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Find the Longest subarray such that difference between adjacent elements is K

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  • Last Updated : 31 Mar, 2022
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Given an array arr[] of size N, and integer K. The task is to find the longest subarray with the difference between adjacent elements as K.

Examples:

Input: arr[] = { 5, 5, 5, 10, 8, 6, 12, 13 }, K =1
Output: {12, 13}
Explanation: This is the longest subarray with difference between adjacents as 1.

Input: arr[] = {4, 6, 8, 9, 8, 12, 14, 17, 15}, K = 2
Output: {4, 6, 8}

 

Approach: Starting from the first element of the array, find the first valid sub-array and store its length and starting point. Then starting from the next element (the first element that wasn’t included in the first sub-array), find another valid sub-array and keep on updating the maximum length and start point. Repeat the process until all the valid sub-arrays have been found then print the maximum length sub-array.

Below is the implementation of the above approach.

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the maximum length
// sub-array such that the
// absolute difference between every two
// consecutive elements is K
void getMaxLengthSubarray(int arr[],
                          int N, int K)
{
    int l = N;
    int i = 0, maxlen = 0;
    int max_len_start, max_len_end;
    while (i < l) {
        int j = i;
        while (i + 1 < l
               && (abs(arr[i]
                       - arr[i + 1]) == K)) {
            i++;
        }
 
        // Length of the valid sub-array
        // currently under consideration
        int currLen = i - j + 1;
 
        // Update the maximum length subarray
        if (maxlen < currLen) {
            maxlen = currLen;
            max_len_start = j;
            max_len_end = i;
        }
 
        if (j == i)
            i++;
    }
 
    // Print the maximum length subarray
    for (int p = max_len_start;
         p <= max_len_end; p++)
        cout << arr[p] << " ";
}
 
// Driver code
int main()
{
    int arr[] = { 4, 6, 8, 9, 8, 12,
                 14, 17, 15 };
    int K = 2;
    int N = sizeof(arr) / sizeof(arr[0]);
    getMaxLengthSubarray(arr, N, K);
    return 0;
}


Java




// Java program for the above approach
import java.util.*;
public class GFG
{
 
// Function to return the maximum length
// sub-array such that the
// absolute difference between every two
// consecutive elements is K
static void getMaxLengthSubarray(int arr[],
                          int N, int K)
{
    int l = N;
    int i = 0, maxlen = 0;
    int max_len_start = 0, max_len_end = 0;
    while (i < l) {
        int j = i;
        while (i + 1 < l
               && (Math.abs(arr[i]
                       - arr[i + 1]) == K)) {
            i++;
        }
 
        // Length of the valid sub-array
        // currently under consideration
        int currLen = i - j + 1;
 
        // Update the maximum length subarray
        if (maxlen < currLen) {
            maxlen = currLen;
            max_len_start = j;
            max_len_end = i;
        }
 
        if (j == i)
            i++;
    }
 
    // Print the maximum length subarray
    for (int p = max_len_start;
         p <= max_len_end; p++)
        System.out.print(arr[p] + " ");
}
 
// Driver code
public static void main(String args[])
{
    int arr[] = { 4, 6, 8, 9, 8, 12,
                 14, 17, 15 };
    int K = 2;
    int N =  arr.length; 
    getMaxLengthSubarray(arr, N, K);
}
}
 
// This code is contributed by Samim Hossain Mondal.


Python3




# Python program to implement
# the above approach
 
# Function to return the maximum length
# sub-array such that the
# absolute difference between every two
# consecutive elements is K
def getMaxLengthSubarray(arr, N, K) :
     
    l = N
    i = 0
    maxlen = 0
    while (i < l) :
        j = i
        while (i + 1 < l
               and (abs(arr[i]
                       - arr[i + 1]) == K)) :
            i += 1
         
        # Length of the valid sub-array
        # currently under consideration
        currLen = i - j + 1
 
        # Update the maximum length subarray
        if (maxlen < currLen) :
            maxlen = currLen
            max_len_start = j
            max_len_end = i
         
        if (j == i) :
            i += 1
     
    # Print the maximum length subarray
    for p in range(max_len_start, max_len_end+1, 1) :
        print(arr[p], end=" ")
 
# Driver code
arr = [ 4, 6, 8, 9, 8, 12,
                 14, 17, 15 ]
K = 2
N = len(arr)
getMaxLengthSubarray(arr, N, K)
 
# This code is contributed by avijitmondal1998


C#




// C# program for the above approach
using System;
class GFG
{
 
// Function to return the maximum length
// sub-array such that the
// absolute difference between every two
// consecutive elements is K
static void getMaxLengthSubarray(int []arr,
                          int N, int K)
{
    int l = N;
    int i = 0, maxlen = 0;
    int max_len_start = 0, max_len_end = 0;
    while (i < l) {
        int j = i;
        while (i + 1 < l
               && (Math.Abs(arr[i]
                       - arr[i + 1]) == K)) {
            i++;
        }
 
        // Length of the valid sub-array
        // currently under consideration
        int currLen = i - j + 1;
 
        // Update the maximum length subarray
        if (maxlen < currLen) {
            maxlen = currLen;
            max_len_start = j;
            max_len_end = i;
        }
 
        if (j == i)
            i++;
    }
 
    // Print the maximum length subarray
    for (int p = max_len_start;
         p <= max_len_end; p++)
        Console.Write(arr[p] + " ");
}
 
// Driver code
public static void Main()
{
    int []arr = { 4, 6, 8, 9, 8, 12,
                 14, 17, 15 };
    int K = 2;
    int N =  arr.Length; 
    getMaxLengthSubarray(arr, N, K);
}
}
 
// This code is contributed by Samim Hossain Mondal.


Javascript




<script>
       // JavaScript code for the above approach
 
       // Function to return the maximum length
       // sub-array such that the
       // absolute difference between every two
       // consecutive elements is K
       function getMaxLengthSubarray(arr, N, K)
       {
           let l = N;
           let i = 0, maxlen = 0;
           let max_len_start, max_len_end;
           while (i < l) {
               let j = i;
               while (i + 1 < l
                   && (Math.abs(arr[i]
                       - arr[i + 1]) == K)) {
                   i++;
               }
 
               // Length of the valid sub-array
               // currently under consideration
               let currLen = i - j + 1;
 
               // Update the maximum length subarray
               if (maxlen < currLen) {
                   maxlen = currLen;
                   max_len_start = j;
                   max_len_end = i;
               }
 
               if (j == i)
                   i++;
           }
 
           // Print the maximum length subarray
           for (let p = max_len_start;
               p <= max_len_end; p++)
               document.write(arr[p] + " ");
       }
 
       // Driver code
       let arr = [4, 6, 8, 9, 8, 12,
           14, 17, 15];
       let K = 2;
       let N = arr.length;
       getMaxLengthSubarray(arr, N, K);
 
        // This code is contributed by Potta Lokesh
   </script>


 
 

Output

4 6 8 

 

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

 


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