Euclid's Game
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 7418 | Accepted: 3022 |
Description
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):
an Stan wins.
25 7
11 7
4 7
4 3
1 3
1 0
an Stan wins.
Input
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.
Output
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.
Sample Input
34 12 15 24 0 0
Sample Output
Stan wins Ollie wins
Source
分两种情况 b - a < a b - a > a
第一种情况别无选择，第二种情况必胜，由此可得答案
1 #include <iostream> 2 #include <cstdio> 3 #include <cstring> 4 #include <algorithm> 5 6 using namespace std; 7 8 int a, b; 9 10 bool check() { 11 bool flag = 1; 12 for(;;) { 13 if(a > b) swap(a,b); 14 if(b % a == 0) break; 15 if(b - a > a) break; 16 b -= a; 17 flag = !flag; 18 } 19 20 return flag; 21 } 22 int main() 23 { 24 while(~scanf("%d%d",&a, &b) && (a + b)) { 25 if(check()) { 26 printf("Stan wins "); 27 } else { 28 printf("Ollie wins "); 29 } 30 } 31 //cout << "Hello world!" << endl; 32 return 0; 33 }