How do you solve Combination Sum III on LeetCode?

Combination Sum III (LeetCode #216) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Backtracking allows us to explore combinations efficiently by pruning invalid paths early.

What is the brute force solution for Combination Sum III?

The brute force approach for Combination Sum III is Brute Force, with O(n²) time complexity and O(1) space complexity. We can generate all combinations of numbers from 1 to 9 and check if they meet the conditions. This method is straightforward but inefficient as it explores all possible combinations. The optimal Optimal Solution approach improves this to O(n).

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

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

What are the interview tips for Combination Sum III?

Explain your thought process clearly while coding, especially your choice of data structures. Be prepared to discuss edge cases, such as when k is larger than the maximum possible sum. Practice writing clean, efficient code, as readability is important in interviews.

What are common mistakes when solving Combination Sum III?

Failing to check if the sum exceeds n early in the backtracking process. Not handling the case where k numbers cannot possibly sum to n due to their minimum sum.

#216

Combination Sum III

Medium

ArrayBacktrackingBacktrackingCombination Generation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

We can use backtracking to build combinations incrementally. This approach is more efficient as it avoids unnecessary checks by pruning paths that exceed the target sum.

⚙️

Algorithm

3 steps

1Step 1: Create a backtracking function that takes the current combination, current sum, and the next number to consider.
2Step 2: If the combination length equals k and the sum equals n, add it to the result.
3Step 3: Iterate through the numbers from the current number to 9, adding each to the combination and recursing.

solution.py15 lines

1def combinationSum3(k, n):
2    def backtrack(start, path, target):
3        if len(path) == k and target == 0:
4            result.append(path[:])
5            return
6        for i in range(start, 10):
7            if i > target:
8                break
9            path.append(i)
10            backtrack(i + 1, path, target - i)
11            path.pop()
12
13    result = []
14    backtrack(1, [], n)
15    return result

ℹ

Complexity note: The time complexity is O(n) because we effectively explore combinations without generating all possible subsets, pruning paths that exceed the target.

1Backtracking allows us to explore combinations efficiently by pruning invalid paths early.
2Using a range of 1 to 9 ensures we don't have duplicates and simplifies our checks.

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