题目

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

** 注意事项 **
The different sequences are counted as different combinations.

样例
Given nums = [1, 2, 4], target = 4

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return 6

分析

这个问题的思路是，4可以由nums里面的2,2组成，那么2又可以由nums里面的什么组成呢？就是分别把每个都作为target计算，结果存入dp[target]

代码

public int backPackVI(int[] nums, int target) {
        // Write your code here
        int[] dp = new int[target+1];
        dp[0] = 1;
        for (int i = 1; i <= target; i++) {
            for (int num: nums) {
                if (num <= i) dp[i] += dp[i-num];
            }
        }
        return dp[target];
    }