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In this problem, you are tasked with finding the losers of a circular game. The game is played in a circular arrangement, and each round, we eliminate participants in a specific manner.

Given the total number of participants n, and a step value k which determines how participants are eliminated, continue eliminating participants every k-th turn until only one participant remains. You need to return a list of participants who were eliminated in the order they were eliminated.

Clarifying Questions

  1. Input Constraints: Can the number of participants (n) and the step value (k) be large numbers?
  2. Type of Data: Are the inputs guaranteed to be integers?
  3. Output Order: Should the output list the eliminated participants in the order they were eliminated?
  4. Special Cases: What should be returned if n is 1? (Since there’s only one participant, no one should be eliminated).

Assumptions

Strategy

  1. Circular Elimination: Use a list to simulate the circle of participants.
  2. Index Calculation: Use modular arithmetic to efficiently handle the circular nature of the game.
  3. Elimination Simulation: Use a loop to go through and eliminate participants, keeping track of the current index and removing participants until only one remains.
  4. Track and Store: Store the eliminated participants in a list in the order they were eliminated.

Algorithm

  1. Create a list of participants from 1 to n.
  2. Use a variable to keep track of the current index in the participant list.
  3. Iterate until the list of participants is reduced to one element:
    • Calculate the index of the participant to be eliminated using the step value k.
    • Remove the participant from the list and append them to the result list.
  4. Return the result list containing eliminated participants in order.

Code Implementation

def findLosers(n, k):
    # Step 1: Initialize the participants list
    participants = list(range(1, n + 1))
    eliminated = []
    index = 0

    # Step 2: Eliminate participants until only one remains
    while len(participants) > 1:
        # Calculate the index of the participant to eliminate
        index = (index + k - 1) % len(participants)
        # Remove the participant and add to eliminated list
        eliminated.append(participants.pop(index))

    # Return the list of eliminated participants
    return eliminated

# Example usage:
n = 5
k = 2
print(findLosers(n, k))  # Outputs the order in which participants are eliminated

Time Complexity

The algorithm is effective and clear for smaller values of n. For larger values, an optimized structure (like a linked list) could be used to improve complexity but isn’t shown here for simplicity.

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