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:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// function to check Pronic Number
bool isPronic(int x)
{
    for (int i = 0; i < (int)(sqrt(x)) + 1; i++)
    {

        // Checking Pronic Number
        // by multiplying consecutive
        // numbers
        if (x == i * (i + 1))
        {
            return true;
        }
    }
    return false;
}

// Function to check if any permutation
// of val is a pronic number or not
bool checkRot(int val)
{

    string temp = to_string(val);
    for (int i = 0; i < temp.length(); i++)
    {
        if (isPronic(stoi(temp)) == true)
        {
            return true;
        }
        temp = temp.substr(1, temp.size() - 1) + temp[0];
    }
    return false;
}

// Function to check if all array
// elements can be converted to
// a pronic number or not
bool check(int arr[], int N)
{

    // Traverse the array
    for (int i = 0; i < N; i++)
    {

        // If current element
        // cannot be converted
        // to a pronic number
        if (checkRot(arr[i]) == false)
        {
            return false;
        }
    }
    return true;
}

// Driven Program
int main()
{

    // Given array
    int arr[] = { 321, 402, 246, 299 };
    int N = sizeof(arr) / sizeof(arr[0]);

    // function call
    cout << (check(arr, N) ? "True" : "False");

    return 0;
}

// This code is contributed by Kingash.

Java

// Java program for the above approach

import java.io.*;
import java.lang.*;
import java.util.*;

class GFG {

  // function to check Pronic Number
  static boolean isPronic(int x)
  {

    for (int i = 0; i < (int)(Math.sqrt(x)) + 1; i++) {

      // Checking Pronic Number
      // by multiplying consecutive
      // numbers
      if (x == i * (i + 1)) {
        return true;
      }
    }

    return false;
  }

  // Function to check if any permutation
  // of val is a pronic number or not
  static boolean checkRot(int val)
  {
    String temp = Integer.toString(val);
    for (int i = 0; i < temp.length(); i++)
    {
      if (isPronic(Integer.parseInt(temp)) == true) {
        return true;
      }

      temp = temp.substring(1) + temp.charAt(0);
    }
    return false;
  }

  // Function to check if all array
  // elements can be converted to
  // a pronic number or not
  static boolean check(int arr[], int N)
  {

    // Traverse the array
    for (int i = 0; i < N; i++)
    {

      // If current element
      // cannot be converted
      // to a pronic number
      if (checkRot(arr[i]) == false)
      {
        return false;
      }
    }
    return true;
  }

  // Driver code
  public static void main(String[] args)
  {

    // Given array
    int arr[] = { 321, 402, 246, 299 };
    int N = arr.length;

    // Function call
    System.out.println(
      (check(arr, N) ? "True" : "False"));
  }
}

// This code is contributed by Kingash.

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))

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

class GFG{

  // function to check Pronic Number
  static bool isPronic(int x)
  {
    int val  = (int)Math.Sqrt(x);
    val += 1;
    for (int i = 0; i < val; i++)
    {

      // Checking Pronic Number
      // by multiplying consecutive
      // numbers
      if (x == i * (i + 1))
      {
        return true;
      }
    }
    return false;
  }

  // Function to check if any permutation
  // of val is a pronic number or not
  static bool checkRot(int val)
  {

    string temp = val.ToString();
    for (int i = 0; i < temp.Length; i++)
    {
      int a = Int32.Parse(temp);
      if (isPronic(a) == true)
      {
        return true;
      }
      temp = temp.Substring(1, temp.Length - 1) + temp[0];
    }
    return false;
  }

  // Function to check if all array
  // elements can be converted to
  // a pronic number or not
  static bool check(int []arr, int N)
  {

    // Traverse the array
    for (int i = 0; i < N; i++)
    {

      // If current element
      // cannot be converted
      // to a pronic number
      if (checkRot(arr[i]) == false)
      {
        return false;
      }
    }
    return true;
  }

  // Driven Program
  public static void Main()
  {

    // Given array
    int []arr = { 321, 402, 246, 299 };
    int N = arr.Length;

    // function call
    Console.WriteLine(check(arr, N) ? "True" : "False");
  }
}

// This code is contributed by ipg2016107.

Javascript

<script>

// Javascript program for the above approach

// function to check Pronic Number
function isPronic(x)
{
    for (var i = 0; i < parseInt(Math.sqrt(x)) + 1; i++)
    {

        // Checking Pronic Number
        // by multiplying consecutive
        // numbers
        if (x == i * (i + 1))
        {
            return true;
        }
    }
    return false;
}

// Function to check if any permutation
// of val is a pronic number or not
function checkRot(val)
{

    var temp = (val).toString();
    for (var i = 0; i < temp.length; i++)
    {
        if (isPronic(parseInt(temp)) == true)
        {
            return true;
        }
        temp = temp.substring(1) + temp[0];
    }
    return false;
}

// Function to check if all array
// elements can be converted to
// a pronic number or not
function check(arr, N)
{

    // Traverse the array
    for (var i = 0; i < N; i++)
    {

        // If current element
        // cannot be converted
        // to a pronic number
        if (checkRot(arr[i]) == false)
        {
            return false;
        }
    }
    return true;
}

// Driven Program

// Given array
var arr = [ 321, 402, 246, 299 ]
var N = arr.length;

// function call
document.write(check(arr, N) ? "True" : "False");

// This code is contributed by noob2000.
</script>

Output:

True

Time Complexity: O(N * K * sqrt(val)), where N is the number of elements in the input array, K is the maximum length of a single element in the input array, and val is the maximum value of any element in the input array.
Auxiliary Space: O(1)