# Student Database

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

``````// 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,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;
}``````  