Backtracking

Question 1

What is the pattern and when is it used?

Answer 1

Explores all possibilities, backtracks when invalid.

Use Case: Combinatorial problems, permutations. Example: [Generate Parentheses]. Action: Verbalize use case aloud.

Question 2

What are the key steps?

Answer 2

1. Choose option, recurse.
2. Explore valid paths.
3. Backtrack if invalid, undo choice.

Action: Explain steps for [Generate Parentheses] aloud.

Question 3

How does it apply to [Generate Parentheses]?

Answer 3

• Problem: Generate valid parentheses combinations.
• Approach: Recursively add open/close, backtrack if invalid.
• Action: Verbalize solution logic aloud.

Question 4

What are the complexity and gotchas?

Answer 4

Complexity: Time: O(4^n), Space: O(n).
Gotchas: Invalid combinations, stack overflow.

Action: List edge cases for [Generate Parentheses] aloud.

Question 5

Provide a code example.

Answer 5

```python
from typing import List

def generate_parenthesis(n: int) -> List[str]:
result: List[str] = []
def backtrack(current: str, open_count: int, close_count: int) -> None:
if len(current) == 2 * n:
result.append(current)
return
if open_count < n:
backtrack(current + ‘(‘, open_count + 1, close_count)
if close_count < open_count:
backtrack(current + ‘)’, open_count, close_count + 1)
backtrack(‘’, 0, 0)
return result
~~~

Question 6

Visual

Answer 6