JavaScript Program to Generate Number Sequence

Find the n’th term in the Look-and-say (Or Count and Say) Sequence. The look-and-say sequence is the sequence of the below integers: 
1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211

How is the above sequence generated?
n’th term is generated by reading (n-1)’th term.

The first term is "1"
Second term is "11", generated by reading first term as "One 1" 
(There is one 1 in previous term)
Third term is "21", generated by reading second term as "Two 1"
Fourth term is "1211", generated by reading third term as "One 2 One 1" 
and so on

How to find n’th term? 

Example:

Input: n = 3
Output: 21
Input: n = 5
Output: 111221

Number sequence using Iterative Approach

In this approach, we iteratively generate each term of the sequence starting from the base case “1”. After which we maintain a current term and use it to generate the next term by counting consecutive digits. The process continues until we reach the nth term.

Example: The below code implements a JavaScript Program to generate a number sequence using an iterative approach.

JavaScript

function countAndSay(n) {
    
    // Base case: the first term is always "1"
    let result = "1";

    // Iteratively generate each term starting from the second term
    for (let i = 1; i < n; i++) {
        let temp = "";
        let count = 1;

        // Iterate through each digit in the current term
        for (let j = 1; j < result.length; j++) {
            
            // If the current digit is the same as the 
            //previous one, increment the count
            if (result[j] === result[j - 1]) {
                count++;
            } else {
                
                temp += count + result[j - 1];
                count = 1; 
            }
        }

        // Append the count and the last digit
        temp += count + result[result.length - 1];

        // Update the result to the newly generated term
        result = temp;
    }

    // Return the nth term of the sequence
    return result;
}

// Example usage
const n = 5;
console.log("The " + n + "th term of the Count and Say sequence is: 
            " + countAndSay(n));

Output

The 5th term of the Count and Say sequence is: 111221

Time Complexity: O(2^N)

Auxiliary Space: O(2^N)

Using Recursive Approach

In the recursive approach, we define a function to generate the nth term of the sequence based on the (n-1)th term. After which we recursively call this function to generate each term until we reach the base case. The base case is when n is 1, in which case we return “1” as the first term of the sequence.

Example: The below code implements a Program to generate a number sequence using a recursive approach.

JavaScript

function countAndSayRecursive(n) {
    
    // Base case: the first term is always "1"
    if (n === 1) {
        return "1";
    }

    // Recursive call to generate the 
    // (n-1)th term of the sequence
    const prev = countAndSayRecursive(n - 1);

    let temp = "";
    let count = 1;

    // Iterate through each digit of the (n-1)th term
    for (let i = 1; i < prev.length; i++) {
        
        if (prev[i] === prev[i - 1]) {
            count++;
        } else {

            temp += count + prev[i - 1];
            count = 1;
        }
    }

    // Append the count and the last digit to the temporary result
    temp += count + prev[prev.length - 1];

    // Return the newly generated term
    return temp;
}

// Example usage
const n = 5;
console.log("The " + n + 
            "th term of the Count and Say sequence (recursive approach) is: "
            + countAndSayRecursive(n));

Output

The 5th term of the Count and Say sequence (recursive approach) is: 111221

Time Complexity: O(N*2^N)

Auxiliary Space: O(n)