一、题目描述
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?
思路：动态规划，首先要想清楚下面的这个公式：
f(target) = f(target - nums[0]) + f(target - nums[1]) + ... + f(target - nums[n])
n=nums.size()
c++代码（4ms）
class Solution { public: int combinationSum4(vector<int>& nums, int target) { vector<int> dp(target+1, 0); //dp[i]表示target=i时有多少种组合 dp[0]=1; for(int i=1; i<=target; i++){ for(int num:nums){ if(i>=num){ dp[i] += dp[i-num]; }//if }//for }//for return dp[target]; } };