How do you solve Cracking the Safe on LeetCode?

Cracking the Safe (LeetCode #753) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(k^n) time complexity and O(k^n) space complexity. Key insight: Understanding Eulerian paths can help solve problems involving combinations and sequences efficiently.

What is the brute force solution for Cracking the Safe?

The brute force approach for Cracking the Safe is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible sequences of length n using digits from 0 to k-1. We then check if any of these sequences can be formed by the last n digits of the entered sequence. The optimal Optimal Solution approach improves this to O(k^n).

What algorithm or data structure is used to solve Cracking the Safe?

Cracking the Safe uses the following concepts: String, Depth-First Search, Graph Theory, Eulerian Circuit. The recommended patterns to study are: Graph Traversal, Backtracking.

What are the interview tips for Cracking the Safe?

Always clarify the problem requirements and constraints before jumping into coding. Think about different approaches and their trade-offs; don't hesitate to discuss them with your interviewer. Practice explaining your thought process clearly, as communication is key during technical interviews.

What are common mistakes when solving Cracking the Safe?

Failing to recognize the need for a graph traversal approach, leading to inefficient solutions. Not considering edge cases, such as when n or k is 1.

#753

Cracking the Safe

Hard

StringDepth-First SearchGraph TheoryEulerian CircuitGraph TraversalBacktracking

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(k^n)
Space	O(1)	O(k^n)

💡

Intuition

Time O(k^n)Space O(k^n)

The optimal solution leverages the concept of Eulerian paths in graph theory. We can construct a De Bruijn sequence, which contains every possible combination of n digits exactly once, ensuring the safe unlocks efficiently.

⚙️

Algorithm

3 steps

1Step 1: Use Depth-First Search (DFS) to explore all combinations of n digits.
2Step 2: Keep track of visited edges to ensure each combination is used exactly once.
3Step 3: Construct the result string from the DFS traversal.

solution.py12 lines

1def crackSafe(n, k):
2    visited = set()
3    result = []
4    def dfs(node):
5        for x in range(k):
6            edge = node + str(x)
7            if edge not in visited:
8                visited.add(edge)
9                dfs(edge[1:])
10                result.append(str(x))
11    dfs('0' * (n - 1))
12    return ''.join(result) + ''.join([str(i) for i in range(k)])

ℹ

Complexity note: The time complexity is O(k^n) because we explore all possible combinations of n digits. The space complexity is also O(k^n) due to the storage of visited edges.

1Understanding Eulerian paths can help solve problems involving combinations and sequences efficiently.
2Using DFS allows us to explore all paths without repetition, ensuring every combination is covered.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.