What is the time complexity of Largest Perimeter Triangle?

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

What data structures are used to solve Largest Perimeter Triangle?

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

What are the key insights for solving Largest Perimeter Triangle?

Insight 1: The triangle inequality theorem is crucial: a + b > c must hold for any permutation of sides a, b, and c of a valid triangle. Insight 2: Sorting the input array allows us to efficiently check for the triangle inequality by considering the three largest sides first. Specifically, we can sort in descending order and check if nums[i] < nums[i+1] + nums[i+2] for a sliding window of size 3.

Which companies ask LeetCode 976. Largest Perimeter Triangle in interviews?

This problem is frequently asked at Tesla.

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Largest Perimeter Triangle - LeetCode 976 Solution

Q: How to solve Largest Perimeter Triangle?

The solution employs a greedy approach combined with sorting. First, the input array `nums` is sorted in descending order (or ascending, and then iterated backwards). Then, it iterates through the sorted array, checking if the triangle inequality holds for each triplet of consecutive elements. If a triplet satisfies the inequality (a < b + c where a is the largest side of the potential triangle, and b and c are the other two sides), the sum of the triplet is returned as the largest possible perimeter. If no such triplet is found after iterating through the entire array, 0 is returned.

Q: Which companies ask LeetCode 976. Largest Perimeter Triangle in interviews?

This problem is frequently asked at Tesla.

Largest Perimeter Triangle - Complete Solution Guide

Largest Perimeter Triangle is LeetCode problem 976, 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 integer array nums , return the largest perimeter of a triangle with a non-zero area, formed from three of these lengths . If it is impossible to form any triangle of a non-zero area, return 0 . Example 1: Input: nums = [2,1,2] Output: 5 Explanation: You can form a triangle with three side lengths: 1, 2, and 2. Example 2: Input: nums = [1,2,1,10] Output: 0 Explanation: You cannot use the side lengths 1, 1, and 2 to form a triangle. You cannot use the side lengths 1, 1, and 10 to form a

Detailed Explanation

The problem asks us to find the largest possible perimeter of a triangle that can be formed using three side lengths from a given array of integers. The array represents the lengths of potential sides. A valid triangle must have a non-zero area, which means the sum of any two sides must be greater than the third side (triangle inequality theorem). If no such triangle can be formed, we should return 0.

Solution Approach

The solution employs a greedy approach combined with sorting. First, the input array `nums` is sorted in descending order (or ascending, and then iterated backwards). Then, it iterates through the sorted array, checking if the triangle inequality holds for each triplet of consecutive elements. If a triplet satisfies the inequality (a < b + c where a is the largest side of the potential triangle, and b and c are the other two sides), the sum of the triplet is returned as the largest possible perimeter. If no such triplet is found after iterating through the entire array, 0 is returned.

Step-by-Step Algorithm

Step 1: Sort the input array `nums` in descending order.
Step 2: Iterate through the sorted array from the beginning (or from the end in the case of ascending sort) up to the third-to-last element (nums.length - 2).
Step 3: In each iteration (indexed by `i`), check if `nums[i] < nums[i + 1] + nums[i + 2]`. This checks the triangle inequality condition.
Step 4: If the inequality holds true, return the sum `nums[i] + nums[i + 1] + nums[i + 2]` as the largest perimeter.
Step 5: If the loop completes without finding a valid triangle, return 0.

Key Insights

Insight 1: The triangle inequality theorem is crucial: a + b > c must hold for any permutation of sides a, b, and c of a valid triangle.
Insight 2: Sorting the input array allows us to efficiently check for the triangle inequality by considering the three largest sides first. Specifically, we can sort in descending order and check if nums[i] < nums[i+1] + nums[i+2] for a sliding window of size 3.
Insight 3: Sorting the array enables a greedy approach. By considering the largest sides first, if we find a valid triangle, it will necessarily have the largest possible perimeter.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(1)

Topics

This problem involves: Array, Math, Greedy, Sorting.

Companies

Asked at: Tesla.

