Allocate minimum number of pages in C++

Allocate a minimum number of pages is a programming problem. Let's discuss this problem in detail and see what can be the solution to it.

Statement

You are given the number of pages of n different books. Also, there are m students to whom the books are to be assigned. The books are arranged in ascending order of the number of pages. And every student can be assigned some consecutive books. The program should return the maximum number of pages read by a student which should be minimum.

Let's take an example to understand this problem in a better way,

Input : books[] = {13 , 43, 65, 87, 92}
   m = 2
Output : 179

Explanation

In this problem, we have two students who are reading books. So, there can be the following ways to distribute books between them.

CASE 1 − [13] , [43, 65, 87, 92 ]

This makes the maximum number of pages read by a student is 13 / 287

CASE 2 − [13, 43] , [65, 87,92]

This makes the maximum number of pages read by a student is 56/ 244

CASE 3 − [13, 43 , 65] , [87, 92]

This makes the maximum number of pages read by a student is 121 / 179

CASE 4 − [13, 43 , 65 , 87] , [92]

This makes the maximum number of pages read by a student is 208 / 92

Out of all these 4 cases, the result is 179

This example must have made the problem clear to you. Now, let's understand the logic behind it and create a program for it.

To solve this problem an easy approach is using the binary search algorithm. For this binary search approach, initialize minimum and a maximum number of pages as 0 and sum of pages of all books. And then fix the mid of these values as the intermediate result which will change as the algo proceeds further.

Now, using the mid-value we will try to find the possibility to find the final solution. If the current mid has chances to become a solution, then the lower half i.e minimum to mid is searching. If this case is not true then the other half i.e. mid to maximum is searched.

This method can be used to find the solution to this problem but as the number of students increases this algorithm tends to provide a less reliable solution.

Example

 Live Demo

#include<bits/stdc++.h>
using namespace std;
bool isPossible(int arr[], int n, int m, int curr_min) ;
int min_pages(int arr[], int n, int m) ;
int main(){
   int n = 5;
   int books[] = {13 , 43, 65, 87, 92};
   cout<<"The number of page in books are :\n";
   for(int i = 0 ; i< n; i++){
      cout<<books[i]<<"\t";
   }
   int m = 2;
   cout<<"\nMinimum number of pages = "<<min_pages(books, n, m)<<endl;
   return 0;
}
bool isPossible(int arr[], int n, int m, int curr_min){
   int studentsRequired = 1;
   int curr_sum = 0;
   for (int i = 0; i < n; i++){
      if (arr[i] > curr_min)
         return false;
      if (curr_sum + arr[i] > curr_min){
         studentsRequired++;
         curr_sum = arr[i];
         if (studentsRequired > m)
            return false;
      }
      else
         curr_sum += arr[i];
   }
   return true;
}
int min_pages(int arr[], int n, int m){
   long long sum = 0;
   if (n < m)
      return -1;
   for (int i = 0; i < n; i++)
      sum += arr[i];
   int minimum = 0, maximum = sum;
   int result = INT_MAX;
   while (minimum <= maximum){
      int mid = (minimum + maximum) / 2;
      if (isPossible(arr, n, m, mid)){
         result = min(result, mid);
         maximum = mid - 1;
      }
      else
         minimum = mid + 1;
   }
   return result;
}

Output

The number of page in books are :
13 43 65 87 92
Minimum number of pages = 179