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

Allocate Minimum Pages using Binary Search on Answer

📖 Scenario: You are a librarian who needs to allocate books to students. Each book has a certain number of pages. You want to assign books to students so that the maximum number of pages assigned to any student is as small as possible.This helps keep the workload balanced among students.

🎯 Goal: Build a program that finds the minimum possible maximum pages assigned to a student by using binary search on the answer.

📋 What You'll Learn

Create a slice called books with these exact page counts: 100, 200, 300, 400

Create an integer variable called students and set it to 2

Write a function isPossible that takes books, students, and a max page limit, and returns true if allocation is possible

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

Print the minimum max pages after allocation

💡 Why This Matters

🌍 Real World

This problem models distributing tasks or workloads evenly among workers to avoid overload.

💼 Career

Understanding binary search on answer is useful in optimization problems common in software engineering and coding interviews.

1

Create the books slice

Create a slice called books with these exact page counts: 100, 200, 300, 400

DSA Go

# Create the books slice with exact page counts
# Your code here

Hint

Use books := []int{100, 200, 300, 400} to create the slice.

2

Add the students variable

Create an integer variable called students and set it to 2

DSA Go

package main

func main() {
    books := []int{100, 200, 300, 400}
    // Create students variable and set to 2
    // Your code here
}

Hint

Use students := 2 to create the variable.

3

Write the isPossible function

Write a function called isPossible that takes books []int, students int, and maxPages int as parameters and returns bool. It should return true if it is possible to allocate books to students such that no student reads more than maxPages pages.

DSA Go

package main

func main() {
    books := []int{100, 200, 300, 400}
    students := 2
}

// Write isPossible function below
// Your code here

Hint

Check if any single book has more pages than maxPages. If yes, return false. Otherwise, count how many students are needed if we limit pages to maxPages.

4

Find and print the minimum maximum pages

Use binary search between the maximum pages in books and the sum of all pages in books to find the minimum maximum pages that can be allocated to students. Print the result using fmt.Println.

DSA Go

package main

import "fmt"

func main() {
    books := []int{100, 200, 300, 400}
    students := 2

    // Use binary search to find minimum max pages
    // Your code here
}

func isPossible(books []int, students int, maxPages int) bool {
    count := 1
    currentSum := 0
    for _, pages := range books {
        if pages > maxPages {
            return false
        }
        if currentSum+pages > maxPages {
            count++
            currentSum = pages
            if count > students {
                return false
            }
        } else {
            currentSum += pages
        }
    }
    return true
}

Hint

Use binary search between the max single book pages and total pages. Use isPossible to check feasibility. Print the final minimum max pages.

Practice

1. What is the main goal of the Allocate Minimum Pages problem using binary search on answer?

easy

A. To maximize the total number of pages assigned

B. To minimize the maximum number of pages assigned to a student

C. To find the student with the least pages

D. To count the total number of pages in all books

Solution

1. Step 1: Understand the problem objective

   The problem asks to allocate books to students such that the maximum pages assigned to any student is minimized.

2. Step 2: Identify the binary search approach

   We use binary search on the range of possible maximum pages to find the minimum feasible maximum.

3. Final Answer:

   To minimize the maximum number of pages assigned to a student -> Option B

4. Quick Check:

   Goal = minimize max pages [OK]

Hint: Minimize max pages per student using binary search [OK]

Common Mistakes:

• Confusing minimizing max pages with maximizing total pages
• Thinking the problem counts students instead of pages
• Ignoring the binary search on answer approach

2. Which of the following is the correct way to initialize the binary search boundaries for the Allocate Minimum Pages problem in Go?

easy

A. low := 0; high := sum of all pages

B. low := 0; high := max pages in a single book

C. low := max pages in a single book; high := sum of all pages

D. low := number of students; high := number of books

Solution

1. Step 1: Determine minimum and maximum boundaries

   The minimum possible max pages is the largest single book pages, because no book can be split.

2. Step 2: Set high boundary as total pages

   The maximum possible max pages is the sum of all pages if one student reads all books.

3. Final Answer:

   low := max pages in a single book; high := sum of all pages -> Option C

4. Quick Check:

   Boundaries = max single book to total pages [OK]

Hint: Low = max single book pages, High = sum of all pages [OK]

Common Mistakes:

• Setting low to 0 which is invalid
• Setting high less than sum of pages
• Confusing number of students with page boundaries

3. Given books with pages [10, 20, 30, 40] and 2 students, what is the minimum maximum pages allocated per student?

medium

A. 40

B. 70

C. 50

D. 60

Solution

1. Step 1: Check possible max pages allocations

   Try max pages = 50: allocation could be [10,20,30] and [40], but first student has 60 pages, which is >50, so invalid.

2. Step 2: Try max pages = 60

   Allocation: [10,20,30] = 60 pages, [40] = 40 pages. Both <= 60, valid allocation.

3. Final Answer:

   60 -> Option D

4. Quick Check:

   Minimum max pages = 60 [OK]

Hint: Try mid values to check feasibility [OK]

Common Mistakes:

• Choosing max single book pages as answer without checking allocation
• Assuming equal split always works
• Not verifying allocation feasibility

4. Identify the bug in this Go code snippet for checking allocation feasibility:

func isPossible(books []int, students int, mid int) bool {
    count := 1
    sum := 0
    for _, pages := range books {
        if pages > mid {
            return false
        }
        sum += pages
        if sum > mid {
            count++
            sum = pages
        }
    }
    return count <= students
}

medium

A. No bug, code is correct

B. count should increment before sum addition

C. sum should reset to 0 instead of pages after count++

D. Function should return true if count >= students

Solution

1. Step 1: Analyze sum reset logic

   When sum exceeds mid, count increments and sum resets to current pages, which is correct to start new allocation.

2. Step 2: Check return condition

   Returns true if count of students needed is less than or equal to available students, which is correct.

3. Final Answer:

   No bug, code is correct -> Option A

4. Quick Check:

   Sum reset and count logic correct [OK]

Hint: Reset sum to current pages after exceeding mid [OK]

Common Mistakes:

• Resetting sum to 0 instead of current pages
• Returning true when count exceeds students
• Incrementing count too early

5. You have books with pages [12, 34, 67, 90] and 2 students. Using binary search on answer, what is the minimum maximum pages allocated? Also, explain why allocating [12, 34] to one student and [67, 90] to another is not optimal.

hard

A. 113; Because max pages is 157 which is more than minimum possible

B. 67; Because 67 is the median of pages

C. 90; Because 90 is the largest single book pages

D. 113; Because max pages is 90 which is less than 113

Solution

1. Step 1: Calculate sum and max single book pages

   Sum = 12+34+67+90 = 203; max single book = 90; low=90, high=203.

2. Step 2: Check allocation with mid = (90+203)/2 = 146

   Try allocation: [12,34,67] = 113 pages, [90] = 90 pages; max = 113 <= 146, feasible.

3. Step 3: Try smaller mid to find minimum max pages

   Try mid=113: allocation same as above, feasible. Try mid=112: allocation fails.

4. Step 4: Explain why [12,34] and [67,90] is not optimal

   Allocation sums: 46 and 157; max is 157 which is greater than minimum max pages 113.

5. Final Answer:

   113; Because max pages is 157 which is more than minimum possible -> Option A

6. Quick Check:

   Minimum max pages = 113; given allocation max = 157 [OK]

Hint: Check allocations sums to find minimal max pages [OK]

Common Mistakes:

• Assuming largest single book pages is answer
• Not verifying allocation sums
• Confusing median with allocation max pages