Allocate Minimum Number of Pages.cpp

/*
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. 
Example : 
 

Input : pages[] = {12, 34, 67, 90}
        m = 2
Output : 113
Explanation:
There are 2 number of students. Books can be distributed 
in following fashion : 
  1) [12] and [34, 67, 90]
      Max number of pages is allocated to student 
      2 with 34 + 67 + 90 = 191 pages
  2) [12, 34] and [67, 90]
      Max number of pages is allocated to student
      2 with 67 + 90 = 157 pages 
  3) [12, 34, 67] and [90]
      Max number of pages is allocated to student 
      1 with 12 + 34 + 67 = 113 pages

Of the 3 cases, Option 3 has the minimum pages = 113.
*/


bool isValid(int arr[], int n, int m, int max) {

	int student = 1; // 1st student
	int sum = 0; // total pages student have
	for(int i = 0; i < n; i++) {
		sum += arr[i];
		if(sum > max) {
		student++;
		sum = arr[i];
		}
		if(student > m)
		return false;
	}
	return true;

}

int findPages(int arr[], int n, int m)
{ 
	if(n < m) return -1;
	int start = -1; // max
	int end = 0; // total
	for(int i = 0; i < n; i++) {
		start = max(arr[i],start);
		end += arr[i];
	}
	int ans = -1;
	int mid;
	while(start <= end) { // binary search
		mid = start + (end - start) / 2;
		if(isValid(arr, n, m, mid)) {
		ans = mid;
		end = mid - 1;
		}
		else {
		start = mid + 1;
		}
	}
	return ans;
}