Introduction

In this blog post, we will explore how to solve the LeetCode problem "753" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

There is a safe protected by a password. The password is a sequence of n digits where each digit can be in the range [0, k - 1]. The safe has a peculiar way of checking the password. When you enter in a sequence, it checks the most recent n digits that were entered each time you type a digit. For example, the correct password is "345" and you enter in "012345": After typing 0, the most recent 3 digits is "0", which is incorrect. After typing 1, the most recent 3 digits is "01", which is incorrect. After typing 2, the most recent 3 digits is "012", which is incorrect. After typing 3, the most recent 3 digits is "123", which is incorrect. After typing 4, the most recent 3 digits is "234", which is incorrect. After typing 5, the most recent 3 digits is "345", which is correct and the safe unlocks. Return any string of minimum length that will unlock the safe at some point of entering it. Example 1: Input: n = 1, k = 2 Output: "10" Explanation: The password is a single digit, so enter each digit. "01" would also unlock the safe. Example 2: Input: n = 2, k = 2 Output: "01100" Explanation: For each possible password: - "00" is typed in starting from the 4th digit. - "01" is typed in starting from the 1st digit. - "10" is typed in starting from the 3rd digit. - "11" is typed in starting from the 2nd digit. Thus "01100" will unlock the safe. "10011", and "11001" would also unlock the safe. Constraints: 1 <= n <= 4 1 <= k <= 10 1 <= kn <= 4096

Explanation

Here's the breakdown of the solution:

• De Bruijn Sequence: The problem can be modeled as finding a De Bruijn sequence. A De Bruijn sequence of order n over an alphabet of size k is a cyclic sequence in which every possible length-n string occurs exactly once as a substring. Concatenating such a sequence (minus the overlap) gives us the shortest string that contains all possible passwords.
• Graph Traversal: We can represent the problem as traversing a graph. Each node in the graph represents a prefix of length n-1, and an edge represents appending a digit to that prefix. We aim to visit every edge exactly once (Eulerian path).

• Greedy Approach: We use a greedy approach to traverse the graph, prioritizing exploring new edges (digits) whenever possible to maximize the length of the sequence before needing to revisit previously used prefixes.

• Runtime Complexity: O(kⁿ), Storage Complexity: O(kⁿ)

Code

    def crackSafe(n: int, k: int) -> str:
    """
    Finds the shortest string that unlocks a safe with password of length n and digits in range [0, k-1].
    """

    seen = set()
    result = ""
    total = k ** n

    def dfs(node):
        nonlocal result
        for i in range(k):
            nextNode = node[1:] + str(i)
            if nextNode not in seen:
                seen.add(nextNode)
                dfs(nextNode)
                result += str(i)

    startNode = "0" * (n - 1)
    seen.add(startNode)
    dfs(startNode)

    return result + "0" * (n - 1)