Maximum length subsequence with difference between adjacent elements as either 0 or 1

30 Apr, 2021
Given an array of n integers. The problem is to find maximum length of the subsequence with difference between adjacent elements as either 0 or 1.Examples:  
Input : arr[] = {2, 5, 6, 3, 7, 6, 5, 8}
Output : 5
The subsequence is {5, 6, 7, 6, 5}.

Input : arr[] = {-2, -1, 5, -1, 4, 0, 3}
Output : 4
The subsequence is {-2, -1, -1, 0}.
Source: Expedia Interview Experience | Set 12 
The solution to this problem closely resembles the Longest Increasing Subsequence problem. The only difference is that here we have to check whether the absolute difference between the adjacent elements of the subsequence is either 0 or 1. 
C++
Java
Python3
C#
PHP
Javascript
// C++ implementation to find maximum length// subsequence with difference between adjacent// elements as either 0 or 1#include <bits/stdc++.h>using namespace std; // function to find maximum length subsequence// with difference between adjacent elements as// either 0 or 1int maxLenSub(int arr[], int n){    int mls[n], max = 0;         // Initialize mls[] values for all indexes    for (int i=0; i<n; i++)        mls[i] = 1;         // Compute optimized maximum length subsequence    // values in bottom up manner    for (int i=1; i<n; i++)        for (int j=0; j<i; j++)            if (abs(arr[i] - arr[j]) <= 1 &&                    mls[i] < mls[j] + 1)                mls[i] = mls[j] + 1;         // Store maximum of all 'mls' values in 'max'       for (int i=0; i<n; i++)        if (max < mls[i])            max = mls[i];         // required maximum length subsequence    return max;       } // Driver program to test aboveint main(){    int arr[] = {2, 5, 6, 3, 7, 6, 5, 8};    int n = sizeof(arr) / sizeof(arr[0]);    cout << "Maximum length subsequence = "         << maxLenSub(arr, n);    return 0;}
// JAVA Code for Maximum length subsequence// with difference between adjacent elements// as either 0 or 1import java.util.*; class GFG {         // function to find maximum length subsequence    // with difference between adjacent elements as    // either 0 or 1     public static int maxLenSub(int arr[], int n)    {        int mls[] = new int[n], max = 0;                  // Initialize mls[] values for all indexes        for (int i = 0; i < n; i++)            mls[i] = 1;                  // Compute optimized maximum length        // subsequence values in bottom up manner        for (int i = 1; i < n; i++)            for (int j = 0; j < i; j++)                if (Math.abs(arr[i] - arr[j]) <= 1                      && mls[i] < mls[j] + 1)                    mls[i] = mls[j] + 1;                  // Store maximum of all 'mls' values in 'max'           for (int i = 0; i < n; i++)            if (max < mls[i])                max = mls[i];                  // required maximum length subsequence        return max;           }         /* Driver program to test above function */    public static void main(String[] args)    {        int arr[] = {2, 5, 6, 3, 7, 6, 5, 8};        int n = arr.length;        System.out.println("Maximum length subsequence = "+                               maxLenSub(arr, n));               }}   // This code is contributed by Arnav Kr. Mandal.
# Python implementation to find maximum length# subsequence with difference between adjacent# elements as either 0 or 1 # function to find maximum length subsequence# with difference between adjacent elements as# either 0 or 1def maxLenSub( arr, n):    mls=[]    max = 0         #Initialize mls[] values for all indexes    for i in range(n):        mls.append(1)         #Compute optimized maximum length subsequence    # values in bottom up manner    for i in range(n):        for j in range(i):            if (abs(arr[i] - arr[j]) <= 1 and mls[i] < mls[j] + 1):                mls[i] = mls[j] + 1                     # Store maximum of all 'mls' values in 'max'    for i in range(n):        if (max < mls[i]):            max = mls[i]         #required maximum length subsequence    return max     #Driver program to test abovearr = [2, 5, 6, 3, 7, 6, 5, 8]n = len(arr)print("Maximum length subsequence = ",maxLenSub(arr, n)) #This code is contributed by "Abhishek Sharma 44"
// C# Code for Maximum length subsequence// with difference between adjacent elements// as either 0 or 1using System; class GFG {         // function to find maximum length subsequence    // with difference between adjacent elements as    // either 0 or 1    public static int maxLenSub(int[] arr, int n)    {        int[] mls = new int[n];        int max = 0;         // Initialize mls[] values for all indexes        for (int i = 0; i < n; i++)            mls[i] = 1;         // Compute optimized maximum length        // subsequence values in bottom up manner        for (int i = 1; i < n; i++)            for (int j = 0; j < i; j++)                if (Math.Abs(arr[i] - arr[j]) <= 1                    && mls[i] < mls[j] + 1)                    mls[i] = mls[j] + 1;         // Store maximum of all 'mls' values in 'max'        for (int i = 0; i < n; i++)            if (max < mls[i])                max = mls[i];         // required maximum length subsequence        return max;    }     /* Driver program to test above function */    public static void Main()    {        int[] arr = { 2, 5, 6, 3, 7, 6, 5, 8 };        int n = arr.Length;        Console.Write("Maximum length subsequence = " +                                    maxLenSub(arr, n));    }} // This code is contributed by Sam007
<?php// PHP implementation to find maximum length// subsequence with difference between adjacent// elements as either 0 or 1 // function to find maximum length subsequence// with difference between adjacent elements as// either 0 or 1function maxLenSub($arr, $n){    $mls = array(); $max = 0;         // Initialize mls[] values    // for all indexes    for($i = 0; $i < $n; $i++)        $mls[$i] = 1;         // Compute optimized maximum    // length subsequence    // values in bottom up manner    for ($i = 1; $i < $n; $i++)        for ( $j = 0; $j < $i; $j++)            if (abs($arr[$i] - $arr[$j]) <= 1 and                         $mls[$i] < $mls[$j] + 1)                $mls[$i] = $mls[$j] + 1;         // Store maximum of all    // 'mls' values in 'max'    for($i = 0; $i < $n; $i++)        if ($max < $mls[$i])            $max = $mls[$i];         // required maximum    // length subsequence    return $max;    }     // Driver Code    $arr = array(2, 5, 6, 3, 7, 6, 5, 8);    $n = count($arr);    echo "Maximum length subsequence = "        , maxLenSub($arr, $n);         // This code is contributed by anuj_67.?>
<script> // Javascript Code for// Maximum length subsequence// with difference between// adjacent elements// as either 0 or 1     // function to find maximum    // length subsequence    // with difference between    // adjacent elements as    // either 0 or 1     function  maxLenSub(arr, n)    {        let mls = new Array(n).fill(1), max = 0;                  // Initialize mls[] values for all indexes        for (let i = 0; i < n; i++)            mls[i] = 1;                  // Compute optimized maximum length        // subsequence values in bottom up manner        for (let i = 1; i < n; i++)            for (let j = 0; j < i; j++)                if (Math.abs(arr[i] - arr[j]) <= 1                      && mls[i] < mls[j] + 1)                    mls[i] = mls[j] + 1;                  // Store maximum of all 'mls' values in 'max'           for (let i = 0; i < n; i++)            if (max < mls[i])                max = mls[i];                  // required maximum length subsequence        return max;           }           // driver program         let arr = [2, 5, 6, 3, 7, 6, 5, 8];        let n = arr.length;        document.write("Maximum length subsequence = "+                               maxLenSub(arr, n));         </script>
Output:  
Maximum length subsequence = 5
Time Complexity: O(n2) Auxiliary Space: O(n)Maximum length subsequence with difference between adjacent elements as either 0 or 1 | Set 2This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
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