Python3 Program to Check if all array elements can be converted to pronic numbers by rotating digits

Given an array arr[] of size N, the task is to check if it is possible to convert all of the array elements to a pronic number by rotating the digits of array elements any number of times.

Examples:

Input: {321, 402, 246, 299} 
Output: True 
Explanation:
arr[0] ? Right rotation once modifies arr[0] to 132 (= 11 × 12). 
arr[1] ? Right rotation once modifies arr[0] to 240 (= 15 × 16). 
arr[2] ? Right rotation twice modifies arr[2] to 462 (= 21 × 22). 
arr[3] ? Right rotation twice modifies arr[3] to 992 (= 31 × 32).

Input: {433, 653, 402, 186}
Output: False

Approach: Follow the steps below to solve the problem:

• Traverse the array and check for each array element, whether it is possible to convert it to a pronic number.
• For each array element, apply all the possible rotations and check after each rotation, whether the generated number is pronic or not.
• If it is not possible to convert any array element to a pronic number, print “False”.
• Otherwise, print “True”.

Below is the implementation of the above approach:

Python3

# Python implementation of
# the above approach

# Function to check if a number
# is a pronic number or not
def isPronic(n):

  for i in range(int(n**(1 / 2)) + 1):
    if i * (i + 1) == n:
      return True

  return False

# Function to check if any permutation
# of n is a pronic number or not
def checkRot(n):

  temp = str(n)

  for i in range(len(temp)):

    if isPronic(int(temp)):
      return True

    temp = temp[1:]+temp[0]

  return False

# Function to check if all array
# elements can be converted to
# a pronic number or not
def check(arr):

  # Traverse the array
  for i in arr:

    # If current element
    # cannot be converted
    # to a pronic number
    if not checkRot(i):
      return False
  return True

# Driver Code
arr = [ 321, 402, 246, 299 ]
print(check(arr))

Output:

True

Time Complexity: O(N^3/2)
Auxiliary Space: O(1)

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