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.
给出一个全为正整数且无重复数字的数组，找出加起来是一个正整数目标值的方法个数
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.
这道题可以用dfs+记忆化解决，但是我这里用dp来解决。思路为：既然target是数组中数字的组合，target - nums[i]和target有一定的关系。假设dp[i]为数组的元素加起来为i的方法个数，递推关系式为：dp[target] = sum(dp[target - nums[i]])，即把加上每个nums的元素到达target的方法数（dp[target - nums[i]]）相加的总和就是数组元素加起来为target的方法总数
class Solution(object): def combinationSum4(self, nums, target): """ :type nums: List[int] :type target: int :rtype: int """ dp = [1] + [0] * target for index in range(target + 1): # 把每个target - nums[i]的方法数相加 for n in nums: # nums的当前元素要小于target，否则抛弃该元素 if n <= index: dp[index] += dp[index - n] return dp[target]新闻热点
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