
An active Player in the game of technology


Brian Baliach


I’m continuing the weekly challenge series, and this time we’re tackling a foundational favorite: Generate Parentheses. The goal is to produce all well-formed strings of parentheses for a given n pairs of parenthesis, and it’s a perfect showcase for two core ideas in algorithm design: backtracking and recursion. I’ll walk through the problem, explain why these techniques fit, and then break down the TypeScript implementation line by line.

---

## Problem Overview

Here’s the problem statement:

```plaintext
You are given an integer n. Return all well-formed parentheses strings that you can generate with n pairs of parentheses.
```

You can also find a detailed problem statement here:
https://neetcode.io/problems/generate-parentheses?list=neetcode150

Also, here's my public GitHub repo that has all these coding solutions implemented:
https://github.com/TylerMutai/coding-challenges-solutions/tree/main/ts-coding-challenges-solutions

The task is to enumerate every valid combination, ensuring each string is balanced (every opening parenthesis has a matching closing one, and order is correct).

---

## 1. Understanding Backtracking and Recursion

Before diving into code, let’s clarify the two techniques driving the solution.

Backtracking is a systematic way to explore all possible configurations by making a sequence of choices, recursing deeper when a choice looks promising, and undoing it (“backtracking”) when it doesn’t. It shines when we need to generate combinations under constraints, which is exactly our situation.

Recursion is a function calling itself with smaller subproblems. Here, it naturally models "build the string one character at a time", carrying the current state along (how many open/closed parenthesis we’ve used) until we reach a complete, valid result. Together, recursion provides the structure of exploration, and backtracking provides the discipline to try, revert, and try again.

---

## 2. TypeScript Solution

Let’s look at the core implementation:

```typescript
/**
 * You are given an integer n.
 * Return all well-formed parentheses strings that you can generate with n pairs of parentheses.
 */

const generateParenthesis = (n: number) => {

  const result: string[] = [];
  const stack: string[] = [];

  const backtrack = (openN: number, closeN: number) => {
    if (openN === closeN && openN === n && closeN === n) {
      result.push(stack.join(""));
    }

    if (openN < n) {
      stack.push("(");
      backtrack(openN + 1, closeN);
      stack.pop();
    }

    if (closeN < openN) {
      stack.push(")");
      backtrack(openN, closeN + 1);
      stack.pop();
    }
  };

  backtrack(0, 0);
  return result;
};

console.log(generateParenthesis(3));
```

---

## 3. Step-By-Step Explanation

Let’s unpack the key decisions and constraints inside the algorithm.

---

### a) State and Constraints

We track two counters:
- openN: how many "(" we’ve used so far.
- closeN: how many ")" we’ve used so far.

The constraints that keep the string valid:
- We can’t use more than n opening parentheses:
  ```typescript
  if (openN < n) { ... }
  ```
- We can only close if we have an unmatched "(" available, which basically means we can't use a closing parenthesis if the currently open parenthesis are less than the closing parenthesis:
  ```typescript
  if (closeN < openN) { ... }
  ```

These checks prevent invalid prefixes from ever forming.

---

### b) The Backtracking Function

```typescript
const backtrack = (openN: number, closeN: number) => { ... }
```

This function builds strings incrementally using a stack (array of characters) as our current path. At each call:
- If we’ve placed n open parentheses and n closed parentheses, we have a complete, valid string and add it to our results array:
  ```typescript
  if (openN === closeN && openN === n && closeN === n) {
    result.push(stack.join(""));
  }
  ```
- Otherwise, we branch by choosing a "(" if allowed, or a ")" if it keeps the string valid. After exploring a branch, we pop to revert the choice and try the next option: __this is the essence of backtracking.__

---

### c) Choosing "("

```typescript
if (openN < n) {
  stack.push("(");
  backtrack(openN + 1, closeN);
  stack.pop();
}
```

We can always add another "(" as long as we haven’t used n of them. Push, explore deeper, then undo.

---

### d) Choosing ")"

```typescript
if (closeN < openN) {
  stack.push(")");
  backtrack(openN, closeN + 1);
  stack.pop();
}
```

We only add ")" if there are more opens than closed so far. This preserves balance at every prefix.

