MEDIUM Backtracking
77. Combinations
📖 Problem
Given two integers n and k, return all possible combinations of k numbers chosen from the range [1, n]. You may return the answer in any order.
🧠 Visual Learning Aid
1 Model the input into the right structure
2 Choose the core technique and invariant
3 Execute step-by-step with a sample
4 Validate complexity and edge cases
JS/TS Refreshers
- •Array methods (`push`, `pop`, `shift`, `slice`)
- •Object/Map/Set usage patterns
- •Function parameter and return typing
- •Recursive function frames
- •Push/pop state undo
- •Pruning branches early
Logical Thinking Concepts
- •Define invariants before coding
- •Check edge cases first (`[]`, single element, duplicates)
- •Estimate time/space before implementation
- •Apply Backtracking reasoning pattern
- •Apply Recursion reasoning pattern
💡 Approach
- → Use backtracking to generate all combinations
- → Start from each number and recursively build combinations
- → Avoid duplicates by only moving forward in array
- → When combination reaches size k, save it
- → Time: O(C(n,k)), Space: O(C(n,k)) for results
🧭 Prerequisites
🛠️ Hints & Pitfalls
Hints
- •Use backtracking to generate all combinations
- •Start from each number and recursively build combinations
- •Avoid duplicates by only moving forward in array
Common Pitfalls
- •When combination reaches size k, save it
- •Time: O(C(n,k)), Space: O(C(n,k)) for results
🧪 Test Cases
Test Case 1
Not run Input:
combine(4, 2); Expected:
[[1,2], [1,3], [1,4], [2,3], [2,4], [3,4]] Test Case 2
Not run Input:
combine(1, 1); Expected:
[[1]] Test Case 3
Not run Input:
combine(n: number, k: number); Expected:
Computed from hidden reference 📝 Code Editor
📤 Output