Backpack VI

题目描述：
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

The possible combination ways are:
[1, 1, 1, 1]
[1, 1, 2]
[1, 2, 1]
[2, 1, 1]
[2, 2]
[4]
return 6
题目分析：
典型的动态规划问题，状态转移方程：

dp[x+y]+=dp[x]

我们需要一个一维数组dp，其中dp[i]表示目标数为i的解的个数，然后我们从1遍历到target，对于每一个数i，遍历nums数组，如果

i>=x, dp[i] += dp[i - x]

Python代码

class Solution:
    # @param {int[]} nums an integer array and all positive numbers, no duplicates
    # @param {int} target an integer
    # @return {int} an integer
    def backPackVI(self, nums, target):
        # Write your code here
        dp=[0]*(target +1)
        dp[0]=1
        for x in range(target +1):
            for y in nums:
                if x+y<=target:
                    dp[x+y]+=dp[x]
        return dp[target]