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UVA 11762 - Race to 1(概率)

UVA 11762 - Race to 1

题意:给定一个n,每次随即选择一个n以内的质数,假设不是质因子,就保持不变,假设是的话。就把n除掉该因子,问n变成1的次数的期望值

思路:tot为总的质数。cnt为质因子个数,那么f(n)=(1?cnt/tot)?f(n)+f(n/prime)?(1/tot),然后利用记忆化搜索去做就可以

代码:

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

const int N = 1000005;
int t, n, prime[N], pn = 0, vis[N];
double f[N];

void get_table() {
	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;
 	}
}

double dfs(int n) {
	if (f[n] != -1) return f[n];
	f[n] = 0;
	if (n == 1) return f[n];
	int tot = 0, cnt = 0;
	for (int i = 0; i < pn && prime[i] <= n; i++) {
		tot++;
		if (n % prime[i]) continue;
		cnt++;
		f[n] += dfs(n / prime[i]);
 	}
 	f[n] = (f[n] + tot) / cnt;
	return f[n];
}

int main() {
	get_table();
	for (int i = 0; i < N; i++) f[i] = -1;
	int cas = 0;
	scanf("%d", &t);
	while (t--) {
		scanf("%d", &n);
		printf("Case %d: %.7lf\n", ++cas, dfs(n));
 	}
	return 0;
}


UVA 11762 - Race to 1(概率)