2013
12-12

# Euclid’s Game

Two players, Stan and Ollie, play, starting with two natural numbers. Stan, the first player, subtracts any positive multiple of the lesser of the two numbers from the greater of the two numbers, provided that the resulting number must be nonnegative. Then Ollie, the second player, does the same with the two resulting numbers, then Stan, etc., alternately, until one player is able to subtract a multiple of the lesser number from the greater to reach 0, and thereby wins. For example, the players may start with (25,7):

25 7
11 7
4 7
4 3
1 3
1 0

an Stan wins.

The input consists of a number of lines. Each line contains two positive integers giving the starting two numbers of the game. Stan always starts.

For each line of input, output one line saying either Stan wins or Ollie wins assuming that both of them play perfectly. The last line of input contains two zeroes and should not be processed.

34 12
15 24
0 0

Stan wins
Ollie wins

/*
* 如果面对a==b 或者a>=2*b则先手比赢
* 如果b<a<2*b.那么只有一条路，变成a-b,b;
* 这个时候互换大小变成b,a-b.
* 这样一直循环，看谁面对a==b || a>=2*b的情况
*/

#include <iostream>
#include <string.h>
#include <algorithm>
#include <stdio.h>
using namespace std;

int main()
{
int a,b;
while(scanf("%d%d",&a,&b)==2)
{
if(a==0||b==0)break;
if(a<b)swap(a,b);
bool flag=true;
while(1)
{
if(a==b || a/b>=2)break;
a=a-b;
swap(a,b);
flag=!flag;
}
if(flag)printf("Stan wins\n");
else printf("Ollie wins\n");
}
return 0;
}