Largest Perimeter Triangle | LeetCode 976

Easy

Array Math Greedy Sorting

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

Solution Code

Available in:

import java.util.Arrays;

class Solution {
    public int largestPerimeter(int[] nums) {
        Arrays.sort(nums);
        for (int i = nums.length - 1; i >= 2; i--) {
            if (nums[i - 2] + nums[i - 1] > nums[i]) {
                return nums[i - 2] + nums[i - 1] + nums[i];
            }
        }
        return 0;
    }
}

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Problem Info

Description

Problem 976: Largest Perimeter Triangle - Detailed explanation and solution approaches.

Topics

Array Math Greedy Sorting

Companies

Tesla

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:976

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

5 steps

1
Step 1: Sort the input array `nums` in descending order.
2
Step 2: Iterate through the sorted array from the beginning (or from the end in the case of ascending sort) up to the third-to-last element (nums.length - 2).
3
Step 3: In each iteration (indexed by `i`), check if `nums[i] < nums[i + 1] + nums[i + 2]`. This checks the triangle inequality condition.
4
Step 4: If the inequality holds true, return the sum `nums[i] + nums[i + 1] + nums[i + 2]` as the largest perimeter.
5
Step 5: If the loop completes without finding a valid triangle, return 0.

💡

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)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The dominant operation is sorting the array, which typically has a time complexity of O(n log n) using comparison-based sorting algorithms like merge sort or quicksort. The subsequent iteration through the sorted array takes O(n) time. Therefore, the overall time complexity is O(n log n). The space complexity is O(1) because the sorting is done in-place (or uses a constant amount of extra space), and we only use a few constant extra variables.

📖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

Brute-Force Approach

Generate all possible combinations of three numbers from the array and check if they form a valid triangle. Keep track of the maximum perimeter found so far.

Time: O(n^3)Space: O(1)

Trade-offs: This approach is simple to understand but is inefficient for larger input arrays due to its cubic time complexity. The provided solution is much more efficient.

✨

Key Insights

1Insight 1: The triangle inequality theorem is crucial: a + b > c must hold for any permutation of sides a, b, and c of a valid triangle.
2Insight 2: Sorting the input array allows us to efficiently check for the triangle inequality by considering the three largest sides first. Specifically, we can sort in descending order and check if nums[i] < nums[i+1] + nums[i+2] for a sliding window of size 3.
3Insight 3: Sorting the array enables a greedy approach. By considering the largest sides first, if we find a valid triangle, it will necessarily have the largest possible perimeter.

📚

Key Terms Explained

For Students

Array

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

Greedy Algorithm

Making the best choice at each step without looking ahead.

Sorting

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

Edge Cases

Edge case 1: Input array has fewer than 3 elements. The code correctly returns 0 in this case because no triangle can be formed.
Edge case 2: The input array contains very large numbers that could potentially lead to integer overflow when summing them. While not explicitly handled in the provided solutions, it's a potential concern that could be addressed using larger integer data types if needed (e.g., `long` in Java or C++).
Edge case 3: The input contains duplicate numbers. The sorting and the triangle inequality check will still work correctly, and the solution handles this case without any issues.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to sort the input array before applying the greedy approach. Sorting is crucial to ensure that the algorithm efficiently finds the largest possible perimeter.

✗Common mistake 2: Incorrectly applying the triangle inequality. The condition a < b + c (where a is the longest side) must be checked, but beginners might accidentally swap variables or use incorrect operators.

✗Common mistake 3: Not handling the edge case where no valid triangle can be formed. The solution should return 0 in this case.

✅

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: In computer graphics, determining if a set of vertices can form a valid triangle is essential for rendering 3D models. This algorithm can be used to validate triangle meshes.

🏦Real-world scenario 2: In surveying and mapping, determining if three measured distances can form a closed triangle is important for accuracy. This algorithm can be used to check the validity of the measurements.

💡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: August 16, 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

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

@AlgoMasterJul 14

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 7

❓

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 "Largest Perimeter Triangle"?

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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