maximum_number_of_groups_entering_a_competition.py

"""
You are given a positive integer array grades which represents the grades of students in a university. You would like to enter all these students into a competition in ordered non-empty groups, such that the ordering meets the following conditions:

The sum of the grades of students in the ith group is less than the sum of the grades of students in the (i + 1)th group, for all groups (except the last).
The total number of students in the ith group is less than the total number of students in the (i + 1)th group, for all groups (except the last).
Return the maximum number of groups that can be formed.

 

Example 1:

Input: grades = [10,6,12,7,3,5]
Output: 3
Explanation: The following is a possible way to form 3 groups of students:
- 1st group has the students with grades = [12]. Sum of grades: 12. Student count: 1
- 2nd group has the students with grades = [6,7]. Sum of grades: 6 + 7 = 13. Student count: 2
- 3rd group has the students with grades = [10,3,5]. Sum of grades: 10 + 3 + 5 = 18. Student count: 3
It can be shown that it is not possible to form more than 3 groups.
Example 2:

Input: grades = [8,8]
Output: 1
Explanation: We can only form 1 group, since forming 2 groups would lead to an equal number of students in both groups.
 

Constraints:

1 <= grades.length <= 105
1 <= grades[i] <= 105

"""

class Solution:
    def maximumGroups(self, grades: List[int]) -> int:
        N, k = len(grades), 1
        while k * (k+1) // 2 <= N: 
            k += 1
        return k-1