Length of longest subsequence consisting of distinct adjacent elements

Last Updated : 21 Jun, 2022

Given an array arr[], the task is to find the length of the longest subsequence of the array arr[] such that all adjacent elements in the subsequence are different.

Examples:

Input: arr[] = {4, 2, 3, 4, 3}
Output: 5
Explanation:
The longest subsequence where no two adjacent elements are equal is {4, 2, 3, 4, 3}. Length of the subsequence is 5.

Input: arr[] = {7, 8, 1, 2, 2, 5, 5, 1}
Output: 6
Explanation: Longest subsequence where no two adjacent elements are equal is {7, 8, 1, 2, 5, 1}. Length of the subsequence is 5.

Naive Approach: The simplest approach is to generate all possible subsequence of the given array and print the maximum length of that subsequence having all adjacent elements different.

Time Complexity: O(2^N)
Auxiliary Space: O(1)

Efficient Approach: Follow the steps below to solve the problem:

Initialize count to 1 to store the length of the longest subsequence.
Traverse the array over the indices [1, N – 1] and for each element, check if the current element is equal to the previous element or not. If found to be not equal, then increment count by 1.
After completing the above steps, print the value of count as the maximum possible length of subsequence.

Below is the implementation of the above approach:

C++

   // C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function that finds the length of
// longest subsequence having different
// adjacent elements
void longestSubsequence(int arr[], int N)
{
    // Stores the length of the
    // longest subsequence
    int count = 1;
 
    // Traverse the array
    for (int i = 1; i < N; i++) {
 
        // If previous and current
        // element are not same
        if (arr[i] != arr[i - 1]) {
 
            // Increment the count
            count++;
        }
    }
 
    // Print the maximum length
    cout << count << endl;
}
 
// Driver Code
int main()
{
    int arr[] = { 7, 8, 1, 2, 2, 5, 5, 1 };
 
    // Size of Array
    int N = sizeof(arr) / sizeof(arr[0]);
 
    // Function Call
    longestSubsequence(arr, N);
 
    return 0;
}
 
  

Java

   // Java program for the 
// above approach
import java.util.*;
 
class GFG{
    
// Function that finds the length of
// longest subsequence having different
// adjacent elements
static void longestSubsequence(int arr[], 
                               int N)
{
  // Stores the length of the
  // longest subsequence
  int count = 1;
 
  // Traverse the array
  for (int i = 1; i < N; i++) 
  {
    // If previous and current
    // element are not same
    if (arr[i] != arr[i - 1]) 
    {
      // Increment the count
      count++;
    }
  }
 
  // Print the maximum length
  System.out.println(count);
}
 
// Driver Code
public static void main(String args[])
{
  int arr[] = {7, 8, 1, 2, 
               2, 5, 5, 1};
 
  // Size of Array
  int N = arr.length;
 
  // Function Call
  longestSubsequence(arr, N);
}
}
 
// This code is contributed by bgangwar59
 
  

Python3

   # Python3 program for the above approach
 
# Function that finds the length of
# longest subsequence having different
# adjacent elements
def longestSubsequence(arr, N):
     
    # Stores the length of the
    # longest subsequence
    count = 1
 
    # Traverse the array
    for i in range(1, N, 1):
         
        # If previous and current
        # element are not same
        if (arr[i] != arr[i - 1]):
             
            # Increment the count
            count += 1
 
    # Print the maximum length
    print(count)
 
# Driver Code
if __name__ == '__main__':
     
    arr = [ 7, 8, 1, 2, 2, 5, 5, 1 ]
     
    # Size of Array
    N = len(arr)
     
    # Function Call
    longestSubsequence(arr, N)
 
# This code is contributed by ipg2016107
 
  

C#

   // C# program for the 
// above approach
using System;
  
class GFG{
     
// Function that finds the length of
// longest subsequence having different
// adjacent elements
static void longestSubsequence(int[] arr, 
                               int N)
{
   
  // Stores the length of the
  // longest subsequence
  int count = 1;
  
  // Traverse the array
  for(int i = 1; i < N; i++) 
  {
     
    // If previous and current
    // element are not same
    if (arr[i] != arr[i - 1]) 
    {
       
      // Increment the count
      count++;
    }
  }
  
  // Print the maximum length
  Console.WriteLine(count);
}
  
// Driver Code
public static void Main()
{
  int[] arr = { 7, 8, 1, 2, 
                2, 5, 5, 1 };
   
  // Size of Array
  int N = arr.Length;
   
  // Function Call
  longestSubsequence(arr, N);
}
}
 
// This code is contributed by susmitakundugoaldanga
 
  

Javascript

   <script>
 
// JavaScript program to implement
// the above approach
 
// Function that finds the length of
// longest subsequence having different
// adjacent elements
function longestSubsequence(arr, N)
{
  // Stores the length of the
  // longest subsequence
  let count = 1;
  
  // Traverse the array
  for (let i = 1; i < N; i++)
  {
    // If previous and current
    // element are not same
    if (arr[i] != arr[i - 1])
    {
      // Increment the count
      count++;
    }
  }
  
  // Print the maximum length
  document.write(count);
}
 
// Driver Code
 
    let arr = [7, 8, 1, 2,
               2, 5, 5, 1];
  
  // Size of Array
  let N = arr.length;
  
  // Function Call
  longestSubsequence(arr, N);
           
</script>
 
  

Output:

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

Length of longest non-decreasing subsequence such that difference between adjacent elements is at most one

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Length of longest subsequence consisting of distinct adjacent elements

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