Number of Arithmetic Triplets

Problem Description

You are given a 0-indexed, strictly increasing integer array nums and a positive integer diff. A triplet (i, j, k) is an arithmetic triplet if the following conditions are met:

• i < j < k
• nums[j] - nums[i] == diff
• nums[k] - nums[j] == diff

Return the number of unique arithmetic triplets.

Key Insights

• The triplet must be formed by three indices, which are strictly increasing.
• The difference between the elements must equal the given diff for both pairs in the triplet.
• A hash set can be used to efficiently determine if the required values for forming the triplet exist in the array.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To solve this problem, we will use a hash set to store the elements of the nums array. We will then iterate through each element in the array and check if the two required counterparts exist in the set to form a valid triplet. If they do, we will increment our count of valid triplets.

1. Create a hash set from the nums array for O(1) lookup times.
2. Loop through each element in the nums array:
   • For each element, check if both element + diff and element + 2 * diff are in the hash set.
   • If both are present, increment the triplet count.
3. Return the count.

Code Solutions