Allocate Minimum Pages Binary Search on Answer in DSA Typescript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to find the maximum number of pages in the books array.

DSA Typescript

function maxPages(books: number[]): number {
  let max = 0;
  for (let i = 0; i < books.length; i++) {
    if (books[i] [1] max) {
      max = books[i];
    }
  }
  return max;
}

Drag options to blanks, or click blank then click option'

A!=

B<

C==

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' instead of '>' causes max to stay at 0.

Using '==' or '!=' does not update max correctly.

We compare each book's pages to the current max and update max if the current book has more pages.

2fill in blank

medium

Complete the code to check if it is possible to allocate books such that no student reads more than maxPages.

DSA Typescript

function isPossible(books: number[], students: number, maxPages: number): boolean {
  let studentCount = 1;
  let currentSum = 0;
  for (let i = 0; i < books.length; i++) {
    if (currentSum + books[i] > [1]) {
      studentCount++;
      currentSum = books[i];
      if (studentCount > students) {
        return false;
      }
    } else {
      currentSum += books[i];
    }
  }
  return true;
}

Drag options to blanks, or click blank then click option'

Astudents

BmaxPages

Cbooks.length

DcurrentSum

Attempts:

3 left

💡 Hint

Common Mistakes

Comparing with students or books.length instead of maxPages.

Not resetting currentSum when allocating to a new student.

We check if adding the current book exceeds maxPages, then allocate to next student.

3fill in blank

hard

Fix the error in the binary search loop condition to correctly find the minimum maximum pages.

DSA Typescript

function allocateMinimumPages(books: number[], students: number): number {
  let start = 0;
  let end = books.reduce((a, b) => a + b, 0);
  let result = end;
  while (start [1] end) {
    let mid = Math.floor((start + end) / 2);
    if (isPossible(books, students, mid)) {
      result = mid;
      end = mid - 1;
    } else {
      start = mid + 1;
    }
  }
  return result;
}

Drag options to blanks, or click blank then click option'

A<=

B>=

C<

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>=' or '>' causes the loop to never run or run incorrectly.

Using '<=' can cause off-by-one errors.

The binary search should continue while start is less than end to avoid infinite loop.

4fill in blank

hard

Fill both blanks to correctly initialize the binary search boundaries for allocating minimum pages.

DSA Typescript

function allocatePages(books: number[], students: number): number {
  let start = [1];
  let end = [2];
  let result = end;
  while (start < end) {
    let mid = Math.floor((start + end) / 2);
    if (isPossible(books, students, mid)) {
      result = mid;
      end = mid - 1;
    } else {
      start = mid + 1;
    }
  }
  return result;
}

Drag options to blanks, or click blank then click option'

AMath.max(...books)

B0

Cbooks.length

Dbooks.reduce((a, b) => a + b, 0)

Attempts:

3 left

💡 Hint

Common Mistakes

Starting from 0 causes incorrect lower bound.

Using books.length as boundary is incorrect.

Start with the largest single book pages and end with the sum of all pages.

5fill in blank

hard

Fill all three blanks to complete the function that allocates minimum pages using binary search and helper function.

DSA Typescript

function allocateMinPages(books: number[], students: number): number {
  let start = [1];
  let end = [2];
  let result = end;
  while (start < end) {
    let mid = Math.floor((start + end) / 2);
    if ([3](books, students, mid)) {
      result = mid;
      end = mid - 1;
    } else {
      start = mid + 1;
    }
  }
  return result;
}

Drag options to blanks, or click blank then click option'

AMath.max(...books)

Bbooks.reduce((a, b) => a + b, 0)

CisPossible

Dstudents

Attempts:

3 left

💡 Hint

Common Mistakes

Using students as a boundary instead of sum of pages.

Calling a wrong function instead of isPossible.

Initialize start and end correctly and call isPossible to check feasibility.

Practice

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

easy

A. To assign pages randomly among students

B. To maximize the total number of pages assigned

C. To find the average number of pages per student

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

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 D

4. Quick Check:

   Goal = minimize max pages [OK]

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

Common Mistakes:

• Trying to maximize pages instead of minimizing
• Ignoring the maximum pages constraint
• Confusing total pages with max pages per student

2. Which of the following is the correct TypeScript syntax to declare the binary search boundaries for the Allocate Minimum Pages problem given an array pages?

easy

A. let low = pages.length; let high = Math.max(...pages);

B. let low = Math.min(...pages); let high = pages.length;

C. let low = 0; let high = pages.reduce((a, b) => a + b, 0);

D. let low = 0; let high = Math.min(...pages);

Solution

1. Step 1: Determine low and high boundaries

   Low is minimum possible max pages (0 or max single book pages), high is sum of all pages (max total pages).

