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++

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// 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;
}

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Java

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// 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

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Python3

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# Python3 program for the above approach
  
# Function to check if the number 
# is a Nude number 
def isNudeNum(n):
      
    # Variable initialization 
    flag = 0
    copy =
  
    # 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

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C#

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// 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

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Output: 

4

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

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