QUESTION

Given number of pages in n different books and m students. The books are arranged in ascending order of number of pages. Every student is assigned to read some consecutive books. The task is to assign books in such a way that the maximum number of pages assigned to a student is minimum. Take Number of books,n, number of pages in n books and the number of students, m as input.

“TESTCASE_1”: “4\n12 34 67 90\n2\n###—###SEPERATOR—###—\nMinimum number of pages = 113”, “TESTCASE_2”: “6\n30 55 72 98 102 139\n3\n###—###SEPERATOR—###—\nMinimum number of pages = 200”, “TESTCASE_3”: “3\n10 22 30\n2\n###—###SEPERATOR—###—\nMinimum number of pages = 32”, “TESTCASE_4”: “0\n###—###SEPERATOR—###—\n0”, “TESTCASE_5”: “0\n###—###SEPERATOR—###—\n0

ANSWER

// C++ program for optimal allocation of pages
#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;
 
    // Count total number of pages
    for (int i = 0; i < n; i++)
        sum += arr[i];
 
    // initialize start as 0 pages and end as
    // total pages
    int start = 0, end = sum;
    int result = INT_MAX;
 
    // traverse until start <= end
    while (start <= end)
    {
        // check if it is possible to distribute
        // books by using mid is current minimum
        int mid = (start + end) / 2;
        if (isPossible(arr, n, m, mid))
        {
            // if yes then find the minimum distribution
            result = min(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;
}
 
// Drivers code
int main()
{
    //Number of pages in books
    int arr[100],n,m,i;
  cin>>n;
  for(i=0;i<n;i++)
    cin>>arr[i];
  cin>>m;
 
    cout << "Minimum number of pages = "
         << findPages(arr, n, m) << endl;
    return 0;
}