EliminationGame.java

package com.fishercoder.solutions;

import java.util.ArrayList;
import java.util.List;

/**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 class EliminationGame {
    
    //then I turned to Discuss and found this post: https://discuss.leetcode.com/topic/55870/share-my-solutions-for-contest-2
    //instead of literally removing half of the elements in each scan, this solution is just moving the pointer to point to next start position
    //So brilliant!
    public int lastRemaining(int n) {
        int remaining = n;
        int start = 1;
        int step = 2;
        boolean forward = true;
        while(remaining > 1){
            remaining /= 2;
            if(forward) start = start + step*remaining - step/2;
            else start = start - step*remaining + step/2;
            step *= 2;
            forward = !forward;
        }
        return start;
    }

    //I tried brute force, all producing the correct output, but got TLE by OJ.
    public static int lastRemaining_brute_force_TLE(int n) {
        List<Integer> list  = new ArrayList();
        for(int i = 0; i < n; i++){
            list.add(i+1);
        }
        boolean forward = true;
        while(list.size() > 1){
            int size = list.size()/2;
            if(list.size() == 1) return list.get(0);
            if(forward){
                if(list.size() == 1) return list.get(0);
                for(int i = 0; i <= size && i < list.size(); i++){
                    list.remove(i);
                }
                forward = false;
            } else {
                if(list.size() == 1) return list.get(0);
                for(int i = list.size()-1, count = 0; i >= 0 && count <= size; count++){
                    list.remove(i);
                    i -= 2;
                }
                forward = true;
            }
        }
        return list.get(0);
    }
    
    public static void main(String...strings){
        System.out.println(lastRemaining_brute_force_TLE(5204));
        System.out.println(lastRemaining_brute_force_TLE(5058));
//        System.out.println(lastRemaining(10));
//        System.out.println(lastRemaining(9));
//        System.out.println(lastRemaining(3));
    }

}