leetcode EliminationGame
z
 2019-04-09 10:36:27   
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public class EliminationGame {
  /**
   * There is a list of sorted integers from 1 to n. Starting from left to right,
   * remove the first number and every other number afterward until you reach the end of the list.
   *
   * Repeat the previous step again, but this time from right to left,
   * remove the right most number and every other number from the remaining numbers.
   *
   * We keep repeating the steps again, alternating left to right and right to left,
   * until a single number remains.
   *
   * Find the last number that remains starting with a list of length n.
   *
   * Example:
   *
   * Input:
   * n = 9,
   * 1 2 3 4 5 6 7 8 9
   * 2 4 6 8
   * 2 6
   * 6
   *
   * Output:
   * 6
   */
  public int lastRemaining(int n) {
    boolean left = true;
    int head = 1;
    int step = 1;
    int remain = n;
    while(remain !=1){
      if (left || remain%2 == 1){
        head = head + step;

      }
      remain = remain/2;
      step = step * 2;
      left = !left;
    }
    return head;
  }
}