Combination Sum, Word Search & Generate Parentheses

Subsets & Combinations Generation

Generates all valid combinations by branching on `Include` vs `Exclude` decisions at each recursive step.

Production Code Example:

import java.util.*;
public class GenerateParenthesesDemo {
    public List<String> generateParentheses(int n) {
        List<String> res = new ArrayList<>();
        backtrack(res, "", 0, 0, n);
        return res;
    }
    private void backtrack(List<String> res, String curr, int open, int close, int max) {
        if (curr.length() == max * 2) { res.add(curr); return; }
        if (open < max) backtrack(res, curr + "(", open + 1, close, max);
        if (close < open) backtrack(res, curr + ")", open, close + 1, max);
    }
}

Key Complexity & Algorithmic Takeaways:

When implementing Combination Sum, Word Search & Generate Parentheses in coding interviews and production applications, keep these core guidelines in mind:

• Time Complexity Analysis: Always evaluate best-case, average-case, and worst-case time complexities ($O(1)$, $O(\log n)$, $O(n)$, $O(n \log n)$, $O(n^2)$).
• Space Complexity & Memory Bounds: Account for auxiliary memory usage, call stack frame recursion overhead, and heap allocations.
• Edge Cases & Validation: Test empty inputs, null pointers, single-element collections, duplicate values, and integer overflow bounds.
• Optimal vs Naive Solutions: Start with a clear brute-force solution, then optimize using techniques like Hashing, Two Pointers, Windowing, or Dynamic Programming.

Summary Takeaway:

Mastering Combination Sum, Word Search & Generate Parentheses provides the foundational problem-solving skills needed to pass technical coding interviews at top tech companies and write ultra-performant software systems.