What is the time complexity of Number of Unequal Triplets in Array?

The optimal solution has a time complexity of O(n^3).

What data structures are used to solve Number of Unequal Triplets in Array?

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

What are the key insights for solving Number of Unequal Triplets in Array?

Insight 1: The brute-force approach of checking all possible triplets is straightforward but may not be the most efficient. Insight 2: No specific data structures like hash tables or sorting are strictly necessary for a working solution, although they might offer optimization opportunities in other approaches. The provided solution uses a simple nested loop.

Which companies ask LeetCode 2475. Number of Unequal Triplets in Array in interviews?

This problem is frequently asked at Paytm.

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Number of Unequal Triplets in Array - LeetCode 2475 Solution

Q: How to solve Number of Unequal Triplets in Array?

The provided code uses a brute-force approach. It iterates through all possible triplets (i, j, k) using three nested loops. For each triplet, it checks if the three elements at those indices are pairwise distinct. If they are, the `count` is incremented. Finally, the function returns the total `count` of such triplets.

Number of Unequal Triplets in Array - Complete Solution Guide

Number of Unequal Triplets in Array is LeetCode problem 2475, 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 array of positive integers nums . Find the number of triplets (i, j, k) that meet the following conditions: 0 <= i < j < k < nums.length nums[i] , nums[j] , and nums[k] are pairwise distinct . In other words, nums[i] != nums[j] , nums[i] != nums[k] , and nums[j] != nums[k] . Return the number of triplets that meet the conditions. Example 1: Input: nums = [4,4,2,4,3] Output: 3 Explanation: The following triplets meet the conditions: - (0, 2, 4) because 4 != 2 != 3 - (1,

Detailed Explanation

The problem asks you to find the number of triplets (i, j, k) in a given array `nums` where 0 ≤ i < j < k < nums.length, and nums[i], nums[j], and nums[k] are all different from each other. In simpler terms, you need to count how many combinations of three distinct numbers exist within the array, considering only increasing indices (i < j < k). The input is a 0-indexed array of positive integers, and the output is the count of such triplets.

Solution Approach

The provided code uses a brute-force approach. It iterates through all possible triplets (i, j, k) using three nested loops. For each triplet, it checks if the three elements at those indices are pairwise distinct. If they are, the `count` is incremented. Finally, the function returns the total `count` of such triplets.

Step-by-Step Algorithm

Step 1: Initialize a `count` variable to 0.
Step 2: Iterate through the array using three nested loops to generate all possible triplets (i, j, k) where i < j < k.
Step 3: For each triplet, check if nums[i] ≠ nums[j], nums[i] ≠ nums[k], and nums[j] ≠ nums[k].
Step 4: If all three elements are distinct, increment the `count`.
Step 5: After iterating through all triplets, return the final `count`.

Key Insights

Insight 1: The brute-force approach of checking all possible triplets is straightforward but may not be the most efficient.
Insight 2: No specific data structures like hash tables or sorting are strictly necessary for a working solution, although they might offer optimization opportunities in other approaches. The provided solution uses a simple nested loop.
Insight 3: The constraints (array length ≤ 100) significantly limit the input size, making a brute-force approach computationally feasible. For larger arrays, a more optimized algorithm would be necessary.

Complexity Analysis

Time Complexity: O(n^3)

Space Complexity: O(1)

Topics

This problem involves: Array, Hash Table, Sorting.

Companies

Asked at: Paytm.

Number of Unequal Triplets in Array | LeetCode 2475

Easy

Array Hash Table Sorting

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

Solution Code

Available in:

class Solution {
    public int unequalTriplets(int[] nums) {
        int count = 0;
        int n = nums.length;
        for (int i = 0; i < n - 2; i++) {
            for (int j = i + 1; j < n - 1; j++) {
                for (int k = j + 1; k < n; k++) {
                    if (nums[i] != nums[j] && nums[i] != nums[k] && nums[j] != nums[k]) {
                        count++;
                    }
                }
            }
        }
        return count;
    }
}

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Problem Info

Description

Problem 2475: Number of Unequal Triplets in Array - Detailed explanation and solution approaches.

Topics

Array Hash Table Sorting

Companies

Paytm

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2475

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: Initialize a `count` variable to 0.
2
Step 2: Iterate through the array using three nested loops to generate all possible triplets (i, j, k) where i < j < k.
3
Step 3: For each triplet, check if nums[i] ≠ nums[j], nums[i] ≠ nums[k], and nums[j] ≠ nums[k].
4
Step 4: If all three elements are distinct, increment the `count`.
5
Step 5: After iterating through all triplets, return the final `count`.

💡

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^3)

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is O(n³) because of the three nested loops, each iterating up to n (the length of the array) times in the worst case. The space complexity is O(1) because the algorithm only uses a constant amount of extra space to store the `count` variable and loop indices. No additional data structures are used that scale with the input size.

📖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

Optimized Brute Force (with early exit)

A slightly optimized brute force approach. If the first two elements are equal, you can skip to the next iteration of the outer loop, because no combination with those two elements will have distinct values.

Time: O(n³), but potentially faster in practice with many duplicatesSpace: O(1)

Trade-offs: Offers a small improvement in speed if there are many duplicate elements. For small arrays, the benefit is minimal. The added complexity of the early exit condition might outweigh the performance gain in some scenarios.

✨

Key Insights

1Insight 1: The brute-force approach of checking all possible triplets is straightforward but may not be the most efficient.
2Insight 2: No specific data structures like hash tables or sorting are strictly necessary for a working solution, although they might offer optimization opportunities in other approaches. The provided solution uses a simple nested loop.
3Insight 3: The constraints (array length ≤ 100) significantly limit the input size, making a brute-force approach computationally feasible. For larger arrays, a more optimized algorithm would be necessary.

📚

Key Terms Explained

For Students

Array

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

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Sorting

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

Edge Cases

Edge case 1: An array with all identical elements will result in a count of 0, as no triplets can have distinct elements. The code handles this correctly.
Edge case 2: An empty array or an array with less than three elements will also result in a count of 0, as there are no triplets to form. The loop conditions implicitly handle this.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to check all three pairwise comparisons (nums[i] != nums[j], nums[i] != nums[k], nums[j] != nums[k]).

✗Common mistake 2: Not properly handling the loop indices to ensure i < j < k. Incorrect loop bounds can lead to incorrect results or runtime errors.

✅

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 datasets to find combinations of unique data points. For example, identifying unique combinations of features in a machine learning dataset.

🏦Real-world scenario 2: Combinatorial problems where you need to count unique combinations with constraints on order. Example: Finding the number of ways to select a committee of three people from a group, where the order of selection doesn't matter (but each person is unique).

💡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: October 14, 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

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

@InterviewProJun 29

❓

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.

How do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

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 "Number of Unequal Triplets in Array"?

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

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