377. Combination Sum IV -Medium

Question

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

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.

Solution

• 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]