Count Special Triplets · Interview Problem

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Leetcode

Medium

Arrays

Hash Maps

Combinatorics

Count Special Triplets

Count the number of special triplets in an array according to the problem's validity rule.

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Problem Statement

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.

Examples

Sample cases returned by the problem API.

Example 1

Input

nums = [1, 2, 1, 2, 1]

Output

Explanation

Illustrative example: there are four valid index triplets that satisfy the special condition for this array.

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