 2: Efficiently checking if a row minimum is also a column maximum requires a way to quickly access column maximums (often using a separate array).
Insight 3: The problem's constraints (matrix size limited to 50x50) suggest that a brute-force approach (checking all row minimums against all column maximums) is acceptable.

Complexity Analysis

Time Complexity: O(m*n)

Space Complexity: O(m+n)

Topics

This problem involves: Array, Matrix.

Companies

Asked at: Cisco.

Lucky Numbers in a Matrix | LeetCode 1380

Easy

Array Matrix

Time: O(m*n)Space: O(m+n)

Solution Code

Available in:

import java.util.ArrayList;
import java.util.List;

class Solution {
    public List<Integer> luckyNumbers(int[][] matrix) {
        List<Integer> luckyNumbers = new ArrayList<>();
        int m = matrix.length;
        int n = matrix[0].length;

        for (int i = 0; i < m; i++) {
            int minInRow = Integer.MAX_VALUE;
            int colIndex = -1;

            for (int j = 0; j < n; j++) {
                if (matrix[i][j] < minInRow) {
                    minInRow = matrix[i][j];
                    colIndex = j;
                }
            }

            boolean isMaxInCol = true;
            for (int k = 0; k < m; k++) {
                if (matrix[k][colIndex] > minInRow) {
                    isMaxInCol = false;
                    break;
                }
            }

            if (isMaxInCol) {
                luckyNumbers.add(minInRow);
            }
        }

        return luckyNumbers;
    }
}

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Problem Info

Description

Problem 1380: Lucky Numbers in a Matrix - Detailed explanation and solution approaches.

Topics

Array Matrix

Companies

Cisco

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:1380

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

4 steps

1
Step 1: Iterate through each row of the matrix and find the minimum element in that row. Store these minimums in a `row_min` list/array.
2
Step 2: Iterate through each column of the matrix and find the maximum element in that column. Store these maximums in a `col_max` list/array.
3
Step 3: Compare the `row_min` and `col_max` lists/arrays. Identify elements that exist in both lists/arrays. These are the lucky numbers.
4
Step 4: Return the list/array of lucky numbers.

💡

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(m*n)

💾

Space Complexity

O(m+n)

📝

Why?

The first two steps (finding row minimums and column maximums) each require iterating through the entire matrix (m x n elements). The third step (comparing the two lists) takes O(m+n) time in the worst case (all elements are potential lucky numbers). Therefore, the dominant factor is the O(m*n) iterations, and space complexity is determined by the size of the two lists, which is proportional to the number of rows (m) and columns (n).

📖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

Single-Pass Approach

Iterate through the matrix once. For each element, check if it's the minimum in its row and the maximum in its column. This avoids creating intermediate `row_min` and `col_max` arrays.

Time: O(m*n)Space: O(1)

Trade-offs: This approach uses slightly less memory, but might be less readable for beginners. The constant-time space complexity improvement is marginal because m and n are small.

✨

Key Insights

1Insight 1: Finding the minimum value in each row and the maximum value in each column is crucial. This requires iterating through the matrix in two different ways.
2Insight 2: Efficiently checking if a row minimum is also a column maximum requires a way to quickly access column maximums (often using a separate array).
3Insight 3: The problem's constraints (matrix size limited to 50x50) suggest that a brute-force approach (checking all row minimums against all column maximums) is acceptable.

📚

Key Terms Explained

For Students

Array

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

Edge Cases

Edge case 1: An empty matrix. The solutions handle this implicitly; the loops won't execute, and an empty list will be returned.
Edge case 2: A matrix with only one row or one column. The algorithms still correctly identify the lucky number (if it exists).

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to check both minimum in row and maximum in column conditions. Some solutions might only check one condition, leading to incorrect results.

✗Common mistake 2: Incorrectly handling cases with multiple lucky numbers. The solution should return all lucky numbers, not just the first one found.

✅

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: Identifying optimal values in a dataset with row and column dependencies. For example, finding the most cost-effective product from multiple vendors considering both individual product cost (row) and overall vendor pricing (column).

🏦Real-world scenario 2: Data analysis involving feature selection. A lucky number might highlight a feature that has both minimum importance (row) and maximum correlation to a target variable (column).

💡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.

👨‍💻 From Experience

This is one of the first problems I solved when learning Array. It's a great foundation for more complex problems.

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: September 29, 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

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

@DevExpert92Jul 13

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Lucky Numbers 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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