Want to print each iteration of factorial program

[sbabu]

def _factorial_sample_(n):
    if n == 0 or n == 1:
        return 1
    else:
        result = n * _factorial_sample_(n-1)
        print("n is ", n, "*", result )
        return result


print(_factorial_sample_(10))

[sandeep_ganga]

I would use something like,

def _factorial_sample_(n):
    if n == 0 or n == 1:
        return 1
    else:
        #result = n * _factorial_sample_(n-1)
        print("\nGiven number to find factorial is ", n ,"\n")
        i=n
        fact=1
        while(i>0):
            print( " ",fact," * ",i)
            fact=fact*i
            print("temp_computed_result= ",fact)
            i -= 1
        print("\nfactorial of ",n," is : ", fact)
        return fact
  
  
print(_factorial_sample_(5))

Output:
python 6jan.py

Given number to find factorial is  5

  1  *  5
temp_computed_result=  5
  5  *  4
temp_computed_result=  20
  20  *  3
temp_computed_result=  60
  60  *  2
temp_computed_result=  120
  120  *  1
temp_computed_result=  120

factorial of  5  is :  120
120

Best Regards,
Sandeep

GANGA SANDEEP KUMAR

[sbabu]

Thanks Mr.Sandeep,

Here I am trying to do it through recurssion. I need to save the previous result and print it. So I can understand how the program is working.

[perfringo]

I need to save the previous result and print it. So I can understand how the program is working.

There are other possibilities to understand recursion - for example visualisation. There is Thonny which is suited for beginners and has built-in stack visualisation for understanding recursion (first screenshot on their webpage); line-by-line debugger etc. Maybe it's worth a try for better understanding what is going on.

[sbabu]

Hi Perfringo,

I used Thonny. I understand what it is doing. Still I want to learn how to save the old result and print it.

[python]def _factorial_sample_(n):
    previous=0
    if n == 0 or n ==1:
        return 1
    else:
        result = n * _factorial_sample_(n-1)
        previous = result
        print (previous)
        print("n is ",n, "result",previous)
        return result 


print(_factorial_sample_(5))

[/python]

Output:
2
n is  2 result 2
6
n is  3 result 6
24
n is  4 result 24
120

I want to print
n is 4 and old result is 6 the current result is 24
n is 5 and old result is 24 the current result is 120
how do I bring this 6 value into the print statement.

Thanks

[perfringo]

I observe following problematic areas:
- base case is not printed out (one can't understand if whole 'process' is not printed out)
- this function is not defensive against negative values (RecursionError)

For better understanding one can write (requires 3.6 <= Python due to f-strings):

def _factorial_sample_(n): 
    if n < 0: 
        raise ValueError('No factorials for negative numbers') 
    if n == 0 or n == 1: 
        print(f'n is {n}, carrying over {1}, this is base case') 
        return 1 
    else: 
        result = n * _factorial_sample_(n-1) 
        print(f'n is {n}, carrying over {result}') 
        return result

With different arguments one will get:

>>> _factorial_sample_(5)                                                                                     
n is 1, carrying over 1, this is base case
n is 2, carrying over 2
n is 3, carrying over 6
n is 4, carrying over 24
n is 5, carrying over 120
120
>>> _factorial_sample_(0)
n is 0, carrying over 1, this is base case
1
>>> _factorial_sample_(1)                                                                                     
n is 1, carrying over 1, this is base case
1
>>> _factorial_sample_(-5)
/.../
ValueError: No factorials for negative numbers

To your original problem: you probably should use memoization

[sbabu]

n is 1, carrying over 1, this is base case
n is 2, carrying over 2 How do we bring the top 1 here such that we can print 2 X 1 = 2
n is 3, carrying over 6 How do we bring the top 2 here such that we can print 3 X 2 = 6
n is 4, carrying over 24 same thing
n is 5, carrying over 120

I was told to save it in an intermediary variable. How to do that?

Thanks.