2. Step 2: Check correct syntax for sum

   Using reduce sums all pages correctly for high boundary.

3. Final Answer:

   let low = 0; let high = pages.reduce((a, b) => a + b, 0); -> Option C

4. Quick Check:

   low = 0, high = sum pages [OK]

Hint: Sum array for high, zero or max page for low [OK]

Common Mistakes:

• Setting low as pages.length instead of page count
• Using min pages as high boundary
• Incorrect sum calculation syntax

3. Consider the following TypeScript code snippet for checking feasibility in Allocate Minimum Pages problem:

function isPossible(pages: number[], students: number, maxPages: number): boolean {
  let requiredStudents = 1;
  let currentSum = 0;
  for (let page of pages) {
    if (page > maxPages) return false;
    if (currentSum + page > maxPages) {
      requiredStudents++;
      currentSum = page;
    } else {
      currentSum += page;
    }
  }
  return requiredStudents <= students;
}

What is the output of isPossible([10, 20, 30, 40], 2, 50)?

medium

A. false

B. SyntaxError

C. true

D. RuntimeError

Solution

1. Step 1: Trace allocation with maxPages = 50

   Assign pages: 10+20=30 (still <=50), add 30 would exceed 50, so new student starts with 30, then 40 exceeds 50 if added, so new student starts with 40.

2. Step 2: Count required students

   We used 3 students but only 2 allowed, so requiredStudents=3 > 2 means return false. But check carefully: 10+20=30, next 30 alone fits in second student, 40 alone needs third student.

3. Final Answer:

   false -> Option A

4. Quick Check:

   Required students = 3 > 2, so false [OK]

Hint: Count students needed, compare with allowed [OK]

Common Mistakes:

• Ignoring that a single book can exceed maxPages
• Miscounting students when sum exceeds maxPages
• Assuming sum of all pages fits in one student

4. The following TypeScript function attempts to find the minimum maximum pages but has a bug. Identify the bug.

function findMinPages(pages: number[], students: number): number {
  let low = Math.min(...pages);
  let high = pages.reduce((a, b) => a + b, 0);
  let result = high;
  while (low <= high) {
    let mid = Math.floor((low + high) / 2);
    if (isPossible(pages, students, mid)) {
      result = mid;
      high = mid - 1;
    } else {
      low = mid + 1;
    }
  }
  return result;
}

medium

A. High should be min page, not sum of pages

B. Low should start from max page, not min page

C. Mid calculation causes infinite loop

D. Result variable is not updated

Solution

1. Step 1: Analyze low boundary initialization

   Low should be the maximum single book pages, because no student can get less than the largest book.

2. Step 2: Identify impact of wrong low

   Starting low at minimum page can cause incorrect feasibility checks and longer search.

3. Final Answer:

   Low should start from max page, not min page -> Option B

4. Quick Check:

   Low = max page [OK]

Hint: Low boundary = max single book pages [OK]

Common Mistakes:

• Setting low to min page instead of max page
• Confusing high boundary with low
• Not updating result inside loop

5. Given books with pages [12, 34, 67, 90] and 3 students, what is the minimum maximum pages allocated to any student using binary search on answer?

hard

A. 90

B. 113

C. 67

D. 34

Solution

1. Step 1: Set search boundaries

   Low = max pages = 90, High = sum pages = 12+34+67+90=203.

2. Step 2: Binary search feasibility checks

   Mid = (90+203)//2=146. Check if possible with maxPages=146: allocate [12+34+67=113] to student1, 90 to student2, only 2 students needed <=3, possible. So high=145.

3. Step 3: Narrow down to minimum max pages

   Continuing: mid=103 possible [12+34=46,67,90] 3 students. mid=96 possible. mid=92 possible. mid=90: [12+34=46], [67], [90] all <=90, 3 students <=3 feasible, high=89. Loop ends with result=90.

4. Step 4: Re-evaluate minimum max pages

   Check if 113 is feasible with 3 students: [12+34+67=113], [90] 2 students needed <=3, so 113 is feasible but not minimum.

5. Step 5: Check if 90 is feasible

   Allocations: [12+34=46], [67], [90] 3 students needed <=3, feasible.

6. Final Answer:

   90 -> Option A

7. Quick Check:

   Minimum max pages = 90 [OK]

Hint: Binary search between max page and sum pages [OK]

Common Mistakes:

• Misallocating at max=90 thinking 4 students needed
• Miscounting students during allocation
• Confusing with 2 students (113)