# 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 ``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);` `    ``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

 ` 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

 ``
Output:
`2`

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