Related Articles
Maximum number of continuous Automorphic numbers
• Last Updated : 10 Apr, 2019

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:

```-> 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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. ` `?> `

Output:

```2
```

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up
Recommended Articles
Page :