How do you solve Freedom Trail on LeetCode?

Freedom Trail (LeetCode #514) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * m²) time complexity and O(n * m) space complexity. Key insight: Understanding the relationship between ring and key is crucial.

What is the brute force solution for Freedom Trail?

The brute force approach for Freedom Trail is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we try to align each character of the key with the ring by checking all possible positions. This method is straightforward but inefficient, as it explores all potential rotations for each character in the key. The optimal Optimal Solution approach improves this to O(n * m²).

What algorithm or data structure is used to solve Freedom Trail?

Freedom Trail uses the following concepts: String, Dynamic Programming, Depth-First Search, Breadth-First Search. The recommended patterns to study are: Dynamic Programming, Backtracking.

What are the interview tips for Freedom Trail?

Explain your thought process clearly during the interview. Consider edge cases, such as when the ring or key is empty. Practice similar problems to build confidence with dynamic programming.

What are common mistakes when solving Freedom Trail?

Not considering all possible positions for each character. Failing to optimize with dynamic programming when applicable.

#514

Freedom Trail

Hard

StringDynamic ProgrammingDepth-First SearchBreadth-First SearchDynamic ProgrammingBacktracking

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n * m²)
Space	O(1)	O(n * m)

💡

Intuition

Time O(n * m²)Space O(n * m)

The optimal solution leverages dynamic programming to store the minimum steps required to reach each character in the key from any position in the ring. This avoids redundant calculations and significantly reduces the time complexity.

⚙️

Algorithm

3 steps

1Step 1: Create a DP table where dp[i][j] represents the minimum steps to spell the first i characters of the key starting from position j in the ring.
2Step 2: Initialize the DP table with base cases for the first character of the key.
3Step 3: Fill the DP table iteratively by calculating the minimum steps for each character in the key from all possible positions in the ring.

solution.py18 lines

1def findRotateSteps(ring, key):
2    from collections import defaultdict
3    index_map = defaultdict(list)
4    for i, char in enumerate(ring):
5        index_map[char].append(i)
6
7    dp = [[float('inf')] * len(ring) for _ in range(len(key) + 1)]
8    for j in range(len(ring)):
9        dp[0][j] = 0
10
11    for i in range(1, len(key) + 1):
12        for j in range(len(ring)):
13            for target_pos in index_map[key[i - 1]]:
14                steps = abs(j - target_pos)
15                steps = min(steps, len(ring) - steps)
16                dp[i][target_pos] = min(dp[i][target_pos], dp[i - 1][j] + steps + 1)
17
18    return min(dp[len(key)])

ℹ

Complexity note: The time complexity is O(n * m²) where n is the length of the key and m is the length of the ring. This is due to iterating through each character of the key and checking all positions in the ring for each character.

1Understanding the relationship between ring and key is crucial.
2Dynamic programming can significantly optimize solutions for problems involving sequences.

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