Solution Explanation: Strobogrammatic Number II

This problem asks to generate all possible strobogrammatic numbers of a given length n. A strobogrammatic number remains the same when rotated 180 degrees. The solution uses a recursive approach for efficient generation.

Approach:

The core idea is to build strobogrammatic numbers recursively. We start with the base cases:

• n = 0: An empty string "" is the only strobogrammatic number.
• n = 1: "0", "1", and "8" are the only strobogrammatic numbers of length 1.

For n > 1, we recursively generate strobogrammatic numbers of length n-2. Then, for each of these numbers, we append pairs of digits that remain the same when rotated 180 degrees. These pairs are:

• "11"
• "69"
• "88"
• "96"

If n is not equal to the input length, we can also add "00" to the beginning and end. This is because leading zeros are allowed in the recursive calls but not in the final result (they would be filtered out).

Time Complexity Analysis:

The time complexity is exponential, approximately O(5n/2). This is because at each step in the recursion, we branch into up to 5 possibilities (the pairs listed above). In each level of the recursion, the number of digits is roughly halved.

Space Complexity Analysis:

The space complexity is also exponential, O(5n/2), mainly due to storing the generated strobogrammatic numbers in the recursive calls.

Code Explanation (Python):

class Solution:
    def findStrobogrammatic(self, n: int) -> List[str]:
        def dfs(u):
            if u == 0:
                return ['']
            if u == 1:
                return ['0', '1', '8']
            ans = []
            for v in dfs(u - 2):
                for l, r in ('11', '88', '69', '96'):
                    ans.append(l + v + r)
                if u != n:  #Avoid leading zeros in final result
                    ans.append('0' + v + '0')
            return ans
 
        return dfs(n)

The dfs(u) function performs the recursive generation. The base cases (u=0, u=1) are handled first. The core logic involves iterating through strobogrammatic numbers of length u-2 and appending the valid pairs. The condition if u != n ensures leading zeros are avoided in the final result.

Code in Other Languages:

The provided code snippets in Java, C++, and Go follow a very similar structure to the Python example. They all recursively generate the strobogrammatic numbers using the same core logic and handle the base cases and digit pairing in the same manner. The key differences are mostly syntactic variations between the languages. The algorithmic approach remains identical across all the implementations.