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# Length of largest subarray whose all elements are Perfect Number

• Difficulty Level : Easy
• Last Updated : 17 May, 2021

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:
Explanation:
Maximum length sub-array with all elements as perfect number is {6, 28}.
Input: arr[] = {25, 100, 2, 3, 9, 1}
Output:
Explanation:
None of the number is a perfect number

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++

 `// 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);` `    ``cout << contiguousPerfectNumber(arr, n);` `    ``return` `0;``}`

## Java

 `// 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`

## Python3

 `# 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#

 `// 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`

## Javascript

 ``
Output:
`2`

Time Complexity: O(N×√N)
Auxiliary Space Complexity: O(1)

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