377. Combination Sum IV ---------M

 Given an integer array with all positive numbers and no duplicates, find the number of possible combinations that add up to a positive integer target.

Example:

nums = [1, 2, 3]
target = 4

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.

Therefore the output is 7.

 

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?

A:

仔细读题啊， 一开始理解错了。

  ***************           DP  with memorization      ************

class Solution {
public:
    int combinationSum4(vector<int>& nums, int target) {
        sort(nums.begin(), nums.end());
        unordered_map<int, int> map;
        return helper(nums, target, map);
    }
private:
    int helper(vector<int> & nums,  int target, unordered_map<int,int> & map){
        if( target<0){
            return 0;
        }
        if(target == 0 ){
            return 1;
        }
        auto iter = map.find(target);
        if(iter != map.end())
            return iter->second;
        
        int res = 0;
        for(int i = 0;i<nums.size(); i++){
            res += helper(nums, target - nums[i], map);
        }
        map[target] = res;
        return res;
    }
};