Mastering Binary Search on Answer: The Book Allocation Problem

If you've ever prepared for a technical interview at companies like Google, Amazon, or Adobe, you've likely encountered the "Allocate Books" problem. It is a classic challenge that tests your ability to look beyond traditional binary search and apply it to a range of possible answers. In this post, we’ll break down the problem and walk through an efficient Java solution that uses the Binary Search on Answer technique. The Problem Statement You are given an array of integers arr, where arr[i] represents the number of pages in the i^th book. There are k students. The task is to allocate all books to the students such that: Each student gets at least one book. Each student is assigned a contiguous sequence of books. The maximum number of pages assigned to a student is minimized. Example Input: arr = [12, 34, 67, 90], k = 2 Output: 113 Explanation: - Option 1: [12] and [34, 67, 90] → Max = 191 Option 2: [12, 34] and [67, 90] → Max = 157 Option 3: [12, 34, 67] and [90] → Max = 113 The small