# Length of largest subarray whose all elements are Perfect Number

Given an array arr[] of integer elements, the task is to find the length of the largest sub-array of arr[] such that all the elements of the sub-array are Perfect number.

A perfect number is a positive integer that is equal to the sum of its proper divisors.

Examples:

Input: arr[] = {1, 7, 36, 4, 6, 28, 4}
Output: 2
Explanation:
Maximum length sub-array with all elements as perfect number is {6, 28}.

Input: arr[] = {25, 100, 2, 3, 9, 1}
Output: 0
Explanation:
None of the number is a perfect number

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

Approach:

• Traverse the array from left to right and initialize a max_length and current_length variable with 0.
• If the current element is a perfect number then increment current_length variable and continuethe process. Otherwise, set current_length to 0.
• At each step, assign max_length as max_length = max(current_length, max_length).
• Print the value of max_length in the end as it will store the required result.

Below is the implementation of the above approach:

 `// C++ program to find the length of the ` `// largest sub-array of an array every ` `// element of whose is a perfect number ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function that returns true if n is perfect ` `bool` `isPerfect(``long` `long` `int` `n) ` `{ ` `    ``// Variable to store sum of divisors ` `    ``long` `long` `int` `sum = 1; ` ` `  `    ``// Find all divisors and add them ` `    ``for` `(``long` `long` `int` `i = 2; i * i <= n; i++) { ` `        ``if` `(n % i == 0) { ` `            ``if` `(i * i != n) ` `                ``sum = sum + i + n / i; ` `            ``else` `                ``sum = sum + i; ` `        ``} ` `    ``} ` `    ``// Check if sum of divisors is equal to ` `    ``// n, then n is a perfect number ` `    ``if` `(sum == n && n != 1) ` `        ``return` `true``; ` ` `  `    ``return` `false``; ` `} ` ` `  `// Function to return the length of the ` `// largest sub-array of an array every ` `// element of whose is a perfect number ` `int` `contiguousPerfectNumber(``int` `arr[], ``int` `n) ` `{ ` ` `  `    ``int` `current_length = 0; ` `    ``int` `max_length = 0; ` ` `  `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// Check if arr[i] is a perfect number ` `        ``if` `(isPerfect(arr[i])) ` `            ``current_length++; ` `        ``else` `            ``current_length = 0; ` ` `  `        ``max_length = max(max_length, ` `                         ``current_length); ` `    ``} ` ` `  `    ``return` `max_length; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 7, 36, 4, 6, 28, 4 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` ` `  `    ``cout << contiguousPerfectNumber(arr, n); ` ` `  `    ``return` `0; ` `} `

 `// Java program to find the length of the ` `// largest sub-array of an array every ` `// element of whose is a perfect number ` ` `  `import` `java.util.*;      ` ` `  `class` `GFG ` `{ ` `    ``// Function that returns true if n is perfect ` `    ``static` `boolean` `isPerfect(``int` `n) ` `    ``{ ` `        ``// Variable to store sum of divisors ` `        ``int` `sum = ``1``; ` `        ``int` `i; ` `         `  `        ``// Find all divisors and add them ` `        ``for` `( i = ``2``; i * i <= n; i++) { ` `            ``if` `(n % i == ``0``) { ` `                ``if` `(i * i != n) ` `                    ``sum = sum + i + n / i; ` `                ``else` `                    ``sum = sum + i; ` `            ``} ` `        ``} ` `         `  `        ``// Check if sum of divisors is equal to ` `        ``// n, then n is a perfect number ` `        ``if` `(sum == n && n != ``1``) ` `            ``return` `true``; ` `     `  `        ``return` `false``; ` `    ``} ` `     `  `    ``// Function to return the length of the ` `    ``// largest sub-array of an array every ` `    ``// element of whose is a perfect number ` `    ``static` `int` `contiguousPerfectNumber(``int` `arr[], ``int` `n) ` `    ``{ ` `     `  `        ``int` `current_length = ``0``; ` `        ``int` `max_length = ``0``; ` `        ``int` `i; ` `        ``for` `(i = ``0``; i < n; i++) { ` `     `  `            ``// Check if arr[i] is a perfect number ` `            ``if` `(isPerfect(arr[i])) ` `                ``current_length++; ` `            ``else` `                ``current_length = ``0``; ` `     `  `            ``max_length = Math.max(max_length, ` `                            ``current_length); ` `        ``} ` `     `  `        ``return` `max_length; ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `main(String []args) ` `    ``{ ` `        ``int` `arr[] = { ``1``, ``7``, ``36``, ``4``, ``6``, ``28``, ``4` `}; ` `        ``int` `n = arr.length; ` `     `  `        ``System.out.print(contiguousPerfectNumber(arr, n)); ` `     `  `    ``} ` `}  ` ` `  `//This code is contributed by chitranayal `

