Count & Say Problem using JavaScript

The Count-and-Say problem involves generating the nth term of the count-and-say sequence. Each term of the sequence is generated from the previous term by reading the previous term and counting the number of consecutive same digits.

Example:

Input: n = 4;
Output: 1211
Explanation: We will start from 1, which will be pronounced as one one(11) and becomes the  next term of the series
Now, 11 will be pronounced as two one(21), and 21 will be pronounced as one two one one(1211) which will be the 
fourth term of the series and the answer as well.

The below approaches can be used to solve count and say problem in JavaScript:

Iterative Approach

In this approach, we will use the simple JavaScript loops to find the given term in the series bu using it with some conditional statements.

Example: The below code will explain the iterative approach to find the nth term of the count and say series.

JavaScript

function countAndSay(n) {
    if (n === 1) return "1";
    let prevTerm = "1";
    for (let i = 2; i <= n; i++) {
        let count = 1;
        let currentTerm = "";
        for (let j = 0; j < prevTerm.length; j++) {
            if (prevTerm[j] === prevTerm[j + 1]) {
                count++;
            } else {
                currentTerm += count + prevTerm[j];
                count = 1;
            }
        }
        prevTerm = currentTerm;
    }
    return prevTerm;
}
console.log(countAndSay(5));
console.log(countAndSay(7));
console.log(countAndSay(10));

Output

111221
13112221
13211311123113112211

Time Complexity : O(2ⁿ) , where n is the input parameter.

Space Complexity : O(2ⁿ)

Recursive Approach

In this approach, we will create a recursive function with a base case that calls itself again and again until it finds the given term of the series.

Example: The below code implements a recursive function to find the nth term of the series.

JavaScript

function countAndSay(n) {
    if (n === 1) return "1";
    let prevTerm = countAndSay(n - 1);
    let count = 1;
    let currentTerm = "";
    for (let i = 0; i < prevTerm.length; i++) {
        if (prevTerm[i] === prevTerm[i + 1]) {
            count++;
        } else {
            currentTerm += count + prevTerm[i];
            count = 1;
        }
    }
    return currentTerm;
}
console.log(countAndSay(5));
console.log(countAndSay(7));
console.log(countAndSay(10));

Output

111221
13112221
13211311123113112211

Time Complexity : O(n*m) , where n is the input parameter.

Space Complexity : O(n)