動機

當你對遞迴有懷疑就上cache

Problem

You are given an integer array nums and an integer target.

You want to build an expression out of nums by adding one of the symbols '+' and '-' before each integer in nums and then concatenate all the integers.

  • For example, if nums = [2, 1], you can add a '+' before 2 and a '-' before 1 and concatenate them to build the expression +2-1.

Return the number of different expressions that you can build, which evaluates to target.

 

Example 1:

Input: nums = [1,1,1,1,1], target = 3Output: 5Explanation: There are 5 ways to assign symbols to make the sum of nums be target 3.-1 + 1 + 1 + 1 + 1 = 3+1 - 1 + 1 + 1 + 1 = 3+1 + 1 - 1 + 1 + 1 = 3+1 + 1 + 1 - 1 + 1 = 3+1 + 1 + 1 + 1 - 1 = 3

Example 2:

Input: nums = [1], target = 1Output: 1

 

Constraints:

  • 1 <= nums.length <= 20
  • 0 <= nums[i] <= 1000
  • 0 <= sum(nums[i]) <= 1000
  • -1000 <= target <= 1000

Sol

class Solution:
    def findTargetSumWays(self, nums: List[int], target: int) -> int:
        @cache
        def bt(i,acc):
            if i == len(nums):
                return 1 if acc == target else 0
            else:
                return sum([bt(i+1,acc+nums[i]), bt(i+1,acc-nums[i])])
        return bt(0,0)