Subsequences generated by including characters or ASCII value of characters of given string

Given a string str of length N, the task is to print all possible non-empty subsequences of the given string such that the subsequences either contain characters or ASCII values of the characters from the given string.

Examples: 

Input: str = "ab" 
Output: b 98 a ab a98 97 97b 9798 
Explanation: 
Possible subsequence of the strings are { b, a, ab }. 
Possible subsequences of the string generated by including either the characters or the ASCII value of the characters from the given string are { 98, b, a, 97, ab, 97b, a98, 9798 }. 
Therefore, the required output is { b, 98, a, ab, a98, 97, 97b, 9798 }.

Input: str = "a" 
Output: a 97

Approach: Follow the steps below to solve the problem: 

• Iterate over each character of the given string using variable i to generate all possible subsequences of the string.
• For every i^th character, the following three operations can be performed: 
  
  • Include the i^th character of str in a subsequence.
  • Do not include the i^th character of str in a subsequence.
  • Include the ASCII value of i^th character of str in a subsequence.
• Therefore, the recurrence relation to solve this problem is as follows:

FindSub(str, res, i) = { FindSub(str, res, i + 1), FindSub(str, res + str[i], i + 1), FindSub(str, res + ASCII(str[i]), i + 1) } 
res = subsequence of the string 
i = index of a character in str 

• Using the above recurrence relation, print all possible subsequences based on the given conditions.

Below is the implementation of the above approach: 

// C++ program to implement
// the above approach
#include<bits/stdc++.h>
using namespace std;

// Function to print subsequences containing
// ASCII value of the characters or the
// the characters of the given string
void FindSub(string str, string res,
             int i)
{
    
    // Base Case
    if (i == str.length())
    {
        
        // If length of the
        // subsequence exceeds 0
        if (res.length() > 0)
        {
            
            // Print the subsequence
           cout << res << " ";
        }
        return;
    }

    // Stores character present at
    // i-th index of str
    char ch = str[i];

    // If the i-th character is not
    // included in the subsequence
    FindSub(str, res, i + 1);

    // Including the i-th character
    // in the subsequence
    FindSub(str, res + ch, i + 1);

    // Include the ASCII value of the
    // ith character in the subsequence
    FindSub(str, res + to_string(int(ch)), i + 1);
}

// Driver Code
int main()
{
    string str = "ab";
    string res = "";
    
    // Stores length of str
    int N = str.length();

    FindSub(str, res, 0);
}

// This code is contributed by ipg2016107

// Java program to implement
// the above approach
class GFG {

    // Function to print subsequences containing
    // ASCII value of the characters or the
    // the characters of the given string
    static void FindSub(String str, String res,
                        int i)
    {
        // Base Case
        if (i == str.length()) {

            // If length of the
            // subsequence exceeds 0
            if (res.length() > 0) {

                // Print the subsequence
                System.out.print(res + " ");
            }
            return;
        }

        // Stores character present at
        // i-th index of str
        char ch = str.charAt(i);

        // If the i-th character is not
        // included in the subsequence
        FindSub(str, res, i + 1);

        // Including the i-th character
        // in the subsequence
        FindSub(str, res + ch, i + 1);

        // Include the ASCII value of the
        // ith character in the subsequence
        FindSub(str, res + (int)ch, i + 1);
        ;
    }

    // Driver Code
    public static void main(String[] args)
    {

        String str = "ab";

        String res = "";

        // Stores length of str
        int N = str.length();

        FindSub(str, res, 0);
    }
}

# Python3 program to implement
# the above approach

# Function to print subsequences containing
# ASCII value of the characters or the
# the characters of the given string
def FindSub(string , res, i) :
    
    # Base Case
    if (i == len(string)):

        # If length of the
        # subsequence exceeds 0
        if (len(res) > 0) :
            
            # Print the subsequence
            print(res, end=" ");
       
        return;

    # Stores character present at
    # i-th index of str
    ch = string[i];

    # If the i-th character is not
    # included in the subsequence
    FindSub(string, res, i + 1);

    # Including the i-th character
    # in the subsequence
    FindSub(string, res + ch, i + 1);

    # Include the ASCII value of the
    # ith character in the subsequence
    FindSub(string, res + str(ord(ch)), i + 1);

# Driver Code
if __name__ == "__main__" :
    
    string = "ab";

    res = "";

    # Stores length of str
    N = len(string);

    FindSub(string, res, 0);
  
# This code is contributed by AnkitRai01

// C# program to implement
// the above approach
using System;

class GFG{

// Function to print subsequences containing
// ASCII value of the characters or the
// the characters of the given string
static void FindSub(string str, string res,
                    int i)
{
    
    // Base Case
    if (i == str.Length) 
    {
        
        // If length of the
        // subsequence exceeds 0
        if (res.Length > 0)
        {
            
            // Print the subsequence
            Console.Write(res + " ");
        }
        return;
    }

    // Stores character present at
    // i-th index of str
    char ch = str[i];

    // If the i-th character is not
    // included in the subsequence
    FindSub(str, res, i + 1);

    // Including the i-th character
    // in the subsequence
    FindSub(str, res + ch, i + 1);

    // Include the ASCII value of the
    // ith character in the subsequence
    FindSub(str, res + (int)ch, i + 1);
}

// Driver Code
public static void Main(String[] args)
{
    string str = "ab";
    string res = "";

    // Stores length of str
    int N = str.Length;

    FindSub(str, res, 0);
}
}

// This code is contributed by AnkitRai01

<script>

// JavaScript program to implement
// the above approach

// Function to print subsequences containing
// ASCII value of the characters or the
// the characters of the given string
function FindSub(str, res, i) 
{
    
    // Base Case
    if (i === str.length) 
    {

        // If length of the
        // subsequence exceeds 0
        if (res.length > 0)
        {
            
            // Print the subsequence
            document.write(res + " ");
        }
        return;
    }

    // Stores character present at
    // i-th index of str
    var ch = str[i];
    
    // If the i-th character is not
    // included in the subsequence
    FindSub(str, res, i + 1);
    
    // Including the i-th character
    // in the subsequence
    FindSub(str, res + ch, i + 1);
    
    // Include the ASCII value of the
    // ith character in the subsequence
    FindSub(str, res + ch.charCodeAt(0), i + 1);
}

// Driver Code
var str = "ab";
var res = "";

// Stores length of str
var N = str.length;

FindSub(str, res, 0);

// This code is contributed by rdtank

</script>

b 98 a ab a98 97 97b 9798

Time Complexity: O(3^N) 
Auxiliary Space: O(N)

dekay

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Article Tags :

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• Dynamic Programming
• Mathematical
• Recursion
• DSA
• subsequence
• ASCII
• strings

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• Recursion
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