Given an array of distinct integers nums and a target integer target, return the number of possible combinations that add up to target.
The answer is guaranteed to 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?
dynamic programming
this is actually not a direct copy of knapsack problem. it enables duplicates.
i learned from this youtube video https://www.youtube.com/watch?v=niZlmOtG4jM
- the result of dynamic programming can be a super-set, not constrainted to a sequence;
- recursive form of DP is easier to think about. after a good thinking is finished, come back to iterative form.