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Leetcode 3178. Find the Child Who Has the Ball After K Seconds Sure! Let’s dive into solving a LeetCode problem. Below are sections detailing the problem statement, clarifying questions, strategy, code implementation, and analysis of time complexity.

Problem Statement

Given n children standing in a line, numbered from 0 to n-1, and a ball initially given to the child at position start. After every K seconds, the ball is passed to the next child. If the ball is at position i and it’s the end of the line (the ball should be passed to child n-1), it returns to the start of the line (child 0). You need to determine which child has the ball after t seconds.

Clarifying Questions

  1. Is K always less than n? This would facilitate direct modulo calculations.

  2. Is it guaranteed that n and start are non-negative integers and t is a non-negative integer?

  3. Can K be zero? This would imply that the ball is passed to the next child instantly, essentially acting as a rotating array within certain boundaries.

Strategy

With the provided details, the problem boils down to calculating the position after t seconds of iterating through the children. Considering that after reaching the end of the line the ball returns to the start, the problem can be significantly simplified using modulo arithmetic.

  1. Calculate the total moves as t * K since every second counts for exactly K moves.
  2. Use modulo n on the calculated movements to wrap around the children line.
  3. Add this result to the starting position start.
  4. Finally, use modulo n again to ensure it fits within the bounds [0, n-1].

Code

Here is how the solution can be implemented in Java:

public class Solution {
    public int findChildWithBall(int n, int start, int K, int t) {
        // Total moves after t seconds
        int totalMoves = t * K;
        
        // Calculate the final position using modulo arithmetic
        int finalPosition = (start + totalMoves) % n;
        
        return finalPosition;
    }
}

Time Complexity

Summary

This solution utilizes straightforward mathematical operations to calculate the final position of the ball, leveraging the modulo operator to handle the cyclic nature of the problem efficiently.

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