How should I practice Count Decreasing Triplets?

Start by reading the full statement, solve the visible examples, then compare the pattern against related Airbnb online assessment problems in FastPrep.

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Count Decreasing Triplets

Airbnb● MediumFULLTIMEOA

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Problem statement

Given an integer array nums, count the index triplets (i, j, k) such that i < j < k and nums[i] > nums[j] > nums[k].

Return the number of strictly decreasing subsequences of length three. Equal values do not satisfy either strict inequality.

Function

countDecreasingTriplets(nums: int[]) → long

Examples

Example 1

nums = [9,4,6,3,2]return = 7

The valid value triples are (9,4,3), (9,4,2), (9,6,3), (9,6,2), (9,3,2), (4,3,2), and (6,3,2).

Example 2

nums = [5,4,3,2]return = 4

Every choice of three indices is strictly decreasing, so the answer is C(4,3) = 4.

Example 3

nums = [3,3,2,1]return = 2

Either occurrence of 3 can precede 2,1. The two equal 3s cannot form a strict pair with each other.

Constraints

0 <= nums.length <= 200000.
-10^9 <= nums[i] <= 10^9.
The answer fits in a signed 64-bit integer.