LeetCode377. Combination Sum IV

LeetCode377. Combination Sum IV

题目：

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?

题意分析：这道题并没有和前面的几道题一样，而是选择yoga动态规划去解决。

comb[target] = sum(comb[target - nums[i]]), where 0 <= i < nums.length, and target >= nums[i].

代码：

class Solution {  
public:  
    int combinationSum4(vector& nums, int target) {  
        if(nums.size()==0) return 0;  
        vector dp(target+1, 0);  
        dp[0] = 1;  
        for(int i =1; i <= target; i++)  
        {  
            for(auto val: nums)  
                if(val <= i) dp[i] += dp[i-val];  
        }  
        return dp[target];  
    }  
};