// 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;
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;
}
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 << ""
<< findPages(arr, n, m) << endl;
return 0;
}
// This code is contributed by Aditya Kumar (adityakumar129)
// input
// 1
// 4 2
// 12 34 67 90