is the time complexity 3^N and space complexity 3^N???

Assuming you used dfs, the time complexity is 3^(N1) (N1 because there is no branching for the first element) where N is the length of the string because for every instance of recursion you have 3 branches, (+,,*). for example, with "123". at 1 you will produce 3 branches 1+2,12,1*2 and for each of these branches you will get 3 more branches and so on.