top-down from S works fine instead of bottom up from 0.

Other than that this is a typical DP solution.

```
def findTargetSumWays(self, nums, S):
self.dp = [defaultdict(int) for i in range(len(nums))]
return self.get_ways(nums, S, len(nums)-1)
def get_ways(self, nums, S, i):
if i == -1:
return 1 if S == 0 else 0
if S not in self.dp[i]:
self.dp[i][S] = self.get_ways(nums, S + nums[i], i - 1) + self.get_ways(nums, S - nums[i], i - 1)
return self.dp[i][S]
```

Thank you.