Step by Step solution about How to resolve the algorithm Kaprekar numbers step by step in the Python programming language

The first code snippet you provided is a Python function that takes a number n and returns n if it is a Kaprekar number. A Kaprekar number is a number whose square can be split into two positive-integer numbers whose sum is the original number again. For example, 9 is a Kaprekar number, because 9^2=81 and 8+1=9.

The function works by first converting n to a string and then iterating over the string. For each iteration, it splits the string into two parts at the current index, and then converts the two parts back to integers. If the sum of the two integers is equal to n, then the function returns n. Otherwise, it continues to the next iteration.

The second code snippet you provided is a Python function that takes three arguments: a starting number m, an ending number n, and a base base. It returns a list of all the Kaprekar numbers between m and n, inclusive, in the given base.

The function works by first converting m and n to strings in the given base. Then, it iterates over all the numbers between m and n, inclusive, and checks if each number is a Kaprekar number. If it is, it adds the number to the list. Finally, it returns the list of all the Kaprekar numbers.

The third code snippet you provided is a Python function that takes three arguments: a starting number m, an ending number n, and a base base. It returns a list of all the Kaprekar numbers between m and n, inclusive, in the given base.

The function works by first converting m and n to strings in the given base. Then, it iterates over all the numbers between m and n, inclusive, and checks if each number is a Kaprekar number. If it is, it adds the number to the list. Finally, it returns the list of all the Kaprekar numbers.

The fourth code snippet you provided is a Python function that takes two arguments: a base Base and a range of numbers Start and End. It returns a list of all the numbers in the given range that are not divisible by any of the numbers in the given base.

The function works by first creating a list of all the numbers in the given range. Then, it iterates over all the numbers in the given base and removes any number from the list that is divisible by the current number. Finally, it returns the list of all the numbers that are not divisible by any of the numbers in the given base.

The fifth code snippet you provided is a Python function that takes two arguments: a base Base and a range of numbers Start and End. It returns a list of all the Kaprekar numbers in the given range in the given base.

The function works by first converting the start and end numbers to strings in the given base. Then, it iterates over all the numbers in the given range and checks if each number is a Kaprekar number. If it is, it adds the number to the list. Finally, it returns the list of all the Kaprekar numbers in the given range in the given base.

>>> def k(n):
	n2 = str(n**2)
	for i in range(len(n2)):
		a, b = int(n2[:i] or 0), int(n2[i:])
		if b and a + b == n:
			return n
			#return (n, (n2[:i], n2[i:]))

		
>>> [x for x in range(1,10000) if k(x)]
[1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999]
>>> len([x for x in range(1,1000000) if k(x)])
54
>>>


def encode(n, base):
    result = ""
    while n:
        n, d = divmod(n, base)
        if d < 10:
            result += str(d)
        else:
            result += chr(d - 10 + ord("a"))
    return result[::-1]
def Kaprekar(n, base):
    if n == '1':
        return True
    sq = encode((int(n, base)**2), base)
    for i in range(1,len(sq)):
        if (int(sq[:i], base) + int(sq[i:], base) == int(n, base)) and (int(sq[:i], base) > 0) and (int(sq[i:], base)>0):
            return True
    return False
def Find(m, n, base):
    return [encode(i, base) for i in range(m,n+1) if Kaprekar(encode(i, base), base)]

m = int(raw_input('Where to start?\n'))
n = int(raw_input('Where to stop?\n'))
base = int(raw_input('Enter base:'))
KNumbers = Find(m, n, base)
for i in KNumbers:
    print i
print 'The number of Kaprekar Numbers found are',
print len(KNumbers)
raw_input()


Base = 10
N = 6
Paddy_cnt = 1
for n in range(N):
  for V in CastOut(Base,Start=Base**n,End=Base**(n+1)):
    for B in range(n+1,n*2+2):
      x,y = divmod(V*V,Base**B)
      if V == x+y and 0<y:
        print('{1}: {0}'.format(V, Paddy_cnt))
        Paddy_cnt += 1
        break


Base = 16
N = 4
Paddy_cnt = 1
for V in CastOut(Base,Start=1,End=Base**N):
  for B in range(1,N*2-1):
    x,y = divmod(V*V,Base**B)
    if V == x+y and 0<y:
      print('{1}: {0:x}'.format(V, Paddy_cnt))
      Paddy_cnt += 1
      break