Maximize Partitions

Problem Overview

• Partition the integer array performance into contiguous groups so every component is in exactly one group.
• Each group’s bottleneck is the bitwise AND of its elements; the total bottleneck is the sum over all groups.
• Objective: minimize the total bottleneck and, among all minima, maximize the number of partitions; output that maximum.
• Real-world context: modeling system component bottlenecks.
• Asked in Amazon interviews; a classic coding interview problem and interview question.