Decoding Ancient Atlantean Scrolls - codepath/compsci_guides GitHub Wiki

TIP102 Unit 7 Session 1 Advanced (Click for link to problem statements)

Problem 6: Decoding Ancient Atlantean Scrolls

In the mystical city of Atlantis, ancient scrolls have been discovered that contain encoded messages. These messages follow a specific encoding rule: k[encoded_message], where the encoded_message inside the square brackets is repeated exactly k times. Your task is to decode these messages to reveal their original form using a recursive approach.

Problem Highlights

  • 💡 Difficulty: Medium
  • ⏰ Time to complete: 20-30 mins
  • 🛠️ Topics: Recursion, String Manipulation

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

  • Established a set (2-3) of test cases to verify their own solution later.
  • Established a set (1-2) of edge cases to verify their solution handles complexities.
  • Have fully understood the problem and have no clarifying questions.
  • Have you verified any Time/Space Constraints for this problem?
  • Q: What is the main task in this problem?
    • A: The task is to decode a string that follows the encoding rule k[encoded_message] where the message is repeated k times.
  • Q: How should the function handle nested encodings?
    • A: The function should correctly decode nested encodings by using a recursive approach.
HAPPY CASE
Input: "3[Coral2[Shell]]"
Output: "CoralShellShellCoralShellShellCoralShellShell"
Explanation: The string "CoralShellShell" is repeated 3 times.

Input: "2[Poseidon3[Sea]]"
Output: "PoseidonSeaSeaSeaPoseidonSeaSeaSea"
Explanation: The string "PoseidonSeaSeaSea" is repeated 2 times.

EDGE CASE
Input: "4[Fish]"
Output: "FishFishFishFish"
Explanation: The string "Fish" is repeated 4 times without any nested encoding.

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

For Decoding Encoded Strings, we want to consider the following approaches:

  • Recursive Decoding: Use recursion to decode the string by handling nested encodings and correctly multiplying the decoded substrings.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea:

  • Use recursion to decode the string. Start by scanning the string and whenever a number is encountered, use recursion to decode the substring within the brackets. Multiply the decoded substring by the number and continue decoding the rest of the string.

Recursive Approach:

1) Define a helper function `helper(index)` that decodes the string starting from the given index.
2) Initialize an empty string `decoded_string` to store the decoded message.
3) While scanning the string:
    a) If a digit is encountered, extract the full number.
    b) Skip the `[` and recursively decode the substring within the brackets.
    c) Multiply the decoded substring by the number and append it to `decoded_string`.
    d) If `]` is encountered, return the current `decoded_string` and the updated index.
4) Return the fully decoded string from the main function `decode_scroll_recursive`.

⚠️ Common Mistakes

  • Misinterpreting the nested structure of the encodings, leading to incorrect decoding.
  • Failing to correctly handle multiple digits in the repeat count.

4: I-mplement

Implement the code to solve the algorithm.

def decode_scroll_recursive(scroll):
    def helper(index):
        decoded_string = "
        while index < len(scroll):
            if scroll[index].isdigit():
                # Extract the full number (could be multiple digits)
                num = 0
                while index < len(scroll) and scroll[index].isdigit():
                    num = num * 10 + int(scroll[index])
                    index += 1
                # The next character should be '[', so move to the character after it
                index += 1
                # Recursively decode the substring within the brackets
                decoded_substring, index = helper(index)
                # Multiply the decoded substring by the number and add it to the result
                decoded_string += decoded_substring * num
            elif scroll[index] == ']':
                # Return the decoded string and the current index when encountering a closing bracket
                return decoded_string, index + 1
            else:
                # Regular character, just add to the result string
                decoded_string += scroll[index]
                index += 1
        return decoded_string, index
    
    # Start the recursive decoding from index 0
    final_decoded_string, _ = helper(0)
    return final_decoded_string

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

  • Trace through the decode_scroll_recursive function with the input "3[Coral2[Shell]]". The function should return "CoralShellShellCoralShellShellCoralShellShell" after correctly decoding the nested structure.
  • Test the function with edge cases like "4[Fish]". The function should return "FishFishFishFish".

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

Time Complexity:

  • Time Complexity: O(N), where N is the length of the string. The function processes each character exactly once.
  • Space Complexity: O(N), due to the recursion stack and the space needed to store the decoded string. The depth of recursion is proportional to the nesting level of the encoded messages.

Discussion:

  • This recursive approach effectively decodes the string by correctly handling nested structures and multiple repeat counts.
  • While the recursive approach is clear and intuitive for problems with nested structures, it could be optimized by using iterative methods or tail recursion if supported by the language.