Is Combination Sum IV easy or hard?

Combination Sum IV is rated Medium difficulty. The challenge is recognizing that order matters, which turns the problem into counting permutations using dynamic programming rather than simple combination counting.

How to solve Combination Sum IV in O(n * target)?

Use a bottom-up dynamic programming table. Create a dp array where dp[i] stores the number of combinations that sum to i. Initialize dp[0] = 1 and for each i from 1 to target, iterate through nums and update dp[i] += dp[i - num] when num <= i. This ensures each state is computed once.

What is the best approach for Combination Sum IV?

Dynamic Programming with tabulation is the most common solution. Define dp[i] as the number of ordered combinations that produce sum i, initialize dp[0] = 1, and build results up to the target. For each value i, iterate through the numbers and add dp[i - num]. This runs in O(n * target) time with O(target) space.

What data structure is used in Combination Sum IV?

The core structure is a one-dimensional dynamic programming array that stores counts of ways to reach each sum. Some implementations also use recursion with a memoization map or array to cache intermediate results.

What is the time complexity of Combination Sum IV?

The optimal dynamic programming solution runs in O(n * target) time where n is the number of integers in the array. Each target value from 1 to target iterates through the entire array. Space complexity is O(target) for the DP array.

Combination Sum IV Python or Java solution approach?

Both Python and Java implementations typically use the same DP logic. Define an array dp of size target + 1, set dp[0] = 1, then iterate from 1 to target and update dp[i] using values from dp[i - num]. The algorithm remains O(n * target) regardless of language.

Is Combination Sum IV asked at Google, Amazon, or Meta?

Combination Sum style problems appear frequently in interviews at companies like Amazon, Google, and Meta because they test dynamic programming and recurrence thinking. Variations may ask for combinations, permutations, or constraints on reuse of elements.

Description Solution Video 11:39

377. Combination Sum IV

Q: What is the best approach for Combination Sum IV?

Dynamic Programming with tabulation is the most common solution. Define dp[i] as the number of ordered combinations that produce sum i, initialize dp[0] = 1, and build results up to the target. For each value i, iterate through the numbers and add dp[i - num]. This runs in O(n * target) time with O(target) space.

Q: What data structure is used in Combination Sum IV?

The core structure is a one-dimensional dynamic programming array that stores counts of ways to reach each sum. Some implementations also use recursion with a memoization map or array to cache intermediate results.

Q: What is the time complexity of Combination Sum IV?

The optimal dynamic programming solution runs in O(n * target) time where n is the number of integers in the array. Each target value from 1 to target iterates through the entire array. Space complexity is O(target) for the DP array.

Q: Combination Sum IV Python or Java solution approach?

Both Python and Java implementations typically use the same DP logic. Define an array dp of size target + 1, set dp[0] = 1, then iterate from 1 to target and update dp[i] using values from dp[i - num]. The algorithm remains O(n * target) regardless of language.

Q: Is Combination Sum IV asked at Google, Amazon, or Meta?

Combination Sum style problems appear frequently in interviews at companies like Amazon, Google, and Meta because they test dynamic programming and recurrence thinking. Variations may ask for combinations, permutations, or constraints on reuse of elements.

Medium55.0% acceptance7 companies

Given an array of distinct integers nums and a target integer target, return the number of possible combinations that add up to target.

The test cases are generated so that the answer can fit in a 32-bit integer.

Example 1:

Input: nums = [1,2,3], target = 4
Output: 7
Explanation:
The possible combination ways are:
(1, 1, 1, 1)
(1, 1, 2)
(1, 2, 1)
(1, 3)
(2, 1, 1)
(2, 2)
(3, 1)
Note that different sequences are counted as different combinations.

Example 2:

Input: nums = [9], target = 3
Output: 0

Constraints:

1 <= nums.length <= 200
1 <= nums[i] <= 1000
All the elements of nums are unique.
1 <= target <= 1000

Follow up: What if negative numbers are allowed in the given array? How does it change the problem? What limitation we need to add to the question to allow negative numbers?