Generating all possible Subsequences using Recursion

Difficulty Level : Easy
Last Updated : 21 Oct, 2021

Given an array. The task is to generate and print all of the possible subsequences of the given array using recursion.

Examples:

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Input : [1, 2, 3]
Output : [3], [2], [2, 3], [1], [1, 3], [1, 2], [1, 2, 3]

Input : [1, 2]
Output : [2], [1], [1, 2]

Approach: For every element in the array, there are two choices, either to include it in the subsequence or not include it. Apply this for every element in the array starting from index 0 until we reach the last index. Print the subsequence once the last index is reached.

Below diagram shows the recursion tree for array, arr[] = {1, 2}.

Below is the implementation of the above approach.

C++

// C++ code to print all possible
// subsequences for given array using
// recursion
#include <bits/stdc++.h>
using namespace std;
 
void printArray(vector<int> arr, int n)
{
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    cout << endl;
}
 
// Recursive function to print all
// possible subsequences for given array
void printSubsequences(vector<int> arr, int index,
                       vector<int> subarr)
{
    // Print the subsequence when reach
    // the leaf of recursion tree
    if (index == arr.size())
    {
        int l = subarr.size();
 
        // Condition to avoid printing
        // empty subsequence
        if (l != 0)
            printArray(subarr, l);
    }
    else
    {
        // Subsequence without including
        // the element at current index
        printSubsequences(arr, index + 1, subarr);
 
        subarr.push_back(arr[index]);
 
        // Subsequence including the element
        // at current index
        printSubsequences(arr, index + 1, subarr);
    }
    return;
}
 
// Driver Code
int main()
{
    vector<int> arr{1, 2, 3};
    vector<int> b;
 
    printSubsequences(arr, 0, b);
 
    return 0;
}
 
// This code is contributed by
// sanjeev2552

Java

// Java code to print all possible
// subsequences for given array using
// recursion
import java.io.*;
import java.util.*;
 
class GFG{
       
// Recursive function to print all
// possible subsequences for given array
public static void printSubsequences(int[] arr, int index,
                                     ArrayList<Integer> path)
{
     
    // Print the subsequence when reach
    // the leaf of recursion tree
    if (index == arr.length)
    {
         
        // Condition to avoid printing
        // empty subsequence
        if (path.size() > 0)
            System.out.println(path);
    }
     
    else
    {
         
        // Subsequence without including
        // the element at current index
        printSubsequences(arr, index + 1, path);
         
        path.add(arr[index]);
         
        // Subsequence including the element
        // at current index
        printSubsequences(arr, index + 1, path);
         
        // Backtrack to remove the recently
        // inserted element
        path.remove(path.size() - 1);
    }
    return;
}
 
// Driver code
public static void main(String[] args)
{
    int[] arr = { 1, 2, 3 };
       
      // Auxiliary space to store each path
      ArrayList<Integer> path = new ArrayList<>();
       
      printSubsequences(arr, 0, path);
}
}
 
// This code is contributed by Mukul Sharma

Python3

# Python3 code to print all possible 
# subsequences for given array using 
# recursion
   
# Recursive function to print all
# possible subsequences for given array
def printSubsequences(arr, index, subarr):
       
    # Print the subsequence when reach 
    # the leaf of recursion tree
    if index == len(arr):
           
        # Condition to avoid printing
        # empty subsequence
        if len(subarr) != 0:
            print(subarr)
       
    else:
        # Subsequence without including 
        # the element at current index
        printSubsequences(arr, index + 1, subarr)
           
        # Subsequence including the element
        # at current index
        printSubsequences(arr, index + 1, 
                            subarr+[arr[index]])
       
    return
           
arr = [1, 2, 3]
   
printSubsequences(arr, 0, [])
 
#This code is contributed by Mayank Tyagi

Javascript

<script>
// Javascript code to print all possible
// subsequences for given array using
// recursion
 
// Recursive function to print all
// possible subsequences for given array
function printSubsequences(arr, index, path)
{
 
  // Print the subsequence when reach
  // the leaf of recursion tree
  if (index == arr.length)
  {
   
    // Condition to avoid printing
    // empty subsequence
    if (path.length > 0) document.write(`[${path}]<br>`);
  }
  else
  {
   
    // Subsequence without including
    // the element at current index
    printSubsequences(arr, index + 1, path);
 
    path.push(arr[index]);
 
    // Subsequence including the element
    // at current index
    printSubsequences(arr, index + 1, path);
 
    // Backtrack to remove the recently
    // inserted element
    path.pop();
  }
  return;
}
 
// Driver code
let arr = [1, 2, 3];
 
// Auxiliary space to store each path
let path = new Array();
 
printSubsequences(arr, 0, path);
 
// This code is contributed by gfgking
</script>

Output:

[3]
[2]
[2, 3]
[1]
[1, 3]
[1, 2]
[1, 2, 3]

Time Complexity:
$O(2^n)$

My Personal Notes

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Generating all possible Subsequences using Recursion

C++

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Python3

Javascript