Allocate Minimum Pages Binary Search on Answer in DSA Typescript - Build from Scratch

Allocate Minimum Pages using Binary Search on Answer

📖 Scenario: You are managing a library where books are arranged in a row. Each book has a certain number of pages. You want to allocate these books to a fixed number of students such that each student gets a continuous sequence of books. Your goal is to minimize the maximum number of pages assigned to any student.This is a common problem in resource allocation where fairness and balance are important.

🎯 Goal: Build a TypeScript program that uses binary search on the answer to find the minimum possible maximum pages allocated to a student.You will create the data structure for books, set the number of students, implement the binary search logic, and finally print the minimum maximum pages.

📋 What You'll Learn

Create an array called books with the exact values [12, 34, 67, 90]

Create a variable called students and set it to 2

Write a function called isPossible that takes mid as input and returns true if allocation is possible with max pages <= mid, else false

Use binary search between the max pages of a single book and the sum of all pages to find the minimum max pages

Print the final minimum maximum pages using console.log

💡 Why This Matters

🌍 Real World

This problem models fair resource allocation such as dividing tasks, workloads, or resources among people or machines to balance load.

💼 Career

Understanding binary search on answer is useful in software engineering roles involving optimization, scheduling, and system design.

1

Create the books array

Create an array called books with the exact values [12, 34, 67, 90]

DSA Typescript

# Your code here

Hint

Use const books: number[] = [12, 34, 67, 90]; to create the array.

2

Set the number of students

Create a variable called students and set it to 2

DSA Typescript

const books: number[] = [12, 34, 67, 90];
# Your code here

Hint

Use const students: number = 2; to set the number of students.

3

Implement the isPossible function

Write a function called isPossible that takes a number mid and returns true if it is possible to allocate books to students such that no student reads more than mid pages, otherwise returns false

DSA Typescript

const books: number[] = [12, 34, 67, 90];
const students: number = 2;

// Write the isPossible function below
# Your code here

Hint

Check if each book can be allocated without exceeding mid pages per student. Increase student count when needed.

4

Use binary search to find minimum maximum pages and print result

Use binary search between maxPages (maximum pages in a single book) and totalPages (sum of all pages) to find the minimum maximum pages. Print the result using console.log

DSA Typescript

const books: number[] = [12, 34, 67, 90];
const students: number = 2;

function isPossible(mid: number): boolean {
    let studentCount = 1;
    let pagesSum = 0;
    for (const pages of books) {
        if (pages > mid) {
            return false;
        }
        if (pagesSum + pages > mid) {
            studentCount++;
            pagesSum = pages;
            if (studentCount > students) {
                return false;
            }
        } else {
            pagesSum += pages;
        }
    }
    return true;
}

// Use binary search to find minimum max pages and print
# Your code here

Hint

Use binary search between the max single book pages and total pages. Update the result when allocation is possible.