count-special-quadruplets

Count Special Quadruplets

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countQuadruplets

Given a 0-indexed integer array <code>nums</code>, return the number of distinct quadruplets <code>(a, b, c, d)</code> such that:

<ul>
	<li><code>nums[a] + nums[b] + nums[c] == nums[d]</code>, and</li>
	<li><code>a &lt; b &lt; c &lt; d</code></li>
</ul>

&nbsp;
Example 1:

<pre>
Input: nums = [1,2,3,6]
Output: 1
Explanation: The only quadruplet that satisfies the requirement is (0, 1, 2, 3) because 1 + 2 + 3 == 6.
</pre>

Example 2:

<pre>
Input: nums = [3,3,6,4,5]
Output: 0
Explanation: There are no such quadruplets in [3,3,6,4,5].
</pre>

Example 3:

<pre>
Input: nums = [1,1,1,3,5]
Output: 4
Explanation: The 4 quadruplets that satisfy the requirement are:
- (0, 1, 2, 3): 1 + 1 + 1 == 3
- (0, 1, 3, 4): 1 + 1 + 3 == 5
- (0, 2, 3, 4): 1 + 1 + 3 == 5
- (1, 2, 3, 4): 1 + 1 + 3 == 5
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>4 &lt;= nums.length &lt;= 50</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 100</code></li>
</ul>

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