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post Persistence

asdf1 (3)
Hi there... I cannot seem to figure this out.

I need to write a function that finds the multiplicative persistence of a given number.

The persistence is the number of products needed to get a single digit.

For example: (the Persistence for 76 would go like this)
76 = 42 (7*6) = 8 (4*2)
so the persistence is 2.

(for 57)
57 = 35 (5*7) = 15 (3*5) = 5 (1*5)
so the persistence is 3.

All I need is a value returning function for this.

In order to get the digits out alone I used modulus; however, I just got tied up somewhere.

Here's the start of what I was trying to do: (value is initialized earlier btw so that's not the problem)

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int Persistent(int value)
{
   int product = 1;
   int n;
   int i;
 
   for (i=0; value > 0; i++)
   {
       n = product;
       product = n*(value%10);
       value = value / 10;
   }
   return i;
}

Obviously the code does not work, but I cannot seem to think of what I am suppose to do.

Thanks in advance for the help.
screw (145)
My solution:

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#include <iostream>
#include <sstream>

using namespace std;

int Persistent(int value)
{
	stringstream ss; // for converting
	int counter = 0;
	
	while (value > 10)
	{
		int nnumber = 1;
		ss.clear();
		ss << value;
		string s;
		ss >> s; // convert the number to string
		//cout << "string: " << s <<endl;
		
		for (int i = 0, n; i < s.size(); i++)
		{						
			ss.clear();
			ss << s[i]; // disassemble the chars of string to numbers
			ss >> n;	
			//cout << "n: " << n << endl;;
			nnumber *= n;
		}
		value = nnumber;
		cout << "element: " << value << endl;
		counter++;	
	}
	
	return counter;
	
}

int main()
{
	int originalNumber = 83;
	cout << "original number: " << originalNumber << endl;
	cout << " number of element: " << Persistent(83);
	return 0;
}


Of course there are problem if you want to disassemble a number which contains zero values. i.e. 160 => 1 * 6 * 0 = 0
Last edited on
asdf1 (3)
Thanks for that; however, I probably should have mentioned the rules to this. I am not allowed to use the string counters that you have implemented in your function.

I have to break down the numbers using binary-type tools.

For example:
value = 66

the number should pull 6 from 66 by using 66%10. Then, it multiplies that times the other 6, which is 66/10.
You now have 6*6 = 36. So the function then should pull the 6 through 36%10, and the 3 from 36/10.
You now have 3*6 = 18. So the function then should pull the 8 through 18%10, and the 1 from 18/10.
You now have 1*8 = 8.
The function will now give the persistent a value of 3, because it took three times to get a single digit.

I understand the logic to the situation; however, I am unable to figure out how to get the first new number (36) to multiply together.

Thanks very much for your help though.
Disch (6854)
You shouldn't use strings to do numerical work anyway.

I don't normally like to solve problems directly -- but I couldn't resist with this one.

read: code is untested

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int Persist( int value )
{
  int count = 0;  // number of times we multiplied all digits together

  while( value > 9 )  // loop until it has only 1 digit remaining
  {
    int temp = 1;

    do
    {
      temp *= (value % 10);  // multiply 'temp' by the low digit
      value /= 10;    // drop the low digit
    }while(value > 0);  // loop until no digits remaining

    value = temp;  // 'temp' is all digits multiplied together.  Put back in value
    ++count;
  }

  return count;
}
Last edited on
screw (145)
I hope that you thought like this:

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#include <iostream>
#include <sstream>

using namespace std;

int Persistent(int value)
{
	
	int counter = 0;
	
	while (value > 10)
	{
		int newvalue = 1;
		int tmpvalue = value;
		
		
		while (tmpvalue > 0)
		{						
			// I get the last digit
			int tmp = tmpvalue % 10;
			newvalue *= tmp;
			// last digit is cut
			tmpvalue /= 10;
		}
		value = newvalue;
		cout << "element: " << value << endl;
		counter++;	
	}
	
	return counter;
	
}

int main()
{
	int originalNumber = 83;
	cout << "original number: " << originalNumber << endl;
	cout << " number of element: " << Persistent(83);
	return 0;
}


ps. Sorry my doubled solution.
Last edited on
asdf1 (3)
Thank you so much for the help guys. I'm using Disch's code.. it works perfect. Now for the rest of the program, but I'm going to try and get it on my own before asking. I was just confused with that function.
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