2012-12-08 09:47:38Morris
[UVA][博奕] 10368 - Euclid's Game
Problem B: 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.
Sample input
34 12 15 24 0 0
Output for sample input
Stan wins Ollie wins
說是最小數字的倍數，其實不然的只有幾種可能需要考慮而已，因為轉一轉就會再次回到相同狀態，考慮其中兩種就好。
#include <stdio.h>
#define LL long long
int dfs(LL a, LL b) { //a < b
if(!a)
return 0;
int win = 0;
win |= !dfs(b%a, a);
if(b/a != 1 && win == 0)
win |= !dfs(b, b+b%a);
return win;
}
int main() {
LL a, b, c;
while(scanf("%lld %lld", &a, &b) == 2) {
if(a == 0 && b == 0)
break;
if(a > b)
c = a, a = b, b = c;
printf("%s wins\n", dfs(a, b) ? "Stan" : "Ollie");
}
return 0;
}