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
Table of Content
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.
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));
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 usageconst 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.
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));
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 usageconst 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)
Using Dynamic Programming Approach
In the dynamic programming approach, we use an array to store the previously computed terms of the sequence. This way, we avoid recalculating the terms multiple times, which helps to optimize the process and reduce time complexity. We generate each term based on the previous term stored in the array and continue this process until we reach the nth term.
Example: The below code implements a JavaScript program to generate a number sequence using a dynamic programming approach.
function countAndSay(n) {
if (n === 1) return "1";
let sequence = ["1"];
for (let i = 1; i < n; i++) {
let prevTerm = sequence[i - 1];
let nextTerm = "";
let count = 1;
for (let j = 1; j < prevTerm.length; j++) {
if (prevTerm[j] === prevTerm[j - 1]) {
count++;
} else {
nextTerm += count + prevTerm[j - 1];
count = 1;
}
}
nextTerm += count + prevTerm[prevTerm.length - 1];
sequence.push(nextTerm);
}
return sequence[n - 1];
}
console.log(countAndSay(3));
console.log(countAndSay(5));
console.log(countAndSay(8));
function countAndSay(n) { if (n === 1) return "1"; let sequence = ["1"]; for (let i = 1; i < n; i++) { let prevTerm = sequence[i - 1]; let nextTerm = ""; let count = 1; for (let j = 1; j < prevTerm.length; j++) { if (prevTerm[j] === prevTerm[j - 1]) { count++; } else { nextTerm += count + prevTerm[j - 1]; count = 1; } } nextTerm += count + prevTerm[prevTerm.length - 1]; sequence.push(nextTerm); } return sequence[n - 1];}console.log(countAndSay(3));console.log(countAndSay(5));console.log(countAndSay(8));Output
21 111221 1113213211
Time Complexity: O(N*2^N)
Auxiliary Space: O(N*2^N)
