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))