JavaScript Program to Find i’th Index Character in a Binary String Obtained After n Iterations

Given a decimal number m, convert it into a binary string and apply n iterations. In each iteration, 0 becomes “01” and 1 becomes “10”. Find the (based on indexing) index character in the string after the nth iteration.

Input: m = 5, n = 2, i = 3
Output: 1
Input: m = 3, n = 3, i = 6
Output: 1

Approach 1

• Convert a decimal number into its binary representation and store it as a string ‘s’.
• Iterate ‘n’ times, and in each iteration, replace ‘0’ with “01” and ‘1’ with “10” in the string ‘s’ by running another loop over its length, storing the modified string in ‘s1’ after each iteration.
• After all, iterations, return the character at the ‘ith’ index in the final string ‘s’.

Javascript

// Javascript Program to find ith
// character in a binary String.

let s = "";

// Function to store binary Representation
function binary_conversion(m) {
    while (m !== 0) {
        let tmp = m % 2;
        s += tmp.toString();
        m = Math.floor(m / 2);
    }

    s = s.split("").reverse().join("");
}

// Function to find ith character
function find_character(n, m, i) {
    // Function to change decimal to binary
    binary_conversion(m);

    let s1 = "";

    for (let x = 0; x < n; x++) {
        let temp = "";

        for (let y = 0; y < s.length; y++) {
            temp += s[y] === '1' ? "10" : "01";
        }

        // Assign temp String in s String
        s = temp;
    }

    return s[i] === '1' ? 1 : 0;
}
let m = 5, n = 2, i = 8;
console.log(find_character(n, m, i));

Output

1

Time Complexity: O(N)

Space Complexity: O(N), where N is the length of string.

Approach 2

• In this approach, we calculate the ith character in a binary string after n iterations.
• It converts a decimal number M into its binary representation, finds the block number where the character is, and handles special cases when k corresponds to the root digit.
• We use bitwise operations to efficiently determine whether to flip the root digit or not.
• The result is then printed, providing the desired character within the modified binary string.

Javascript

// Javascript program to find ith
// Index character in a binary
// string obtained after n iterations

// Function to find
// the i-th character
function KthCharacter(m, n, k) {

    // Distance between two
    // consecutive elements
    // after N iterations
    let distance = Math.pow(2, n);
    let Block_number = Math.floor(k / distance);
    let remaining = k % distance;

    let s = new Array(32).fill(0);
    let x = 0;

    // Binary representation of M using a while loop
    while (m > 0) {
        s[x] = m % 2;
        m = Math.floor(m / 2);
        x++;
    }

    // kth digit will be
    // derived from root
    // for sure
    let root = s[x - 1 -
        Block_number];

    if (remaining == 0) {
        console.log(root);
        return;
    }

    // Check whether there is
    // need to flip root or not
    let flip = true;
    while (remaining > 1) {
        if ((remaining & 1) > 0) {
            flip = !flip;
        }
        remaining = remaining >> 1;
    }

    if (flip) {
        console.log((root > 0) ? 0 : 1);
    }
    else {
        console.log(root);
    }
}
let m = 5, k = 5, n = 3;
KthCharacter(m, n, k);

Output

1

Time Complexity: O(log N)

Space Complexity: O(1)