2358 - Maximum Number of Groups Entering a Competition.

Medium

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 <code>i^th</code> group is less than the sum of the grades of students in the <code>(i + 1)^th</code> group, for all groups (except the last).

• The total number of students in the <code>i^th</code> group is less than the total number of students in the <code>(i + 1)^th</code> 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:

• 1^st group has the students with grades = 12. Sum of grades: 12. Student count: 1

• 2^nd group has the students with grades = 6,7. Sum of grades: 6 + 7 = 13. Student count: 2

• 3^rd 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:

• <code>1 <= grades.length <= 10⁵</code>

• <code>1 <= gradesi<= 10⁵</code>