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 <= 2001 <= nums[i] <= 1000nums 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?
class Solution {
public:
vector<int> dp;
Solution() {
dp.resize(1001);
fill(dp.begin(), dp.end(), -1);
}
int combinationSum4(vector<int>& nums, int target, int sum=0) {
if(sum>target) return 0; // overshoot
else if (sum==target) return 1; // counter++
else if (dp[sum]!=-1) return dp[sum]; // if memoised already
int res=0;
for (auto n: nums){
if(sum+n<=target)
res+=combinationSum4(nums, target, sum+n);
}
return dp[sum] = res;
}
};