Morris' Blog

2012-09-19 22:08:35Morris

[UVA] 10139 - Factovisors

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Problem D: Factovisors

The factorial function, n! is defined thus for n a non-negative integer:

   0! = 1
   n! = n * (n-1)!   (n > 0)

We say that a divides b if there exists an integer k such that

   k*a = b

The input to your program consists of several lines, each containing two non-negative integers, n and m, both less than 2^31. For each input line, output a line stating whether or not m divides n!, in the format shown below.

Sample Input

Output for Sample Input

9 divides 6!
27 does not divide 6!
10000 divides 20!
100000 does not divide 20!
1009 does not divide 1000!

#include <stdio.h>
int p[5500], pt = 0;
void sieve() {
    int i, j, m[50000] = {};
    for(i = 2; i < 50000; i++)
        if(m[i] == 0) {
            p[pt++] = i;
            for(j = i+i; j < 50000; j += i)
                m[j] = 1;
        }
}
int solve(int n, int m) {
    int i;
    for(i = 0; i < pt && p[i]*p[i] <= m; i++) {
        if(m%p[i] == 0) {
            int cnt = 0;
            while(m%p[i] == 0)
                cnt++, m /= p[i];
            long long tmp = p[i], cnt2 = 0;
            while(tmp <= n) {
                cnt2 += n/tmp;
                tmp *= p[i];
            }
            if(cnt2 < cnt)  return 0;
        }
    }
    if(m != 1) {
        if(n < m)   return 0;
    }
    return 1;
}
int main() {
    sieve();
    int n, m;
    while(scanf("%d %d", &n, &m) == 2) {
        if(solve(n, m))
            printf("%d divides %d!\n", m, n);
        else
            printf("%d does not divide %d!\n", m, n);
    }
    return 0;
}