#2358

Maximum Number of Groups Entering a Competition

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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 i^th 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 i^th 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.

Solution