Abstract / Summary

Find the largest number of teams that can enter a competition given skill requirements and team member counts.

Note

The full problem description, including helpful examples, can be found on LeetCode.

This problem is ranked as

and has an acceptance rate of about 69% (60k+ submissions).

Typical patterns to solve this problem:

• Array
• Binary Search
• Greedy
• Math

Every single line of code was written by me, 100% from scratch, between August 2023 and August 2024.
However, two years later I set up this website and used various AI tools to generate most of the walkthrough / explanations below.

See this dedicated page for more details.

Overview

The provided Solution class implements a method maximumGroups that determines how many consecutive groups can be formed from a list of student grades when the grades are implicitly ordered from worst to best. The grouping rule requires the first group to contain one student, the second group two students, the third group three, and so on. The algorithm proceeds by iterating through the list, tracking how many students have already been placed into groups and how many groups have been created, stopping when there are not enough remaining students to form the next larger group.

Core Logic

The method begins by initializing two counters: groups, which records the number of groups formed so far, and done, which records the total number of students that have been assigned to groups.

groups = 0
done   = 0  # students grouped so far

A while loop drives the grouping process. The loop condition checks that not all students have been assigned yet.

while done < len(grades):

Inside the loop the number of students still unassigned is computed.

remaining = len(grades) - done

The algorithm then evaluates whether the remaining students are insufficient to create the next group. The size of the next group would be groups + 1. If the number of remaining students is less than or equal to the current number of groups, the loop terminates early because the next required group size would exceed what is left.

if remaining <= groups:
    break

When enough students remain, a new group is formed. The groups counter is incremented to reflect the new group, and done is increased by the size of this newly created group (which equals the updated groups value).

groups += 1
done   += groups

After the loop finishes, the method returns the total number of groups that could be formed.

return groups

Edge-Case Handling

The algorithm gracefully handles an empty input list. Since len(grades) is zero, the while condition done < len(grades) evaluates to false immediately, and the method returns 0, indicating that no groups can be formed.

When the list contains a single element, the first iteration sees remaining equal to 1 and groups equal to 0. The condition remaining <= groups is false, so a group of size 1 is created, groups becomes 1, done becomes 1, and the loop exits. The method returns 1, correctly reflecting that one group can be formed.

If the list length is such that the remaining students are exactly equal to the current number of groups, the early-break condition triggers. For example, with grades length 3, after forming groups of sizes 1 and 2 (groups becomes 2, done becomes 3), remaining becomes 0. The loop condition fails, and the method returns 2. This demonstrates that the code stops precisely when no further group can satisfy the increasing size requirement.

Implicit Performance Optimizations

The implementation relies on a simple integer counter update rather than any auxiliary data structures, keeping the auxiliary memory footprint minimal. Each iteration performs only constant-time arithmetic and a single comparison, ensuring that the loop runs in proportion to the number of groups that can actually be formed rather than the total number of possible group sizes. The early-break check (if remaining <= groups) prevents unnecessary iterations once it becomes impossible to satisfy the next group size, which can significantly reduce the number of loop cycles for inputs where the list length is not large enough to accommodate many groups.

By using the cumulative done counter, the algorithm avoids recomputing the sum of the first k natural numbers on each iteration, thereby eliminating redundant work. This incremental approach means that each step builds directly on the previous state, leading to a tight execution path with minimal overhead.

Think of this code like organizing a group of friends who are all lined up to play a game. You want to arrange them into rows, but each row needs to be a little bit bigger than the one before it. The first row has one person, the next row has two people, the next has three, and so you keep going as long as there are enough friends left to make the next row bigger.

The code starts by counting how many friends are still waiting to be put into a row. It checks if there are enough friends left to make a new group that is bigger than the last one. If there are, it adds one more row and keeps track of how many friends have already joined. If there are not enough friends left to make the next row bigger, it simply stops. It counts how many rows were made until it ran out of enough friends to keep growing.

Several LLMs ranked my code quality on a scale from 1 (very poor) to 10 (outstanding):

not analyzed yet

I wrote a basic crawler to find other solutions to that problem.
Obviously, I did that after I solved the problem myself.

In general, AlgoMonster and WalkCCC solutions are high-quality and always worth a look.
I haven't checked most of the other solutions, but they might be helpful as well.

And of course, the LeetCode forum is always a good place (or even the best) to look for alternative approaches.

(click on a column header to sort the table)

	author
author	solutions
www	AlgoMonster		Java	Python	C++			TS
	WalkCCC		Java	Python	C++
	leetcode.ca		Java	Python	C++	Go	Rust	TS
	Progiez		Java	Python	C++
github	charles-wangkai		Java
	everthis	JS
	fsq				C++
	JoshCrozier	JS
	lkwq007			Python
	varunu28		Java
AlgoMonster	C++, Python, Java, TypeScript
WalkCCC	C++, Python, Java
leetcode.ca	C++, Go, Java, Python, Rust, TypeScript
Progiez	C++, Java, Python
charles-wangkai	Java
everthis	JavaScript
fsq	C++
JoshCrozier	JavaScript
lkwq007	Python
varunu28	Java

There are a few extra pages giving you some insights into my setup:

• Tech Stack - my development environment and tools
• AI - how AI helped me create this website (NOT solving the problems)
• Progress - progression over time
• Quality - code quality