---

### e) Building Results

The recursion starts at:
```typescript
backtrack(0, 0);
```

The result array accumulates every well-formed string. Because we never create invalid prefixes, we don’t need to filter later. Every terminal path is valid by construction.

---

## 4. Example

Given this input:

```typescript
generateParenthesis(3);
```

A valid output is:

```
[
  "((()))",
  "(()())",
  "(())()",
  "()(())",
  "()()()"
]
```

All strings are balanced, and every unique combination is present.

---

## Conclusion

By combining recursion’s natural tree structure with backtracking’s disciplined choice-and-revert strategy, we can generate all well-formed parentheses efficiently. The constraints (limit opens to n, never let closed exceed opens) ensure correctness without post-processing. It’s a clean and scalable pattern you’ll reuse across many combinatorial problems.

If you have questions or ideas for variations (like adding brackets or braces), drop a comment below.
See you in next week’s challenge!


A step-by-step walkthrough of the Generate Parentheses problem using backtracking and recursion in TypeScript.

Weekly Coding Challenge #2: Generating Parentheses with Backtracking and Recursion

If you’ve been following me, you might recall a harrowing tale of a developer coming to grips with recursion. The aptly titled 'Decoding Recursion: The Concept That Had Me Stumped'. But your cogitation and feedback suggest we dig a tad deeper. Brave ones have emerged requesting a practical walkthrough of recursion. In this sequel, we'll take a hands-on approach to recursion using the call stack/heap.

Let's hoist the mainsail and dive in.

### Under the Hood: What Happens When Functions Run?

So, matcha latte in hand, (or is it an afternoon beer?), let’s unravel what’s going on 'under the hood' when functions are involved. Every function in its operation has an allocated memory space. Avoiding the technical jargon for the sake of our shared sanity, let's visualize this as tiny compartments in your computer's brain.

When a function runs, it's like the computer opens that compartment and dumps everything the function needs inside – the variables, calculations, and that little reminder of your lunch break at 12 pm.

This "compartment" goes by a couple of names in the programming world: Stack and Heap. While they are both for storage, they differ slightly in usage. The stack is used for static memory allocation and the heap for dynamic memory allocation.

### Enter Recursion: A Practical Look

Since we're all here for recursion, let's take a prime example - factorial computation. A factorial is the product of a number (n) and all the integers below it. Remember 5! (factorial) equaling 5x4x3x2x1? Yes, that one.

In code form, a basic recursive function for a factorial would look something like (javascript this time, cause turns out, it has a much larger audience):

```javascript
function factorial(n) {
  if (n === 1) {
    return 1;
  } else {
    return n * factorial(n - 1);
  }
}
```

Now, let's visualize this on the call stack.

Every recursive call will add a layer to the stack. It's like a pile of dishes. The first call (n=5) is the first plate. Then n=4, then 3, 2, and finally 1. After that, the result bubbles up, washing the dirty dishes one by one from the top until you reach the clean plate at the bottom, i.e., the final answer.
Remember that in heaps/stacks, data is added in a first come last serve basis.
Here's a visualization:

| Heap         | Result | Code explanation                                                                        |
|--------------|--------|-----------------------------------------------------------------------------------------|
| n==1         | 1      | base case: (n==1) return 1;                                                             |
| n==2         | 1 * 2  | n is 1 (n * factorial(n-1) which comes from previous call above. result then becomes 2. |
| n==3         | 2 * 3  | n is 2, which again comes from previous call above. the result becomes 6.               |
| n==4         | 6 * 4  | n is 6, which again comes from the call above. the result becomes 24.                   |
| n==5         | 24 * 5 | n is 24, the result becomes 120.                                                        |
| final result | 120    | This is what is finally returned. 120.                                                  |


### Stack Overflow: Recursion's Gotcha!

Stack overflow – it isn't just a popular website, folks; it's recursion's Achilles heel. This happens when our recursion burrows too deep, causing the application to run out of memory space. This is because every OS assigns a running program a fixed memory allocation (i.e. 4MB worth of space). If you exhaust this space, you then might get a stack overflow /segmentation fault error. There goes the stack of dirty dishes tumbling down!

This potential drawback highlights how deep understanding of recursion can help developers optimize for performance.

