series.java

import java.util.*;
public class series
{
    public static void main(int n) {
        for(int i=1;i<=n;i++){
            //System.out.println(operate(i));
            System.out.println(i+" -> "+op(i));
        }
    }

    public static int operate(int n){
        List<Integer> deck = new ArrayList<Integer>();
        //1 at top,
        //N at bottom
        for(int i=1;i<=n;i++){
            deck.add(i);
        }
        while(deck.size()>=2) {
            deck.remove(0);
            deck.add(deck.remove(0));
        }
        return deck.get(0);
    }

    public static int op(int n) {
        if((n & (n - 1)) == 0){
            return n;
        } else {
            int k=(int)Math.floor((Math.log(n)/(1.0*Math.log(2))))+1;
            return (int)(Math.pow(2,k)-2*(Math.pow(2,k)-n));
        }
    }

    public static int finalnum(int n){
        if(n<2)return n;
        else {
            if(n<finalnum(n-1)+2){
                return 2;
            } else {
                return finalnum(n-1)+2;
            }
        }
    }

    public static int exp(int a,int b)
    {
        int e=1;
        for(int i=0;i<b;i++)
        {
            e=e*a;
        }
        return e;
    }

    public static int finaln(int num) {
        int alive=0,k;
        for(int i=0;i<num;i++)
        {
            k=exp(2,i);
            if(k>num)
            {
                k=exp(2,i-1);
                int x=num-k;
                alive=(2*x)+1;
                break;
            }
        }
        return alive;
    }
}