How do you solve Find the Losers of the Circular Game on LeetCode?

Find the Losers of the Circular Game (LeetCode #2682) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: The game is circular, so we need to use modulo to wrap around when passing the ball.

What is the brute force solution for Find the Losers of the Circular Game?

The brute force approach for Find the Losers of the Circular Game is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we simulate the game step by step, keeping track of which friends receive the ball. We continue passing the ball until a friend receives it for the second time, then we identify the losers. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Losers of the Circular Game?

Find the Losers of the Circular Game uses the following concepts: Array, Hash Table, Simulation. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Find the Losers of the Circular Game?

Always clarify the rules of the game before jumping into coding. Think about edge cases, such as when n is very small or k is larger than n. Explain your thought process while coding; it shows your understanding of the problem.

What are common mistakes when solving Find the Losers of the Circular Game?

Not using modulo correctly when passing the ball, leading to index out of bounds. Failing to account for the case when all friends receive the ball.

#2682

Find the Losers of the Circular Game

Easy

ArrayHash TableSimulationHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

In the optimal solution, we use a set to track the friends who receive the ball and efficiently determine the losers in a single pass through the friends. This reduces unnecessary checks and speeds up the process.

⚙️

Algorithm

3 steps

1Step 1: Initialize a set to track received friends.
2Step 2: Start passing the ball according to the rules until a friend receives it for the second time.
3Step 3: Create a list of losers by checking which friends are not in the received set.

solution.py9 lines

1def findLosers(n, k):
2    received = set()
3    current = 0
4    i = 1
5    while current not in received:
6        received.add(current)
7        current = (current + i * k) % n
8        i += 1
9    return sorted(set(range(n)) - received)

ℹ

Complexity note: The time complexity is O(n) because we pass the ball a maximum of n times before a friend receives it again, and we use a set to track received friends, which allows for O(1) average time complexity for insert and check operations.

1The game is circular, so we need to use modulo to wrap around when passing the ball.
2Tracking who has received the ball is crucial to determine the losers.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.