Count the number of special triplets in an array according to the problem's validity rule.
Problem
Given an integer array nums, count how many index triplets (i, j, k) satisfy the problem's special condition.
A triplet is valid only when the required ordering of indices holds and the values at those indices match the rule implied by the problem. Your task is to return the total number of valid triplets.
Because the answer may be large, return the count as an integer.
Notes
- Triplets are based on indices, not values.
- The same value may appear multiple times and can contribute to multiple triplets if the indices are distinct.
- You should aim for an approach better than enumerating all
O(n^3)triplets.
Input Format
- An integer array
nums. - The exact special condition determines which index triplets are counted.
Output Format
- Return a single integer: the number of valid special triplets.
Constraints
1 <= nums.length- Values are integers.
- The result fits in a 64-bit signed integer for typical interview constraints.
Example 1
Input
nums = [1, 2, 1, 2, 1]
Output
4
Explanation
Illustrative example: there are four valid index triplets that satisfy the special condition for this array.
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