Factor and factorial, factor factorial

Factor and factorial, factor factorial

Enter a positive integer n (2 <=n <= 100) and multiply the factorial n! = 1*2*3 * · * n is decomposed into the form of prime factor multiplication, and each prime number is output from small to large (2, 3, 5 ,···) index. For example, 825 = 3*5 ^ 2*11 should be expressed as (, 1 ), 0, 1, 2, 0, 1, 2, 3, 5, 7, and 11 respectively. Your program should ignore prime numbers that are larger than the maximum prime factor (otherwise there will be an infinite number of zeros at the end ).

Sample input:

5

53

Sample output:

5! = 3 1 1

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

Program:

# Include <iostream>

# Include <cstring>

Using namespace std;

// Determine the prime number. Note: n cannot be too large.

Int is_prime (int n)

{

For (int I = 2; I * I <= n; I ++)

If (n % I = 0) return 0;

Return 1;

}

// Prime number table

Int prime [100], count = 0;

Int main ()

{

// The exponent of n and each Prime Number

Int n, p [100];

// Construct a prime number table

For (int I = 2; I <= 100; I ++)

If (is_prime (I) prime [count ++] = I;

While (cin> n)

{

Cout <n <"! "<" = ";

Memset (p, 0, sizeof (p ));

Int maxp = 0;

For (int I = 1; I <= n; I ++)

{

// I must be copied to m instead of being modified directly during division.

Int m = I;

For (int j = 0; j <count; j ++)

While (m % prime [j] = 0) // repeatedly divided by prime [j] and accumulated p [j]

{

M = m/prime [j];

P [j] ++;

If (j> maxp) maxp = j; // update the maximum prime factor subscript.

}

}

// Only loop to the maximum subscript

For (int I = 0; I <= maxp; I ++)

Cout <"<p [I];

Cout <endl;

}

Return 0;

}