3583: Count Special Triplets

Problem Statement

You are given an integer array nums.

A special triplet is defined as a triplet of indices (i, j, k) such that:

  • 0 <= i < j < k < n, where n = nums.length
  • nums[i] == nums[j] * 2
  • nums[k] == nums[j] * 2

Return the total number of special triplets in the array.

Since the answer may be large, return it modulo 109 + 7.

Example 1:

Input: nums = [6,3,6]

Output: 1

Explanation:

The only special triplet is (i, j, k) = (0, 1, 2), where:

  • nums[0] = 6, nums[1] = 3, nums[2] = 6
  • nums[0] = nums[1] * 2 = 3 * 2 = 6
  • nums[2] = nums[1] * 2 = 3 * 2 = 6

Example 2:

Input: nums = [0,1,0,0]

Output: 1

Explanation:

The only special triplet is (i, j, k) = (0, 2, 3), where:

  • nums[0] = 0, nums[2] = 0, nums[3] = 0
  • nums[0] = nums[2] * 2 = 0 * 2 = 0
  • nums[3] = nums[2] * 2 = 0 * 2 = 0

Example 3:

Input: nums = [8,4,2,8,4]

Output: 2

Explanation:

There are exactly two special triplets:

  • (i, j, k) = (0, 1, 3)
<ul>
	<li><code>nums[0] = 8</code>, <code>nums[1] = 4</code>, <code>nums[3] = 8</code></li>
	<li><code>nums[0] = nums[1] * 2 = 4 * 2 = 8</code></li>
	<li><code>nums[3] = nums[1] * 2 = 4 * 2 = 8</code></li>
</ul>
</li>
<li><code>(i, j, k) = (1, 2, 4)</code>
<ul>
	<li><code>nums[1] = 4</code>, <code>nums[2] = 2</code>, <code>nums[4] = 4</code></li>
	<li><code>nums[1] = nums[2] * 2 = 2 * 2 = 4</code></li>
	<li><code>nums[4] = nums[2] * 2 = 2 * 2 = 4</code></li>
</ul>
</li>

Constraints:

  • 3 <= n == nums.length <= 105
  • 0 <= nums[i] <= 105

Code Solution