Book Allocation

#include <bits/stdc++.h>
using namespace std;

// Utility function to check if current minimum value
// is feasible or not.
bool isPossible(int arr[], int n, int m, int curr_min)
{
    int studentsRequired = 1;
    int curr_sum = 0;

    // iterate over all books
    for (int i = 0; i < n; i++) {
        // check if current number of pages are greater
        // than curr_min that means we will get the result
        // after mid no. of pages
        if (arr[i] > curr_min)
            return false;

        // count how many students are required
        // to distribute curr_min pages
        if (curr_sum + arr[i] > curr_min) {
            // increment student count
            studentsRequired++;

            // update curr_sum
            curr_sum = arr[i];

            // if students required becomes greater
            // than given no. of students,return false
            if (studentsRequired > m)
                return false;
        }

        // else update curr_sum
        else
            curr_sum += arr[i];
    }
    return true;
}

// function to find minimum pages
int findPages(int arr[], int n, int m)
{
    long long sum = 0;

    // return -1 if no. of books is less than
    // no. of students
    if (n < m)
        return -1;
    int mx = INT_MIN;

    // Count total number of pages
    for (int i = 0; i < n; i++) {
        sum += arr[i];
        mx = max(mx, arr[i]);
    }

    // initialize start as 0 pages and end as
    // total pages
    int start = mx, end = sum;
    int result = INT_MAX;

    // traverse until start <= end
    while (start <= end) {
        // check if it is possible to distribute
        // books by using mid as current minimum
        int mid = (start + end) / 2;
        if (isPossible(arr, n, m, mid)) {
            // update result to current distribution
            // as it's the best we have found till now.
            result = mid;

            // as we are finding minimum and books
            // are sorted so reduce end = mid -1
            // that means
            end = mid - 1;
        }

        else
            // if not possible means pages should be
            // increased so update start = mid + 1
            start = mid + 1;
    }

    // at-last return minimum no. of  pages
    return result;
}

// Driver code
int main()
{
    // Number of pages in books
    int arr[] = { 12, 34, 67, 90 };
    int n = sizeof arr / sizeof arr[0];
    int m = 2; // No. of students

    cout << "Minimum number of pages = "
         << findPages(arr, n, m) << endl;
    return 0;
}