### Wrapping It Up

There you have it - a code soup stirred with the call stack/heap and topped off with a sprinkle of recursion. Hopefully, this has helped demystify the concept a bit. But who knows? Perhaps our odyssey is just starting - linked lists, binary trees, sorting algorithms - all served with that recursion spice, are waiting!

Remember, fellow devs, recursion is a powerful tool and understanding how it works at every level aids in writing better, cleaner, more intuitive and more efficient code... even if it stumps us occasionally!

As always, sail through your coding voyage, one recursion at a time.



Unraveling Recursion: A Practical Look at the Call Stack and Heap

Microservices might be the heroes of scalable and reliable applications today, but let's shift gears and talk about a concept in the software development landscape that is as mind-bending as it is powerful: recursion.

As someone who enjoys the adrenaline rush of conquering coding challenges, I've come across various concepts that are the bread and butter of computer science. Some felt like meeting an old friend on the first day of school—familiar and comforting. Others were like that one high school math problem that kept me up at night. Enter recursion.

Recursion, to put it simply, is like a mythic serpent that swallows its own tail—a function that munches on itself to get to a result. My initial thought was, "Why suffer through this mind-boggling feat when a good ol’ loop could suffice?" But then, as I chewed over recursion, the mist started to fade.

### Imagine This...
Let's play with recursion's call stack visualization. Suppose a group of kids are playing with a neat stack of blocks. Each block has a unique number. The rule is: a player can only place a block on the stack if it decreases the previous number by one. The game starts with 10 and ends with 1—a stack of decrescendoing integers.

So, what does this have to do with recursion? Each block placement is akin to a function call in recursion. You place one block (function call), then another (another call), and another, till you reach the edge case — in our scenario, the number 1 block. That's when the players start to cheer and pass the stacks backwards, unwinding them while they execute some extra celebration (in our case, processing returns).

### Dividing to Conquer
Remember those divide-and-conquer strategies in ancient warfare history? They work magic in recursion too. A problem must be conquerable by breaking it down into smaller, more manageable versions of itself.  Simply take down towers one by one until the main castle surrenders.

### A Quick Dive Into Code
Let's demonstrate recursion with a problem that even I, a seasoned loop-lover, found elegant in its recursive cloak — a classic problem: calculating the factorial of a number.

The factorial of a number n (denoted as n!) is the product of all positive integers up to n. For instance, the factorial of 4 is 4! which equals 4 * 3 * 2 * 1 = 24.

A looping method would have us running circles. Here's a python example (python because, from my perspective, is closest to English):

```python
def factorial_loop(n):
    result = 1
    for i in range(2, n + 1):
        result *= i
    return result
```

But let's sprinkle the magic dust of recursion:

```python
def factorial_recursive(n):
    if n == 1:
        return 1
    else:
        return n * factorial_recursive(n - 1)
```

This second snippet embraces the soul of recursion. We define an edge case — our base condition that stops the infinite tumble down the rabbit hole (n == 1). The function then keeps calling itself, shrinking the problem down each time (n - 1), till it hits that edge case. And then the unwinding begins, with each call resolving and returning its piece of the puzzle, eventually giving us our answer.

### Why Bother With Recursion?
Sure, recursion might seem like overkill for simple problems that a loop can fix. But consider the elegance of solutions it provides for more complex issues like tree traversals, algorithmic problem solving such as the Towers of Hanoi, or graph searches. Sometimes, recursion is not just a solution; it's the most intuitive one.

### Closing Thoughts
Once I got past the intimidating facade of recursion, I found a beautiful and streamlined way of solving certain kinds of problems. Just like my transition from being a REST advocate to appreciating the swiftness of gRPC, embracing recursion has opened up new pathways in my coding journey.

If you're still feeling the heebie-jeebies about recursion, you're not alone. Take it from someone who was once stumped by the concept: the enigma of recursion is worthy of exploration. With each recursive function we write, we're training our minds to see not just the stack of problems but the stack of solutions waiting beneath. Happy recursing!


Decoding Recursion: The Concept That Had Me Stumped

Showing posts from recursion tag

Weekly Coding Challenge #2: Generating Parentheses with Backtracking and Recursion

Unraveling Recursion: A Practical Look at the Call Stack and Heap

Decoding Recursion: The Concept That Had Me Stumped