Josephus Problem Statement

Consider 'N' individuals standing in a circle, numbered consecutively from 1 to N, in a clockwise direction. Initially, the person at position 1 starts counting and will skip K-1 persons (including themselves), eliminating the Kth person. The counting resumes from the next person, repeatedly skipping K-1 persons and eliminating the Kth one, until only one person remains.

Your task is to determine the position of this last surviving person with respect to the original numbering.

Example:

Input:

T = 1
N = 5, K = 2

Output:

3

Explanation:

In the circle numbered from 1 to 5, every 2nd person is removed until only one remains. Thus, position 3 is the last person standing.

Constraints:

1

Question

Josephus Problem Statement

Consider 'N' individuals standing in a circle, numbered consecutively from 1 to N, in a clockwise direction. Initially, the person at position 1 starts counting and will skip K-1 persons (including themselves), eliminating the Kth person. The counting resumes from the next person, repeatedly skipping K-1 persons and eliminating the Kth one, until only one person remains.

Your task is to determine the position of this last surviving person with respect to the original numbering.

Example:

Input:

T = 1
N = 5, K = 2

Output:

Explanation:

In the circle numbered from 1 to 5, every 2nd person is removed until only one remains. Thus, position 3 is the last person standing.

Constraints:

1 <= T <= 50
1 <= N, K <= 10⁴
Time Limit: 1 sec

Accepted Answer

This question is about finding the position of the last person surviving in a circle of N people, where each person kills the Kth person in a clockwise direction.

Implement a function that takes the number of test cases, N, and K as input
For each test case, simulate the killing process by iterating through the circle and skipping K-1 people
Keep track of the position of the last person surviving and return it as the output