How do you solve Combinations on LeetCode?

Combinations (LeetCode #77) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n choose k) time complexity and O(k) space complexity. Key insight: Understanding backtracking is crucial for solving combination problems efficiently.

What is the brute force solution for Combinations?

The brute force approach for Combinations is Brute Force, with O(n choose k) time complexity and O(k) space complexity. The brute force approach generates all possible combinations of numbers from 1 to n and then filters out the combinations that have exactly k elements. This is straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n choose k).

What algorithm or data structure is used to solve Combinations?

Combinations uses the following concepts: Backtracking. The recommended patterns to study are: Backtracking, Recursion.

What are the interview tips for Combinations?

Explain your thought process clearly while coding. Consider edge cases, such as when k equals n. Practice writing recursive functions, as they are common in backtracking problems.

What are common mistakes when solving Combinations?

Forgetting to backtrack properly, which can lead to incorrect combinations. Not handling the base case correctly in recursive functions.

#77

Combinations

Medium

BacktrackingBacktrackingRecursion

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n choose k)	O(n choose k)
Space	O(k)	O(k)

💡

Intuition

Time O(n choose k)Space O(k)

The optimal solution uses backtracking to build combinations incrementally. This avoids generating all combinations upfront and only constructs valid combinations, making it more efficient.

⚙️

Algorithm

4 steps

1Step 1: Initialize a result list to store combinations.
2Step 2: Use a recursive function to build combinations by adding numbers from the current start index.
3Step 3: If the current combination reaches size k, add it to the result.
4Step 4: Backtrack by removing the last added number and continue exploring.

solution.py15 lines

1# Full working Python code
2from typing import List
3
4def combine(n: int, k: int) -> List[List[int]]:
5    result = []
6    def backtrack(start, path):
7        if len(path) == k:
8            result.append(path[:])
9            return
10        for i in range(start, n + 1):
11            path.append(i)
12            backtrack(i + 1, path)
13            path.pop()
14    backtrack(1, [])
15    return result

ℹ

Complexity note: The time complexity remains O(n choose k) since we still explore combinations, but we do it more efficiently. The space complexity is O(k) for storing the current combination.

1Understanding backtracking is crucial for solving combination problems efficiently.
2Recognizing that combinations are unordered helps in avoiding duplicates.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.