2358. Maximum Number of Groups Entering a Competition

Description

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

Solution

maximum-number-of-groups-entering-a-competition.py

class Solution:
    def maximumGroups(self, grades: List[int]) -> int:
        n = len(grades)

        def good(k):
            return (k * (k + 1)) // 2 <= n

        left, right = 0, n

        while left < right:
            mid = (left + right + 1) // 2

            if good(mid):
                left = mid
            else:
                right = mid - 1

        return left