uva/10061sol.cpp at master · liuhb86/uva · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92

/*
10061
How many zeros and how many digits?
*/
#include<iostream>
#include<vector>
#include<cmath>

using namespace std;

#define maxn 1048579

char sv[maxn+2];
int N, B;
vector<int>P;

void Primetable() {
	int i, j;
	for(i = 2; i*i<maxn; ) {
		for(j = i+i; j<= maxn; j+=i)
			sv[j] = 1;
		for(++i; sv[i]; i++);
	}
	P.push_back(2);
	for(i = 3; i<maxn; i+=2)
		if(sv[i] == 0)
			P.push_back(i);
}

int times(int n) {
	int i, sum = 0;
	for(i = n; i<=N; i *= n)
		sum += N/i;
	return sum;
}

int Zeros() {
	int i, k, n = B, zero = 2147483647, t, a, m;
	for(i = 0; i<P.size() && n>1; i++) {
		m = P[i];
		m *= m;
		if(m> n) break;
		if(n % P[i] == 0) {
			k = 0;
			while(n % P[i] == 0) {
				k ++;
				n/= P[i];
			}
			t = times(P[i]);
			a = t/k;
			if(zero>a)
				zero = a;
		}
	}
	if(n>1)
		t = times(n);
	if(zero>t) zero = t;
	return zero;
}

int digit() {
	int i, dig;
	double sum = 0;
	for(i = 1; i<= N; i++)
		sum += log10(i) / log10(B);
	sum += 1e-5;
	dig = ceil(sum);
	return dig;
}

void Cal() {
	int z, dig;
	if(N == 0) {
		cout<<"0 "<<"1\n";
		return;
	}
	if(N == 1) {
		cout<<"0 "<<"1\n";
		return;
	}
	z = Zeros();
	dig = digit();
	cout<<z<<" "<<dig<<endl;
}

int main() {
	Primetable();
	while(cin>>N>>B) {
		Cal();
	}
}