A32.cpp

#include <iostream>
#include <vector>
#include <numeric>
#include <algorithm>

using namespace std;

// Function to check if the allocation is possible
bool isPossible(const vector<int>& books, int n, int m, int maxPages) {
    int studentsRequired = 1;
    int currentSum = 0;

    for (int i = 0; i < n; ++i) {
        if (books[i] > maxPages) return false; // Single book exceeds maxPages
        
        if (currentSum + books[i] > maxPages) {
            studentsRequired++;
            currentSum = books[i];
            
            if (studentsRequired > m) return false;
        } else {
            currentSum += books[i];
        }
    }
    return true;
}

// Function to find the minimum of the maximum number of pages
int allocateBooks(const vector<int>& books, int n, int m) {
    if (m > n) return -1; // Not enough books for all students

    int start = *max_element(books.begin(), books.end());
    int end = accumulate(books.begin(), books.end(), 0);
    int result = -1;

    while (start <= end) {
        int mid = start + (end - start) / 2;

        if (isPossible(books, n, m, mid)) {
            result = mid;
            end = mid - 1; // Try for a smaller maximum
        } else {
            start = mid + 1; // Increase the maximum
        }
    }

    return result;
}

int main() {
    vector<int> books = {10,20,30,40}; // Number of pages in each book
    int students = 2; // Number of students

    int n = books.size();
    int result = allocateBooks(books, n, students);

    if (result != -1) {
        cout << "The minimum of the maximum pages allocated is: " << result << endl;
    } else {
        cout << "Book allocation is not possible." << endl;
    }

    return 0;
}