JavaScript Program to Print all Subsequences of a String

A subsequence is a sequence that can be derived from another sequence by deleting zero or more elements without changing the order of the remaining elements. Subsequences of a string can be found with different methods here, we are using the Recursion method, Iteration method and Bit manipulation method.

Example: The example shows the input string and the corresponding output

Input: 'abc'

Output:
abc 
ab 
ac 
a 
bc 
b 
c

Method 1: Using Recursion

• We can recursively generate subsequences by including or excluding each character in the string.
• Create a function generateSubsequence with two parameters input and output.
• Check input.length==0 by using if condition.
• Here, value of inputString= “abc”.
• Then, call the function generateSubsequence.

Example: This example prints all subsequences of a string in JavaScript using the Recursion method.

Javascript

function generateSubsequence(input, output)
{
    // Base Case
    if (input.length==0) {
        console.log(output);
        return;
    }
    // Include
    generateSubsequence(
        input.substring(1), output + input[0]);

    // Exclude
    generateSubsequence(
        input.substring(1), output);
}
const inputString = 'abc';
generateSubsequence(inputString,"");

Output

abc
ab
ac
a
bc
b
c

Method 2: Using Iteration

• We can use iterative methods to generate all possible combinations of characters in the string.
• Create a function generateSubsequence with one parameter input.
• Inside the function store the length of the input in variable length. Iterate and check conditions by using for loop and if condition respectively.
• Here, the value of inputString= “abc”.
• Then, call the function generateSubsequence with argument inputstring to get output.

Example: This example prints all subsequences of a string in JavaScript using the Iteration method.

Javascript

function generateSubsequences(input) {
    const subsequences = [];
    const length = input.length;

    for (
        let i = 0;
        i < 1 << length;
        i++
    ) {
        let currentSubsequence = "";

        for (
            let j = 0;
            j < length;
            j++
        ) {
            if (i & (1 << j)) {
                currentSubsequence +=
                    input[j];
            }
        }

        subsequences.push(
            currentSubsequence
        );
    }

    return subsequences;
}

const inputString = "abc";
const allSubsequences =
    generateSubsequences(inputString);
console.log(allSubsequences);

Output

[
  '',   'a',   'b',
  'ab', 'c',   'ac',
  'bc', 'abc'
]

Method 3: Using Bit Manipulation

• We can use bit manipulation to represent the inclusion or exclusion of each character in the subsequence.
• Create a function generateSubsequence with one parameter input.
• Inside the function store the length of the input in variable length. Iterate and check conditions by using for loop and if condition respectively.
• Here,the value of inputString= “abc”.
• Then, call the function generateSubsequence with argument inputstring to get output.

Example: This example prints all subsequences of a string in JavaScript using the Bit manipulation method.

Javascript

function generateSubsequences(input) {
    const subsequences = [];
    const length = input.length;

    for (
        let mask = 0;
        mask < 1 << length;
        mask++
    ) {
        let currentSubsequence = "";

        for (
            let bit = 0;
            bit < length;
            bit++
        ) {
            if (mask & (1 << bit)) {
                currentSubsequence +=
                    input[bit];
            }
        }

        subsequences.push(
            currentSubsequence
        );
    }

    return subsequences;
}

const inputString = "abc";
const allSubsequences =
    generateSubsequences(inputString);
console.log(allSubsequences);

Output

[
  '',   'a',   'b',
  'ab', 'c',   'ac',
  'bc', 'abc'
]