UVa 160 Factors and Factorials (数论)

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160 - Factors and Factorials

Time limit: 3.000 seconds

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=96

题目点这：http://uva.onlinejudge.org/external/1/160.pdf

思路：遍历1~n计算质因子个数即可。

你若还想再快点的话，就用[n/p]+[n/p^2]+[n/p^3]+...+1在O(log n/log p)的时间内统计出n!的质因子p的个数。(不过此题n太小，两种方法在时间上相差不大)

完整代码：

/*0.016s*/#include<cstdio>#include<cmath>#include<cstring>int prime[100], c, ans[100];bool vis[110];inline void create_prime(){int i, j;for (i = 2; i <= 11; ++i)if (!vis[i]){prime[c++] = i;for (j = i * i; j < 110; j += i)vis[j] = true;}for (; i < 110; ++i)if (!vis[i])prime[c++] = i;}int main(void){create_prime();int n, temp;while (scanf("%d", &n), n){memset(ans, 0, sizeof(ans));printf("%3d! =", n);for (int i = 2; i <= n; i++){temp = i;for (int j = 0; j < c && prime[j] <= i; j++){while (temp % prime[j] == 0){++ans[prime[j]];temp /= prime[j];}}}for (int i = 0, j = 0; prime[i] <= n; i++, j++){if (j % 15 == 0 && j) printf("\n      ");printf("%3d", ans[prime[i]]);}putchar('\n');}return 0;}