Problem

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, and
  • nums[k] - nums[j] == diff.

Return the number of unique arithmetic triplets.

Examples

Example 1:

Input:
nums = [0,1,4,6,7,10], diff = 3
Output:
 2
Explanation:
(1, 2, 4) is an arithmetic triplet because both 7 - 4 == 3 and 4 - 1 == 3.
(2, 4, 5) is an arithmetic triplet because both 10 - 7 == 3 and 7 - 4 == 3.

Example 2:

Input:
nums = [4,5,6,7,8,9], diff = 2
Output:
 2
Explanation:
(0, 2, 4) is an arithmetic triplet because both 8 - 6 == 2 and 6 - 4 == 2.
(1, 3, 5) is an arithmetic triplet because both 9 - 7 == 2 and 7 - 5 == 2.

Solution

Method 1 - Using Hashset

Code

public int arithmeticTriplets(int[] nums, int diff) {
	int cnt = 0;
	Set<Integer> seen = new HashSet<>();
	for (int num : nums) {
		if (seen.contains(num - diff) && seen.contains(num - diff * 2)) {
			++cnt;
		}
		seen.add(num);
	}
	return cnt;
}

Complexity

  • ⏰ Time complexity: O(n)
  • 🧺 Space complexity: O(n)