LeetCode377. Combination Sum IV

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本文探讨了LeetCode377题“组合总和IV”的解题思路及实现过程，采用动态规划的方法求解给定数组中所有可能的组合方式，使这些组合的元素之和等于目标值。

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<int>& nums, int target) {  
        if(nums.size()==0) return 0;  
        vector<int> 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];  
    }  
};