Bitonic Partitioning

Problem Overview

• Count the ways to split an array into contiguous partitions so the sequence of partition averages is strictly increasing then strictly decreasing, with at least three partitions.
• Input: array arr with 1 < n ≤ 100 and values in [-1e9, 1e9]; Output: number of valid partitionings.
• Domain: array segmentation and sequence analysis where each partition is represented by its average.
• Source: From Rubrik interviews; a coding interview problem and common interview question.