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Maximum number of continuous Automorphic numbers

  • Last Updated : 11 May, 2021

Given an array of N elements. The task is to find the maximum number of the contiguous automorphic numbers in the given array.
Automorphic Numbers: A number is called Automorphic number if and only if its square ends in the same digits as the number itself.

For Example: 

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-> 76 is automorphic, since 76*76 = 5776(ends in 76)
-> 5 is automorphic, since 5*5 = 25(ends in 5)

Examples: 



Input :  arr[] = {22, 6, 1, 625, 2, 1, 9376}
Output : 3

Input : arr[] = {99, 42, 31, 1, 5}
Output : 2

Approach:  

  1. Traverse the array with two variables named current_max and max_so_far. Initialize both of them with 0.
  2. Check at each element if it is automorphic. 
    • Calculate the square of current number.
    • Keep extracting and comparing digits from the end of both the current number and its square.
    • If any mismatch is found, then the number is not automorphic.
    • Otherwise if all of the digits from the current number is extracted without any mismatch, then the number is automorphic.
  3. If a automorphic number is found then increment current_max and compare it with max_so_far
  4. If current_max is greater than max_so_far, then assign max_so_far with current_max
  5. Every time a non automorphic element is found, reset current_max to 0.

Below is the implementation of the above approach:  

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to check Automorphic number
bool isAutomorphic(int N)
{
    // Store the square
    int sq = N * N;
 
    // Start Comparing digits
    while (N > 0) {
 
        // Return false, if any digit of N doesn't
        // match with its square's digits from last
        if (N % 10 != sq % 10)
            return false;
 
        // Reduce N and square
        N /= 10;
        sq /= 10;
    }
 
    return true;
}
 
// Function to find the length of the maximum
// contiguous subarray of automorphic numbers
int maxAutomorphicSubarray(int arr[], int n)
{
    int current_max = 0, max_so_far = 0;
 
    for (int i = 0; i < n; i++) {
 
        // check if element is non automorphic
        if (isAutomorphic(arr[i]) == false)
            current_max = 0;
 
        // If element is automorphic, than update
        // current_max and max_so_far accordingly.
        else {
            current_max++;
            max_so_far = max(current_max, max_so_far);
        }
    }
 
    return max_so_far;
}
 
// Driver Code
int main()
{
    int arr[] = { 0, 3, 2, 5, 1, 9 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    cout << maxAutomorphicSubarray(arr, n);
 
    return 0;
}

Java




// Java implementation of the approach
class GFG
{
     
// Function to check Automorphic number
static boolean isAutomorphic(int N)
{
    // Store the square
    int sq = N * N;
 
    // Start Comparing digits
    while (N > 0)
    {
 
        // Return false, if any digit of N doesn't
        // match with its square's digits from last
        if (N % 10 != sq % 10)
            return false;
 
        // Reduce N and square
        N /= 10;
        sq /= 10;
    }
 
    return true;
}
 
// Function to find the length of the maximum
// contiguous subarray of automorphic numbers
static int maxAutomorphicSubarray(int []arr, int n)
{
    int current_max = 0, max_so_far = 0;
 
    for (int i = 0; i < n; i++)
    {
 
        // check if element is non automorphic
        if (isAutomorphic(arr[i]) == false)
            current_max = 0;
 
        // If element is automorphic, than update
        // current_max and max_so_far accordingly.
        else
        {
            current_max++;
            max_so_far = Math.max(current_max,
                                  max_so_far);
        }
    }
 
    return max_so_far;
}
 
// Driver Code
public static void main(String[] args)
{
    int []arr = { 0, 3, 2, 5, 1, 9 };
    int n = arr.length;
 
    System.out.println(maxAutomorphicSubarray(arr, n));
}
}
 
// This code is contributed by Code_Mech.

Python3




# Python3 implementation of the approach
 
# Function to check Automorphic number
def isAutomorphic(N) :
 
    # Store the square
    sq = N * N;
 
    # Start Comparing digits
    while (N > 0) :
 
        # Return false, if any digit of N doesn't
        # match with its square's digits from last
        if (N % 10 != sq % 10) :
            return False;
 
        # Reduce N and square
        N //= 10;
        sq //= 10;
 
    return True;
 
# Function to find the length of the maximum
# contiguous subarray of automorphic numbers
def maxAutomorphicSubarray(arr, n) :
     
    current_max = 0; max_so_far = 0;
 
    for i in range(n) :
 
