UVA 11859

UVA 11859 - Division Game

题意：给定一个矩阵。每次能选一行中几个数字，把他们变成他们的因子，最后不能变的人输。问能否先手必胜

思路：转变成因子等价于删去一些素数。这样问题转化为了Nim游戏

代码：

#include <stdio.h>
#include <string.h>

const int N = 10005;
int t, n, m, num, cnt[N], vis[N], prime[N], pn = 0;

int main() {
	for (int i = 2; i < N; i++) {
		if (vis[i]) continue;
		prime[pn++] = i;
		for (int j = i; j < N; j += i) {
			vis[j] = 1;
  		}
 	}
 	for (int i = 2; i < N; i++) {
 		int num = i;
   		for (int j = 0; j < pn && prime[j] <= i; j++) {
 			while (num % prime[j] == 0) {
 				cnt[i]++;
 				num /= prime[j];
 			}
   		}
  	}
 	int cas = 0;
	scanf("%d", &t);
	while (t--) {
		int ans = 0;
		scanf("%d%d", &n, &m);
		for (int i = 0; i < n; i++) {
			int sum = 0;
   			for (int j = 0; j < m; j++) {
   				scanf("%d", &num);
				sum += cnt[num];
   			}
   			ans ^= sum;
  		}
  		printf("Case #%d: %s
", ++cas, ans == 0?"NO":"YES");
 	}
	return 0;
}