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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 nonempty 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:  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:
1 <= grades.length <= 10^{5}
1 <= grades[i] <= 10^{5}
Solutions

class Solution { public int maximumGroups(int[] grades) { int n = grades.length; int l = 0, r = n; while (l < r) { int mid = (l + r + 1) >> 1; if (1L * mid * mid + mid > n * 2L) { r = mid  1; } else { l = mid; } } return l; } }

class Solution { public: int maximumGroups(vector<int>& grades) { int n = grades.size(); int l = 0, r = n; while (l < r) { int mid = (l + r + 1) >> 1; if (1LL * mid * mid + mid > n * 2LL) { r = mid  1; } else { l = mid; } } return l; } };

class Solution: def maximumGroups(self, grades: List[int]) > int: n = len(grades) return bisect_right(range(n + 1), n * 2, key=lambda x: x * x + x)  1

func maximumGroups(grades []int) int { n := len(grades) return sort.Search(n, func(k int) bool { k++ return k*k+k > n*2 }) }

function maximumGroups(grades: number[]): number { const n = grades.length; let l = 1; let r = n; while (l < r) { const mid = (l + r + 1) >> 1; if (mid * mid + mid > n * 2) { r = mid  1; } else { l = mid; } } return l; }