What is the time complexity of Prime In Diagonal?

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

What data structures are used to solve Prime In Diagonal?

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

What are the key insights for solving Prime In Diagonal?

Insight 1: The problem involves iterating through the diagonals of the matrix, so indexing is crucial. We need to access elements using `nums[i][i]` and `nums[i][n - 1 - i]` where `n` is the size of the matrix. Insight 2: A prime-checking function (`isPrime`) is necessary to efficiently determine if a number is prime. Optimizations in the `isPrime` function can improve overall efficiency.

Which companies ask LeetCode 2614. Prime In Diagonal in interviews?

This problem is frequently asked at IBM.

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Prime In Diagonal - LeetCode 2614 Solution

Prime In Diagonal - Complete Solution Guide

Prime In Diagonal is LeetCode problem 2614, 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 a 0-indexed two-dimensional integer array nums . Return the largest prime number that lies on at least one of the diagonals of nums . In case, no prime is present on any of the diagonals, return 0. Note that: An integer is prime if it is greater than 1 and has no positive integer divisors other than 1 and itself. An integer val is on one of the diagonals of nums if there exists an integer i for which nums[i][i] = val or an i for which nums[i][nums.length - i - 1] = val . In the abo

Detailed Explanation

The problem asks you to find the largest prime number that appears on either of the main diagonals of a square matrix (2D array). The main diagonals are the top-left to bottom-right diagonal and the top-right to bottom-left diagonal. The input is a square matrix of integers, and the output is the largest prime number found on either diagonal; if no primes are found, the output is 0. A prime number is a whole number greater than 1 that has only two divisors: 1 and itself.

Solution Approach

The solution iterates through the matrix, accessing elements from both diagonals. For each element, it checks if it's a prime number using the `isPrime` helper function. If it's prime, it's compared against the current largest prime found so far, and the largest is updated accordingly. Finally, the largest prime is returned. If no primes are encountered, 0 is returned.

Step-by-Step Algorithm

Step 1: Initialize `maxPrime` to 0. This variable will store the largest prime number encountered.
Step 2: Iterate from `i = 0` to `n - 1`, where `n` is the number of rows (and columns) in the matrix.
Step 3: For each `i`, extract the element from the main diagonal (`nums[i][i]`) and the anti-diagonal (`nums[i][n - 1 - i]`).
Step 4: Call the `isPrime` function to check if each extracted element is prime.
Step 5: If the element is prime, update `maxPrime` to be the maximum of `maxPrime` and the current prime number using `Math.max` (or its equivalent in the chosen language).
Step 6: After iterating through all elements of both diagonals, return `maxPrime`.

Key Insights

Insight 1: The problem involves iterating through the diagonals of the matrix, so indexing is crucial. We need to access elements using `nums[i][i]` and `nums[i][n - 1 - i]` where `n` is the size of the matrix.
Insight 2: A prime-checking function (`isPrime`) is necessary to efficiently determine if a number is prime. Optimizations in the `isPrime` function can improve overall efficiency.
Insight 3: The largest prime needs to be tracked throughout the iteration. A simple variable (`maxPrime` or similar) updated with `Math.max` or a similar function is sufficient.

Complexity Analysis

Time Complexity: O(n * sqrt(n))

Space Complexity: O(n)

Topics

This problem involves: Array, Math, Matrix, Number Theory.

Companies

Asked at: IBM.

Prime In Diagonal | LeetCode 2614

Easy

Array Math Matrix Number Theory

Time: O(n * sqrt(n))Space: O(n)

Solution Code

Available in:

class Solution {
    public int diagonalPrime(int[][] nums) {
        int maxPrime = 0;
        for (int i = 0; i < nums.length; i++) {
            if (isPrime(nums[i][i])) {
                maxPrime = Math.max(maxPrime, nums[i][i]);
            }
            if (isPrime(nums[i][nums.length - i - 1])) {
                maxPrime = Math.max(maxPrime, nums[i][nums.length - i - 1]);
            }
        }
        return maxPrime;
    }

    private boolean isPrime(int n) {
        if (n <= 1) {
            return false;
        }
        for (int i = 2; i * i <= n; i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
}

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Problem Info

Description

Problem 2614: Prime In Diagonal - Detailed explanation and solution approaches.

Topics

Array Math Matrix Number Theory

Companies

IBM

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2614

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
Step 1: Initialize `maxPrime` to 0. This variable will store the largest prime number encountered.
2
Step 2: Iterate from `i = 0` to `n - 1`, where `n` is the number of rows (and columns) in the matrix.
3
Step 3: For each `i`, extract the element from the main diagonal (`nums[i][i]`) and the anti-diagonal (`nums[i][n - 1 - i]`).
4
Step 4: Call the `isPrime` function to check if each extracted element is prime.
5
Step 5: If the element is prime, update `maxPrime` to be the maximum of `maxPrime` and the current prime number using `Math.max` (or its equivalent in the chosen language).
6
Step 6: After iterating through all elements of both diagonals, return `maxPrime`.

💡

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 * sqrt(n))

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is dominated by the prime checking function which has a time complexity of O(sqrt(m)), where m is the largest number in the matrix. The loop iterates 'n' times, where 'n' is the size of the matrix. Thus, the overall time complexity becomes O(n * sqrt(m)). The space complexity is O(1) because we only use a constant amount of extra space to store variables like `maxPrime` and loop counters. The `isPrime` function is optimized to avoid unnecessary checks, improving performance.

📖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

Sieve of Eratosthenes

Pre-compute all primes up to the maximum value in `nums` using the Sieve of Eratosthenes. Then, check if the diagonal elements are present in the pre-computed prime list.

Time: O(m log log m + n), where m is the maximum value in numsSpace: O(m)

Trade-offs: The Sieve approach is faster if the matrix contains many numbers or the maximum number is significantly large, but requires more space to store the list of primes. The provided solution is more space-efficient for smaller matrices with relatively smaller maximum values.

✨

Key Insights

1Insight 1: The problem involves iterating through the diagonals of the matrix, so indexing is crucial. We need to access elements using `nums[i][i]` and `nums[i][n - 1 - i]` where `n` is the size of the matrix.
2Insight 2: A prime-checking function (`isPrime`) is necessary to efficiently determine if a number is prime. Optimizations in the `isPrime` function can improve overall efficiency.
3Insight 3: The largest prime needs to be tracked throughout the iteration. A simple variable (`maxPrime` or similar) updated with `Math.max` or a similar function is sufficient.

📚

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: Empty matrix (nums.length == 0). The solution correctly handles this by returning 0 because there are no diagonals or numbers to check.
Edge case 2: Matrix with no prime numbers. The solution correctly handles this by returning 0.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly calculating the indices for the anti-diagonal. Beginners might use `nums[i][i]` for both diagonals, or they might make a mistake in the `n - 1 - i` index.

✗Common mistake 2: Inefficient prime checking. Using a loop that goes up to `n` instead of `sqrt(n)` for `isPrime` leads to unnecessary computations and a worse time complexity.

✅

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: Analyzing patterns in data matrices. Prime numbers have special properties used in cryptography, and this algorithm might be part of larger systems analyzing data with such patterns.

🏦Real-world scenario 2: Image processing or computer vision tasks. Diagonal analysis can be useful for feature extraction in images, with prime numbers possibly serving as a marker for specific features.

💡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

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ 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: September 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

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

@TechLeadJul 13

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

@DevExpert92Jul 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 "Prime In Diagonal"?

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 math techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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