 `# Python 3 program to find the length of  ` `# the largest sub-array of an array every  ` `# element of whose is a perfect number  ` ` `  ` `  `# Function that returns true if n is perfect  ` `def` `isPerfect( n ):  ` `     `  `    ``# To store sum of divisors  ` `    ``sum` `=` `1` `     `  `    ``# Find all divisors and add them  ` `    ``i ``=` `2` `    ``while` `i ``*` `i <``=` `n:  ` `        ``if` `n ``%` `i ``=``=` `0``:  ` `            ``sum` `=` `sum` `+` `i ``+` `n ``/` `i  ` `        ``i ``+``=` `1` `     `  `    ``# check if the sum of divisors is equal to  ` `    ``# n, then n is a perfect number  ` `     `  `    ``return` `(``True` `if` `sum` `=``=` `n ``and` `n !``=` `1` `else` `False``)  ` ` `  ` `  `# Function to return the length of the  ` `# largest sub-array of an array every  ` `# element of whose is a perfect number ` `def` `contiguousPerfectNumber(arr, n):  ` `    ``current_length ``=` `0` `    ``max_length ``=` `0` ` `  `    ``for` `i ``in` `range``(``0``, n, ``1``):  ` `         `  `        ``# check if arr[i] is a perfect number ` `        ``if` `(isPerfect(arr[i])):  ` `            ``current_length ``+``=` `1` `        ``else``:  ` `            ``current_length ``=` `0` ` `  `        ``max_length ``=` `max``(max_length,  ` `                        ``current_length)  ` `     `  `    ``return` `max_length  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `'__main__'``:  ` `    ``arr ``=` `[``1``, ``7``, ``36``, ``4``, ``6``, ``28``, ``4``] ` `    ``n ``=` `len``(arr)  ` ` `  `    ``print``(contiguousPerfectNumber(arr, n))  `

 `// C# program to find the length of the ` `// largest sub-array of an array every ` `// element of whose is a perfect number ` `using` `System; ` ` `  `class` `GFG{ ` `     `  `// Function that returns true if n is perfect ` `static` `bool` `isPerfect(``int` `n) ` `{ ` `     `  `    ``// Variable to store sum of divisors ` `    ``int` `sum = 1; ` `    ``int` `i; ` `         `  `    ``// Find all divisors and add them ` `    ``for``(i = 2; i * i <= n; i++) ` `    ``{ ` `       ``if` `(n % i == 0) ` `       ``{ ` `           ``if` `(i * i != n) ` `               ``sum = sum + i + n / i; ` `           ``else` `               ``sum = sum + i; ` `       ``} ` `    ``} ` `         `  `    ``// Check if sum of divisors is equal to ` `    ``// n, then n is a perfect number ` `    ``if` `(sum == n && n != 1) ` `    ``{ ` `        ``return` `true``; ` `    ``} ` `    ``return` `false``; ` `} ` `     `  `// Function to return the length of the ` `// largest sub-array of an array every ` `// element of whose is a perfect number ` `static` `int` `contiguousPerfectNumber(``int` `[]arr, ` `                                   ``int` `n) ` `{ ` `    ``int` `current_length = 0; ` `    ``int` `max_length = 0; ` `    ``int` `i; ` `    ``for``(i = 0; i < n; i++) ` `    ``{ ` `        `  `       ``// Check if arr[i] is a perfect number ` `       ``if` `(isPerfect(arr[i])) ` `       ``{ ` `           ``current_length++; ` `       ``} ` `       ``else` `       ``{ ` `           ``current_length = 0; ` `       ``} ` `       ``max_length = Math.Max(max_length, ` `                             ``current_length); ` `    ``} ` `    ``return` `max_length; ` `} ` `     `  `// Driver code ` `public` `static` `void` `Main(String []args) ` `{ ` `    ``int` `[]arr = { 1, 7, 36, 4, 6, 28, 4 }; ` `    ``int` `n = arr.Length; ` `     `  `    ``Console.Write(contiguousPerfectNumber(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by sapnasingh4991 `

Output:
```2
```

Time Complexity: O(N×√N)

Auxiliary Space Complexity: O(1)

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Improved By : chitranayal, sapnasingh4991

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