How do you solve Combination Sum on LeetCode?

Combination Sum (LeetCode #39) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n^target/min(candidates)) time complexity and O(target/min(candidates)) space complexity. Key insight: Backtracking allows us to explore all combinations while pruning paths that exceed the target.

What is the brute force solution for Combination Sum?

The brute force approach for Combination Sum is Brute Force, with O(n^target/min(candidates)) time complexity and O(target/min(candidates)) space complexity. The brute-force approach involves generating all possible combinations of the candidates and checking which ones sum up to the target. This method is straightforward but inefficient as it can lead to a large number of combinations. The optimal Optimal Solution approach improves this to O(n^target/min(candidates)).

What algorithm or data structure is used to solve Combination Sum?

Combination Sum uses the following concepts: Array, Backtracking. The recommended patterns to study are: Backtracking, Recursion.

What are the interview tips for Combination Sum?

Clearly explain your thought process and the steps you plan to take. Be mindful of edge cases, such as when the target is less than the smallest candidate. Practice writing clean and efficient recursive functions, as they are common in backtracking problems.

What are common mistakes when solving Combination Sum?

Not considering the case where the total exceeds the target and continuing the search. Failing to backtrack properly, which can lead to incorrect combinations.

#39

Combination Sum

Medium

ArrayBacktrackingBacktrackingRecursion

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n^target/min(candidates))	O(n^target/min(candidates))
Space	O(target/min(candidates))	O(target/min(candidates))

💡

Intuition

Time O(n^target/min(candidates))Space O(target/min(candidates))

The optimal solution uses backtracking efficiently by avoiding unnecessary paths. It builds combinations incrementally and only continues if the current total does not exceed the target.

⚙️

Algorithm

3 steps

1Step 1: Initialize a result list and a backtracking function.
2Step 2: In the backtracking function, if the current total equals the target, add the current path to the result.
3Step 3: Loop through the candidates, and for each candidate, if adding it to the total does not exceed the target, recursively call the backtracking function.

solution.py11 lines

1def combinationSum(candidates, target):
2    def backtrack(start, path, total):
3        if total == target:
4            result.append(path)
5            return
6        for i in range(start, len(candidates)):
7            if total + candidates[i] <= target:
8                backtrack(i, path + [candidates[i]], total + candidates[i])
9    result = []
10    backtrack(0, [], 0)
11    return result

ℹ

Complexity note: The optimal solution has the same time complexity as the brute force but is more efficient in practice due to pruning unnecessary paths. The space complexity remains the same due to the depth of recursion.

1Backtracking allows us to explore all combinations while pruning paths that exceed the target.
2Using recursion helps manage the state of combinations easily.

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