Longest Subsequence where index of next element is arr[arr[i] + i]

Given an array arr[], the task is to find the maximum length sub-sequence from the array which satisfy the following condition:
Any element can be chosen as the first element of the sub-sequence but the index of the next element will be determined by arr[arr[i] + i] where i is the index of the previous element in the sequence.

Examples:

Input: arr[] = {1, 2, 3, 4, 5}
Output: 1 2 4
arr[0] = 1, arr[1 + 0] = arr[1] = 2, arr[2 + 1] = arr[3] = 4
Other possible sub-sequences are {2, 4}, {3}, {4} and {5}

Input: arr[] = {1, 6, 3, 1, 12, 1, 4}
Output: 3 1 4

Approach:



Below is the implementation of the above approach:

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to print the maximum length sub-sequence
void maxLengthSubSeq(int a[], int n)
{
    // Arrays to store the values to be printed
    int temp[n], print[n];
    int y = 0;
  
    for (int i = 0; i < n; i++) {
        int j = 0;
        int x = 0;
  
        // Store the first value into the temp array
        temp[j++] = a[x];
  
        // Index of the next element
        x = a[x] + x;
  
        // Iterate till index is in range of the array
        while (x < n) {
            temp[j++] = a[x];
            x = a[x] + x;
        }
  
        // If the length (temp) > the length (print) then
        // copy the contents of the temp array into
        // the print array
        if (y < j) {
            for (int k = 0; k < j; k++) {
                print[k] = temp[k];
                y = j;
            }
        }
    }
  
    // Print the contents of the array
    for (int i = 0; i < y; i++)
        cout << print[i] << " ";
}
  
// Driver code
int main()
{
    int a[] = { 1, 2, 3, 4, 5 };
    int n = sizeof(a) / sizeof(a[0]);
    maxLengthSubSeq(a, n);
    return 0;
}
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//Java  implementation of the approach/
  
import java.io.*;
  
class GFG {
      
// Function to print the maximum length sub-sequence
static void maxLengthSubSeq(int a[], int n)
{
    // Arrays to store the values to be printed
    int temp[]=new int[n];
    int print[]=new int[n];
    int y = 0;
  
    for (int i = 0; i < n; i++) {
        int j = 0;
        int x = 0;
  
        // Store the first value into the temp array
        temp[j++] = a[x];
  
        // Index of the next element
        x = a[x] + x;
  
        // Iterate till index is in range of the array
        while (x < n) {
            temp[j++] = a[x];
            x = a[x] + x;
        }
  
        // If the length (temp) > the length (print) then
        // copy the contents of the temp array into
        // the print array
        if (y < j) {
            for (int k = 0; k < j; k++) {
                print[k] = temp[k];
                y = j;
            }
        }
    }
  
    // Print the contents of the array
    for (int i = 0; i < y; i++)
            System.out.print(print[i] + " ");
}
  
// Driver code
    public static void main (String[] args) {
  
    int a[] = { 1, 2, 3, 4, 5 };
    int n = a.length;
    maxLengthSubSeq(a, n);
    }
//This code is contributed by @Tushil.    
}
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# Python 3 implementation of the approach
  
# Function to print the maximum length 
# sub-sequence
def maxLengthSubSeq(a, n):
      
    # Arrays to store the values to be printed
    temp = [0 for i in range(n)]
    print1 = [0 for i in range(n)]
    y = 0
  
    for i in range(0, n, 1):
        j = 0
        x = 0
  
        # Store the first value into 
        # the temp array
        temp[j] = a[x]
        j += 1
  
        # Index of the next element
        x = a[x] + x
  
        # Iterate till index is in range 
        # of the array
        while (x < n):
            temp[j] = a[x]
            j += 1
            x = a[x] + x
          
        # If the length (temp) > the length 
        # (print) then copy the contents of 
        # the temp array into the print array
        if (y < j):
            for k in range(0, j, 1):
                print1[k] = temp[k]
                y = j
              
    # Print the contents of the array
    for i in range(0, y, 1):
        print(print1[i], end = " ")
  
# Driver code
if __name__ == '__main__':
    a = [1, 2, 3, 4, 5]
    n = len(a)
    maxLengthSubSeq(a, n)
  
# This code is contributed by 
# Surendra_Gangwar
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//C# implementation of the approach/
  
using System;
  
public class GFG{
          
// Function to print the maximum length sub-sequence
static void maxLengthSubSeq(int []a, int n)
{
    // Arrays to store the values to be printed
    int []temp=new int[n];
    int []print=new int[n];
    int y = 0;
  
    for (int i = 0; i < n; i++) {
        int j = 0;
        int x = 0;
  
        // Store the first value into the temp array
        temp[j++] = a[x];
  
        // Index of the next element
        x = a[x] + x;
  
        // Iterate till index is in range of the array
        while (x < n) {
            temp[j++] = a[x];
            x = a[x] + x;
        }
  
        // If the length (temp) > the length (print) then
        // copy the contents of the temp array into
        // the print array
        if (y < j) {
            for (int k = 0; k < j; k++) {
                print[k] = temp[k];
                y = j;
            }
        }
    }
  
    // Print the contents of the array
    for (int i = 0; i < y; i++)
            Console.Write(print[i] + " ");
}
  
// Driver code
    static public void Main (){
          
    int []a = { 1, 2, 3, 4, 5 };
    int n = a.Length;
    maxLengthSubSeq(a, n);
    }
//This code is contributed by ajit. 
}
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<?php
// PHP implementation of the approach
  
// Function to print the maximum
// length sub-sequence
function maxLengthSubSeq($a, $n)
{
    $y = 0;
  
    for ($i = 0; $i < $n; $i++)
    {
        $j = 0;
        $x = 0;
  
        // Store the first value into 
        // the temp array
        $temp[$j++] = $a[$x];
  
        // Index of the next element
        $x = $a[$x] + $x;
  
        // Iterate till index is in
        // range of the array
        while ($x < $n)
        {
            $temp[$j++] = $a[$x];
            $x = $a[$x] + $x;
        }
  
        // If the length (temp) > the length 
        // (print) then copy the contents of 
        // the temp array into the print array
        if ($y < $j)
        {
            for ($k = 0; $k < $j; $k++)
            {
                $print[$k] = $temp[$k];
                $y = $j;
            }
        }
    }
  
    // Print the contents of the array
    for ($i = 0; $i < $y; $i++)
        echo $print[$i] . " ";
}
  
// Driver code
$a = array(1, 2, 3, 4, 5);
$n = sizeof($a);
maxLengthSubSeq($a, $n);
  
// This code is contributed
// by Akanksha Rai
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Output:
1 2 4

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