Length of longest subsequence in an Array having all elements as Nude Numbers

Given an array arr[] of N positive integers, the task is to print the length of the longest subsequence of the array such that all of its elements are Nude Numbers.

Examples:

Input: arr[] = {34, 34, 2, 2, 3, 333, 221, 32 }
Output: 4
Explanation:
Longest Nude number subsequence is {2, 2, 3, 333} and hence the answer is 4.
Input: arr[] = {456, 44, 104, 133, 39, 325  }
Output: 1
Explanation:
Longest Nude number subsequence is {44} and hence the answer is 1.

Approach: To solve the problem follow the steps given below:

• Traverse the given array and for each element in the array and check if it is a Nude number or not.
• If the element is a Nude Number, it will be included in the resultant longest subsequence. Hence increment the count of elements in the subsequence by 1.
• Print the value of count after the above steps.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to check if the number
// is a Nude number
bool isNudeNum(int n)
{
    // Variable initialization
    int copy, length, flag = 0;
    copy = n;
    string temp;

    // Integer 'copy' is converted
    // to a string
    temp = to_string(copy);

    // Total digits in the number
    length = temp.length();

    // Loop through all digits and check
    // if every digit divides n or not
    for (int i = 0; i < length; i++) {

        int num = temp[i] - '0';

        if (num == 0 or n % num != 0) {

            // flag is used to keep check
            flag = 1;
        }
    }

    // Return true or false as per
    // the condition
    if (flag == 1)
        return false;

    else
        return true;
}

// Function to find the longest subsequence
// which contain all Nude numbers
int longestNudeSubseq(int arr[], int n)
{
    int answer = 0;

    // Find the length of longest
    // Nude number subsequence
    for (int i = 0; i < n; i++) {
        if (isNudeNum(arr[i]))
            answer++;
    }
    return answer;
}

// Driver Code
int main()
{
    // Given array arr[]
    int arr[] = { 34, 34, 2, 2, 3,
                  333, 221, 32 };

    int n = sizeof(arr) / sizeof(arr[0]);

    // Function Call
    cout << longestNudeSubseq(arr, n)
         << endl;
    return 0;
}

Java

// Java program for the above approach
class GFG{

// Function to check if the number
// is a Nude number
static boolean isNudeNum(int n)
{

    // Variable initialization
    int copy, length, flag = 0;
    copy = n;
    String temp;

    // Integer 'copy' is converted
    // to a String
    temp = String.valueOf(copy);

    // Total digits in the number
    length = temp.length();

    // Loop through all digits and check
    // if every digit divides n or not
    for(int i = 0; i < length; i++)
    {
        int num = temp.charAt(i) - '0';

        if (num == 0 || n % num != 0)
        {

            // flag is used to keep check
            flag = 1;
        }
    }

    // Return true or false as per
    // the condition
    if (flag == 1)
        return false;
    else
        return true;
}

// Function to find the longest subsequence
// which contain all Nude numbers
static int longestNudeSubseq(int arr[], int n)
{
    int answer = 0;

    // Find the length of longest
    // Nude number subsequence
    for(int i = 0; i < n; i++)
    {
        if (isNudeNum(arr[i]))
            answer++;
    }
    return answer;
}

// Driver Code
public static void main(String[] args)
{

    // Given array arr[]
    int arr[] = { 34, 34, 2, 2, 3,
                  333, 221, 32 };

    int n = arr.length;

    // Function call
    System.out.print(longestNudeSubseq(arr, n) + "\n");
}
}

// This code is contributed by PrinciRaj1992

Python3

# Python3 program for the above approach

# Function to check if the number
# is a Nude number
def isNudeNum(n):

    # Variable initialization
    flag = 0
    copy = n

    # Integer 'copy' is converted
    # to a string
    temp = str(copy)

    # Total digits in the number
    length = len(temp)

    # Loop through all digits and check
    # if every digit divides n or not
    for i in range(length):
        num = ord(temp[i]) - ord('0')

        if ((num == 0) or (n % num != 0)):

            # flag is used to keep check
            flag = 1

    # Return true or false as per
    # the condition
    if (flag == 1):
        return False
    else:
        return True

# Function to find the longest subsequence
# which contain all Nude numbers
def longestNudeSubseq(arr, n):

    answer = 0

    # Find the length of longest
    # Nude number subsequence
    for i in range(n):
        if (isNudeNum(arr[i])):
            answer += 1

    return answer

# Driver Code

# Given array arr[]
arr = [ 34, 34, 2, 2, 3,
        333, 221, 32 ]

n = len(arr)

# Function call
print(longestNudeSubseq(arr, n))

# This code is contributed by sanjoy_62

C#

// C# program for the above approach
using System;

class GFG{

// Function to check if the number
// is a Nude number
static bool isNudeNum(int n)
{

    // Variable initialization
    int copy, length, flag = 0;
    copy = n;
    String temp;

    // int 'copy' is converted
    // to a String
    temp = String.Join("", copy);

    // Total digits in the number
    length = temp.Length;

    // Loop through all digits and check
    // if every digit divides n or not
    for(int i = 0; i < length; i++)
    {
        int num = temp[i] - '0';

        if (num == 0 || n % num != 0)
        {

            // flag is used to keep check
            flag = 1;
        }
    }

    // Return true or false as per
    // the condition
    if (flag == 1)
        return false;
    else
        return true;
}

// Function to find the longest subsequence
// which contain all Nude numbers
static int longestNudeSubseq(int []arr, int n)
{
    int answer = 0;

    // Find the length of longest
    // Nude number subsequence
    for(int i = 0; i < n; i++)
    {
        if (isNudeNum(arr[i]))
            answer++;
    }
    return answer;
}

// Driver Code
public static void Main(String[] args)
{

    // Given array []arr
    int []arr = { 34, 34, 2, 2, 3,
                  333, 221, 32 };

    int n = arr.Length;

    // Function call
    Console.Write(longestNudeSubseq(arr, n) + "\n");
}
}

// This code is contributed by amal kumar choubey

Javascript

<script>
    // Javascript program for the above approach

    // Function to check if the number
    // is a Nude number
    function isNudeNum(n)
    {
        // Variable initialization
        let copy, length, flag = 0;
        copy = n;
        let temp;

        // Integer 'copy' is converted
        // to a string
        temp = copy.toString();

        // Total digits in the number
        length = temp.length;

        // Loop through all digits and check
        // if every digit divides n or not
        for (let i = 0; i < length; i++) {

            let num = temp[i].charCodeAt() - '0'.charCodeAt();

            if (num == 0 || n % num != 0) {

                // flag is used to keep check
                flag = 1;
            }
        }

        // Return true or false as per
        // the condition
        if (flag == 1)
            return false;

        else
            return true;
    }

    // Function to find the longest subsequence
    // which contain all Nude numbers
    function longestNudeSubseq(arr, n)
    {
        let answer = 0;

        // Find the length of longest
        // Nude number subsequence
        for (let i = 0; i < n; i++) {
            if (isNudeNum(arr[i]))
                answer++;
        }
        return answer;
    }

    // Given array arr[]
    let arr = [ 34, 34, 2, 2, 3,
                  333, 221, 32 ];

    let n = arr.length;

    // Function Call
    document.write(longestNudeSubseq(arr, n));

    // This code is contributed by divyesh072019.
</script>

Output:

4

Time Complexity: O(N*log₁₀N)
Auxiliary Space: O(1)