Find the Child Who Has the Ball After K Seconds - Problem

You are given two positive integers n and k. There are n children numbered from 0 to n - 1 standing in a queue in order from left to right.

Initially, child 0 holds a ball and the direction of passing the ball is towards the right direction. After each second, the child holding the ball passes it to the child next to them. Once the ball reaches either end of the line, i.e. child 0 or child n - 1, the direction of passing is reversed.

Return the number of the child who receives the ball after k seconds.

Input & Output

Example 1 — Basic Case
$ Input: n = 3, k = 5
Output: 1
💡 Note: Ball moves: 0→1→2→1→0→1. After 5 seconds, ball is at position 1.
Example 2 — Reaches End
$ Input: n = 5, k = 6
Output: 2
💡 Note: Ball moves: 0→1→2→3→4→3→2. After 6 seconds, ball is at position 2.
Example 3 — Single Child
$ Input: n = 1, k = 10
Output: 0
💡 Note: Only one child, so ball always stays at position 0.

Constraints

  • 1 ≤ n ≤ 50
  • 1 ≤ k ≤ 50

Visualization

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Ball Passing Game: Find Child After K Seconds🏀 01234Ball moves right: 0→1→2→3→4Then bounces back left: 4→3→2→1→0Zigzag Pattern Repeats Every 2(n-1) Seconds
Understanding the Visualization
1
Input
n children in line, k seconds to simulate
2
Process
Ball bounces back and forth between ends
3
Output
Position of child holding ball after k seconds
Key Takeaway
🎯 Key Insight: The ball follows a predictable zigzag pattern that can be solved with modular arithmetic
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