Encode and Decode Strings

Let's explore how to encode a list of strings into a single string and then decode it back to the original list. This is a common problem when you need to transmit a list of strings over a network where you can only send a single string.

Naive Solution

A simple approach is to concatenate all the strings together. However, this presents a problem: how do we know where one string ends and the next one begins? If the strings contain special characters, these could be used as delimiters.

Algorithm

1. Encoding: Join all strings in the list into one large string.
2. Decoding: Without delimiters, this approach is fundamentally flawed. We'd need some external knowledge of string lengths.

Code (Illustrative - Doesn't fully work without delimiters)

class Codec:
    def encode(self, strs):
        return "".join(strs)

    def decode(self, s):
        # This naive decode wouldn't work without string lengths
        return [s]

Time and Space Complexity

• Time: Encode is O(n), where n is the total number of characters across all strings. Decode is O(1) if we simply return the whole string as one list element, but in reality, without knowing string lengths, we cannot implement the naive decode effectively.
• Space: Encode is O(1), excluding the space for the output string itself, which would be O(n). Decode is O(1).

Drawbacks

The naive approach doesn't provide a practical decoding mechanism without delimiters or string length information. It's mainly useful as a starting point to understand the core problem.

Optimal Solution: Length-Based Encoding

A much better approach is to prefix each string with its length followed by a delimiter (e.g., #). This provides a clear way to know where each string begins and ends during decoding.

Algorithm

1. Encoding: For each string in the list, prepend its length and a delimiter to the string, then concatenate.
2. Decoding: Read the length of the next string from the encoded string, then extract that many characters. Repeat until the encoded string is empty.

Code (Python)

class Codec:
    def encode(self, strs):
        encoded_string = ""
        for s in strs:
            encoded_string += str(len(s)) + "#" + s
        return encoded_string

    def decode(self, s):
        result = []
        i = 0
        while i < len(s):
            j = i
            while s[j] != '#':
                j += 1
            length = int(s[i:j])
            i = j + 1
            result.append(s[i:i + length])
            i += length
        return result

Example

Let's say strs = ["lint", "code", "love", "you"].

Encoding:

• "lint" becomes "4#lint"
• "code" becomes "4#code"
• "love" becomes "4#love"
• "you" becomes "3#you"

Encoded string: "4#lint4#code4#love3#you"

Decoding:

1. Read "4#", which indicates the next string has length 4.
2. Read the next 4 characters: "lint".
3. Read "4#", which indicates the next string has length 4.
4. Read the next 4 characters: "code".
5. And so on...

Time and Space Complexity

• Time: Encode is O(n), where n is the total number of characters across all strings. Decode is also O(n) since we iterate through the entire encoded string once.
• Space: Encode is O(1), excluding the space for the output string itself, which would be O(n). Decode is O(1), excluding the space to store the list of decoded strings which will be O(n).

Edge Cases

• Empty string in the list: The algorithm handles empty strings correctly because the length will be 0.
• Empty list: The encode function will return an empty string, and the decode function will return an empty list, both of which are valid.
• Very long strings: The conversion of string length to integer can potentially cause an integer overflow issue if the string length is extremely large. This could be addressed by using a larger data type or by splitting very long strings into smaller chunks.
• Delimiter in the strings: If the delimiter character # can appear in the input strings, we'd need to use an escape character, or choose a delimiter character that is disallowed in the input. Another approach is to replace all occurrances of # with a substitute sequence during encoding, and revert during decoding.

This length-based encoding provides a robust and efficient way to serialize and deserialize a list of strings into a single string.