Description
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'+'
before2
and a'-'
before1
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 = 3 Output: 5 Explanation: 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 = 1 Output: 1
Constraints:
1 <= nums.length <= 20
0 <= nums[i] <= 1000
0 <= sum(nums[i]) <= 1000
-1000 <= target <= 1000
Solution
Python3
class Solution:
def findTargetSumWays(self, nums: List[int], target: int) -> int:
N = len(nums)
@cache
def go(index, curr):
if index == N:
return 1 if curr == target else 0
neg = go(index + 1, curr - nums[index])
pos = go(index + 1, curr + nums[index])
return neg + pos
return go(0, 0)