What is the time complexity of Type of Triangle?

The optimal solution has a time complexity of O(1).

What data structures are used to solve Type of Triangle?

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

What are the key insights for solving Type of Triangle?

Insight 1: The triangle inequality theorem is crucial for determining if the input sides can form a valid triangle. Insight 2: Efficiently checking for equilateral, isosceles, and scalene conditions requires comparing the side lengths.

Which companies ask LeetCode 3024. Type of Triangle in interviews?

This problem is frequently asked at IBM.

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Type of Triangle - LeetCode 3024 Solution

Type of Triangle - Complete Solution Guide

Type of Triangle is LeetCode problem 3024, 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 integer array nums of size 3 which can form the sides of a triangle. A triangle is called equilateral if it has all sides of equal length. A triangle is called isosceles if it has exactly two sides of equal length. A triangle is called scalene if all its sides are of different lengths. Return a string representing the type of triangle that can be formed or "none" if it cannot form a triangle. Example 1: Input: nums = [3,3,3] Output: "equilateral" Explanation: Since all

Detailed Explanation

The problem asks to determine the type of triangle that can be formed using three given side lengths. The input is a list of three integers representing the lengths of the sides of a triangle. The output is a string indicating whether the triangle is 'equilateral' (all sides equal), 'isosceles' (exactly two sides equal), 'scalene' (all sides different), or 'none' (the sides cannot form a triangle). A valid triangle must satisfy the triangle inequality theorem: the sum of the lengths of any two sides must be greater than the length of the third side.

Solution Approach

The solution approaches the problem by first checking if a valid triangle can be formed using the triangle inequality theorem. If it is a valid triangle, it then checks if the sides are all equal (equilateral), exactly two are equal (isosceles), or all are different (scalene). The provided solutions efficiently handle these checks using conditional statements. Some solutions use sorting to simplify the equality checks.

Step-by-Step Algorithm

Step 1: Check if a valid triangle can be formed. The sum of any two sides must be greater than the third side. If not, return "none".
Step 2: If it's a valid triangle, check if all three sides are equal. If they are, return "equilateral".
Step 3: If not equilateral, check if exactly two sides are equal. If so, return "isosceles".
Step 4: If neither equilateral nor isosceles, return "scalene".

Key Insights

Insight 1: The triangle inequality theorem is crucial for determining if the input sides can form a valid triangle.
Insight 2: Efficiently checking for equilateral, isosceles, and scalene conditions requires comparing the side lengths.
Insight 3: Sorting the input array simplifies the comparison of side lengths for determining triangle type.

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(1)

Topics

This problem involves: Array, Math, Sorting.

Companies

Asked at: IBM.

Type of Triangle | LeetCode 3024

Easy

Array Math Sorting

Time: O(1)Space: O(1)

Solution Code

Available in:

import java.util.Arrays;

class Solution {
    public String triangleType(int[] nums) {
        Arrays.sort(nums);
        if (nums[0] + nums[1] <= nums[2]) {
            return "none";
        }
        if (nums[0] == nums[1] && nums[1] == nums[2]) {
            return "equilateral";
        } else if (nums[0] == nums[1] || nums[1] == nums[2] || nums[0] == nums[2]) {
            return "isosceles";
        } else {
            return "scalene";
        }
    }
}

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Problem Info

Description

Problem 3024: Type of Triangle - Detailed explanation and solution approaches.

Topics

Array Math Sorting

Companies

IBM

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:3024

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: Check if a valid triangle can be formed. The sum of any two sides must be greater than the third side. If not, return "none".
2
Step 2: If it's a valid triangle, check if all three sides are equal. If they are, return "equilateral".
3
Step 3: If not equilateral, check if exactly two sides are equal. If so, return "isosceles".
4
Step 4: If neither equilateral nor isosceles, return "scalene".

💡

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(1)

⚡ Constant time - Super fast! Same speed regardless of input size.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The algorithm involves a fixed number of comparisons and conditional checks regardless of the input size. The input size is always 3, so the time and space complexities are constant.

📖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 single sorted array

Sort the input array first. This simplifies the equality checks. After the triangle inequality check, only compare nums[0], nums[1], and nums[2] for equality.

Time: O(log n) due to sorting (though n is always 3 here), otherwise O(1)Space: O(1) or O(log n) depending on the sorting algorithm used (In-place sort like in Java is O(1) extra space)

Trade-offs: Sorting adds a small overhead, but it makes the code slightly more readable and easier to understand, especially for those less familiar with triangle properties.

✨

Key Insights

1Insight 1: The triangle inequality theorem is crucial for determining if the input sides can form a valid triangle.
2Insight 2: Efficiently checking for equilateral, isosceles, and scalene conditions requires comparing the side lengths.
3Insight 3: Sorting the input array simplifies the comparison of side lengths for determining triangle type.

📚

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: Input values that do not form a triangle (e.g., [1, 2, 5]). The solution correctly identifies this and returns "none".
Edge case 2: Input values that are all equal to 1. The solution correctly identifies this as an equilateral triangle.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to check for the triangle inequality theorem before checking for triangle type. This leads to incorrect results for invalid triangle inputs.

✗Common mistake 2: Incorrectly handling the isosceles case. Failing to check all combinations of equal sides can lead to misclassifications.

✅

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 geometry-based applications (e.g., CAD software), determining triangle types is essential for various calculations and operations.

🏦Real-world scenario 2: In physics or engineering, understanding triangle properties is crucial for analyzing structures and forces (e.g., analyzing the stability of a triangular truss).

💡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: October 23, 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 14

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

@DevExpert92Jul 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 "Type of 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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