        # check if element is non automorphic
        if (isAutomorphic(arr[i]) == False) :
            current_max = 0;
 
        # If element is automorphic, than update
        # current_max and max_so_far accordingly.
        else :
            current_max += 1;
            max_so_far = max(current_max,
                             max_so_far);
 
    return max_so_far;
 
# Driver Code
if __name__ == "__main__" :
 
    arr = [ 0, 3, 2, 5, 1, 9 ];
    n = len(arr) ;
 
    print(maxAutomorphicSubarray(arr, n));
 
# This code is contributed by Ryuga

C#




// C# implementation of the approach
using System;
 
class GFG
{
     
// Function to check Automorphic number
static bool isAutomorphic(int N)
{
    // Store the square
    int sq = N * N;
 
    // Start Comparing digits
    while (N > 0)
    {
 
        // Return false, if any digit of N doesn't
        // match with its square's digits from last
        if (N % 10 != sq % 10)
            return false;
 
        // Reduce N and square
        N /= 10;
        sq /= 10;
    }
 
    return true;
}
 
// Function to find the length of the maximum
// contiguous subarray of automorphic numbers
static int maxAutomorphicSubarray(int []arr, int n)
{
    int current_max = 0, max_so_far = 0;
 
    for (int i = 0; i < n; i++)
    {
 
        // check if element is non automorphic
        if (isAutomorphic(arr[i]) == false)
            current_max = 0;
 
        // If element is automorphic, than update
        // current_max and max_so_far accordingly.
        else
        {
            current_max++;
            max_so_far = Math.Max(current_max, max_so_far);
        }
    }
 
    return max_so_far;
}
 
// Driver Code
static void Main()
{
    int []arr = { 0, 3, 2, 5, 1, 9 };
    int n = arr.Length;
 
    Console.WriteLine(maxAutomorphicSubarray(arr, n));
 
}
}
 
// This code is contributed by mits

PHP




<?php
// PHP implementation of the approach
 
// Function to check Automorphic number
function isAutomorphic($N)
{
    // Store the square
    $sq = $N * $N;
 
    // Start Comparing digits
    while ($N > 0)
    {
 
        // Return false, if any digit of N doesn't
        // match with its square's digits from last
        if ($N % 10 != $sq % 10)
            return false;
 
        // Reduce N and square
        $N = (int)($N / 10);
        $sq = (int)($sq / 10);
    }
 
    return true;
}
 
// Function to find the length of the maximum
// contiguous subarray of automorphic numbers
function maxAutomorphicSubarray($arr, $n)
{
    $current_max = 0; $max_so_far = 0;
 
    for ($i = 0; $i < $n; $i++)
    {
 
        // check if element is non automorphic
        if (isAutomorphic($arr[$i]) == false)
            $current_max = 0;
 
        // If element is automorphic, than update
        // current_max and max_so_far accordingly.
        else
        {
            $current_max++;
            $max_so_far = max($current_max,
                              $max_so_far);
        }
    }
 
    return $max_so_far;
}
 
// Driver Code
$arr = array(0, 3, 2, 5, 1, 9 );
$n = sizeof($arr);
 
echo(maxAutomorphicSubarray($arr, $n));
 
// This code is contributed by Code_Mech.
?>

Javascript




<script>
 
// Javascript implementation of the approach
 
// Function to check Automorphic number
function isAutomorphic(N)
{
     
    // Store the square
    var sq = N * N;
 
    // Start Comparing digits
    while (N > 0)
    {
         
        // Return false, if any digit of N doesn't
        // match with its square's digits from last
        if (N % 10 != sq % 10)
            return false;
 
        // Reduce N and square
        N = parseInt(N / 10);
        sq = parseInt(sq / 10);
    }
    return true;
}
 
// Function to find the length of the maximum
// contiguous subarray of automorphic numbers
function maxAutomorphicSubarray(arr, n)
{
    var current_max = 0, max_so_far = 0;
 
    for(var i = 0; i < n; i++)
    {
         
        // Check if element is non automorphic
        if (isAutomorphic(arr[i]) == false)
            current_max = 0;
 
        // If element is automorphic, than update
        // current_max and max_so_far accordingly.
        else
        {
            current_max++;
            max_so_far = Math.max(current_max,
                                  max_so_far);
        }
    }
    return max_so_far;
}
 
// Driver Code
var arr = [ 0, 3, 2, 5, 1, 9 ];
var n = arr.length;
 
document.write(maxAutomorphicSubarray(arr, n));
 
// This code is contributed by rrrtnx
 
</script>
Output: 
2

 




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