[perfringo]

As I told - one way is to use memoization. It seems to me that if you are 'told' then it's homework therefore I provide a solution which has caveats and may not pass automated test system:

def factorial(n, d={0:1, 1:1}): 
    if n < 0: 
        raise ValueError('No factorials for negative numbers!') 
    if n in d: 
        print(f'n is {n}, carry over {d[n]}, this is base case') 
        return d[n] 
    else: 
        value = factorial(n-1, d) * n 
        d[n] = value 
        print(f'n is {n}, carry over {n} * {d[n-1]} = {d[n]}') 
        return value

This gives:

>>> factorial(5)                                                                                                        
n is 1, carry over 1, this is base case
n is 2, carry over 2 * 1 = 2
n is 3, carry over 3 * 2 = 6
n is 4, carry over 4 * 6 = 24
n is 5, carry over 5 * 24 = 120
120
>>> factorial(0)
n is 0, carry over 1, this is base case
1
>>> factorial(-5)
/.../
ValueError: No factorials for negative numbers!
# But! Second time in same session:
>>> factorial(5)                                                                                                       
n is 5, carry over 120, this is base case
120
>>> factorial(6)                                                                                                        
n is 5, carry over 120, this is base case
n is 6, carry over 6 * 120 = 720
720

[jefsummers]

In the spirit of this being homework, here is code that almost works. Stores in intermediate variable (output) a list of prior values.
The bug for you to fix is that it does not make the final calculation.

def _factorial_sample_(n,output):
    if n == 0 or n == 1:
        output.append(1)
        return n,output
    else:
        x, output = _factorial_sample_(n-1,output)
        new_val = x * output[-1]
        output.append(new_val)
        print(output)
        return n,output
 
 
print(_factorial_sample_(6,[]))

Output:
[1, 1]
[1, 1, 2]
[1, 1, 2, 6]
[1, 1, 2, 6, 24]
[1, 1, 2, 6, 24, 120]
(6, [1, 1, 2, 6, 24, 120])

[sbabu]

Hi Mr.JefSummers,

I am a self learner. I gathered lot of material and started working on them. What I found is in all of them they just teach syntax with 1 or 2 examples. And give lot of exercises (some will give solutions using techniques which were not discussed).

How do I develop the mindset to think several steps a head, using different scenarios? Are there any exercises to train the brain?

How long did it take for you to become comfortable with basic coding? I am putting 4 hrs every day for the past 2 months. It's taking lot time.

Any advise appreciated.

Thanks again.

---

As I told - one way is to use memoization. It seems to me that if you are 'told' then it's homework therefore I provide a solution which has caveats and may not pass automated test system:

def factorial(n, d={0:1, 1:1}): 
    if n < 0: 
        raise ValueError('No factorials for negative numbers!') 
    if n in d: 
        print(f'n is {n}, carry over {d[n]}, this is base case') 
        return d[n] 
    else: 
        value = factorial(n-1, d) * n 
        d[n] = value 
        print(f'n is {n}, carry over {n} * {d[n-1]} = {d[n]}') 
        return value

This gives:

>>> factorial(5)                                                                                                        
n is 1, carry over 1, this is base case
n is 2, carry over 2 * 1 = 2
n is 3, carry over 3 * 2 = 6
n is 4, carry over 4 * 6 = 24
n is 5, carry over 5 * 24 = 120
120
>>> factorial(0)
n is 0, carry over 1, this is base case
1
>>> factorial(-5)
/.../
ValueError: No factorials for negative numbers!
# But! Second time in same session:
>>> factorial(5)                                                                                                       
n is 5, carry over 120, this is base case
120
>>> factorial(6)                                                                                                        
n is 5, carry over 120, this is base case
n is 6, carry over 6 * 120 = 720
720

Hi perfringo,

I am a self learner. I gathered lot of material and started working on them. What I found is in all of them they just teach syntax with 1 or 2 examples. And give lot of exercises (some will give solutions using techniques which were not discussed).

How do I develop the mindset to think several steps a head, using different scenarios? Are there any exercises to train the brain?

How long did it take for you to become comfortable with basic coding? I am putting 4 hrs every day for the past 2 months. It's taking lot time.

Any advise appreciated.

Thanks again.