UVA 160 - Factors and Factorials

 Factors and Factorials 

The factorial of a number N (written N!) is defined as the product of all the integers from 1 to N. It is often defined recursively as follows:

 

 

 

 

Factorials grow very rapidly--5! = 120, 10! = 3,628,800. One way of specifying such large numbers is by specifying the number of times each prime number occurs in it, thus 825 could be specified as (0 1 2 0 1) meaning no twos, 1 three, 2 fives, no sevens and 1 eleven.

 

Write a program that will read in a number N (  ) and write out its factorial in terms of the numbers of the primes it contains.

 

Input

Input will consist of a series of lines, each line containing a single integer N. The file will be terminated by a line consisting of a single 0.

 

Output

Output will consist of a series of blocks of lines, one block for each line of the input. Each block will start with the number N, right justified in a field of width 3, and the characters `!', space, and `='. This will be followed by a list of the number of times each prime number occurs in N!.

These should be right justified in fields of width 3 and each line (except the last of a block, which may be shorter) should contain fifteen numbers. Any lines after the first should be indented. Follow the layout of the example shown below exactly.

 

Sample input

 

5
53
0

 

Sample output

 

  5! =  3  1  1
 53! = 49 23 12  8  4  4  3  2  2  1  1  1  1  1  1
        1

#include <cstdio>
#include <cstring>
using namespace std;
bool isprime(int a)
{
	int i;
	for (i = 2; i*i <= a;i++)
	if (a%i == 0)
		return false;
	return true;
}
int prime[100], count[100];
int main()
{
	int n;
	int i,num;
	for (i = 2, num = 0; i <= 100;i++)
	if (isprime(i))
	{
		prime[num++] = i;
	}

	while (scanf("%d", &n) == 1 && n)
	{
		memset(count,0,sizeof(count));
		int maxn = 0;
		for (i = 2; i <= n; i++)
		{
			int m = i;
			int j;
			for (j = 0; j < num; j++)
			{
				while (m%prime[j] == 0)
				{
					m = m / prime[j];
					count[j]++;
					if (j>maxn)
						maxn = j;
				}
			}
		}
		printf("%3d! =", n);
		for (i = 0; i <= maxn; i++)
		{
			if (i == 15)
				printf("\n      "); 
			printf("%3d", count[i]);
		}
			
		printf("\n");
	}
	return 0;
}

　　这道题应该特别注意输出格式。