Number of Unequal Triplets in Array

Problem Description

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.

Return the number of triplets that meet the conditions.

Key Insights

• We need to count unique triplets from the array where the elements at the indices are distinct.
• The brute force approach involves checking all combinations of triplets, but this can be optimized.
• Utilizing a hash table can help track the frequency of each number, allowing us to efficiently count valid triplets.
• The constraints allow for a direct O(n^3) solution but also hint at possible optimizations using combinations.

Space and Time Complexity

Time Complexity: O(n^3) in the brute force approach, but can be optimized to O(n^2) with better counting methods.
Space Complexity: O(n) for the hash table to store counts of distinct numbers.

Solution

To solve this problem, we can use a brute force approach to iterate through all possible triplets (i, j, k) and check if the elements at these indices are distinct. Alternatively, we can optimize by using a frequency map to count the occurrences of each number, which can help in determining the distinct elements more efficiently.

1. Create a frequency map to count occurrences of each number.
2. For each combination of three distinct numbers, calculate the number of valid triplets that can be formed with those numbers based on their frequencies.

Code Solutions