Summary of Implementing the Book Allocation Problem Using Binary Search in Java
The Book Allocation Problem aims to allocate a set of books with varying pages among students, ensuring that the maximum pages assigned to any student are minimized. The solution uses binary search to efficiently determine the optimal page allocation.
Problem Overview:
The goal is to distribute n books among m students such that the maximum number of pages a student reads is minimized. - - Each student gets a contiguous block of books, and the solution should ensure a fair distribution where the student reading the most pages is assigned the least possible.
Binary Search Approach:
The search space is defined between the maximum pages of a single book (lower bound) and the total sum of all pages (upper bound).
The midpoint is computed at each iteration and treated as the maximum number of pages a student can read. The helper function countStudents determines how many students are required if the maximum page limit is set to this midpoint.
If the number of students required exceeds m, the lower bound is increased (low = mid + 1). Otherwise, the upper bound is decreased (high = mid - 1), gradually narrowing the search space until the minimum possible page allocation is found.
Helper Function:
countStudents(ArrayList<Integer> arr, int pages): This function counts how many students are needed if each student is limited to reading pages pages. If the total number of pages for a student exceeds the current limit, the next student takes over.
Main Functionality:
findPages: Implements the binary search by adjusting the limits based on the student distribution calculated by countStudents.
It returns the minimum number of pages a student has to read when books are distributed optimally.
Time Complexity: The time complexity is dominated by the binary search (logarithmic complexity) combined with the linear scan of books to count students, resulting in an overall time complexity of O(n * log(sum of pages)).
This method provides an efficient way to solve the book allocation problem by balancing the load among students using binary search.
Key Features:
Binary Search Approach: The solution uses binary search to optimize the maximum number of pages allocated to a student.
Helper Function (countStudents): Determines how many students are required given a page limit, ensuring the distribution is feasible under the current constraints.
Efficient Algorithm: The solution efficiently narrows down the search space using binary search, ensuring the minimal maximum pages allocated to any student.
Testing:
A sample dataset with 5 books and 4 students is included in the main function, with expected output printed for verification.
Example Input:
ArrayList arr = new ArrayList<>(Arrays.asList(25, 46, 28, 49, 24));
int n = 5;
int m = 4;
Summary of Implementing the Book Allocation Problem Using Binary Search in Java
The Book Allocation Problem aims to allocate a set of books with varying pages among students, ensuring that the maximum pages assigned to any student are minimized. The solution uses binary search to efficiently determine the optimal page allocation.
countStudentsdetermines how many students are required if the maximum page limit is set to this midpoint. If the number of students required exceeds m, the lower bound is increased(low = mid + 1). Otherwise, the upper bound is decreased(high = mid - 1), gradually narrowing the search space until the minimum possible page allocation is found.countStudents(ArrayList<Integer> arr, int pages): This function counts how many students are needed if each student is limited to reading pages pages. If the total number of pages for a student exceeds the current limit, the next student takes over.findPages: Implements the binary search by adjusting the limits based on the student distribution calculated bycountStudents.This method provides an efficient way to solve the book allocation problem by balancing the load among students using binary search.
Key Features:
Testing:
A sample dataset with 5 books and 4 students is included in the main function, with expected output printed for verification.
Example Input: ArrayList arr = new ArrayList<>(Arrays.asList(25, 46, 28, 49, 24));
int n = 5;
int m = 4;
Expected Output: The answer is: 71