How do you solve Longest Common Subpath on LeetCode?

Longest Common Subpath (LeetCode #1923) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log m) time complexity and O(n) space complexity. Key insight: Using binary search reduces the number of checks needed to find the longest common subpath.

What is the brute force solution for Longest Common Subpath?

The brute force approach for Longest Common Subpath is Brute Force, with O(n²) time complexity and O(1) space complexity. We can check every possible subpath of each friend's path and see if it appears in all other paths. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log m).

What algorithm or data structure is used to solve Longest Common Subpath?

Longest Common Subpath uses the following concepts: Array, Binary Search, Rolling Hash, Suffix Array, Hash Function. The recommended patterns to study are: Hash Map, Binary Search, Rolling Hash.

What are the interview tips for Longest Common Subpath?

Always clarify the constraints and edge cases before diving into coding. Explain your thought process and reasoning behind each step of your algorithm. Practice writing clean and efficient code, as readability is important in interviews.

What are common mistakes when solving Longest Common Subpath?

Not considering edge cases where paths are very short or have no common subpaths. Failing to optimize checks for common subpaths, leading to timeouts on larger inputs.

#1923

Longest Common Subpath

Hard

ArrayBinary SearchRolling HashSuffix ArrayHash FunctionHash MapBinary SearchRolling Hash

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n log m)Space O(n)

We can use binary search to find the maximum length of the common subpath and a rolling hash to efficiently check for common subpaths in all paths.

⚙️

Algorithm

3 steps

1Step 1: Define a function to check if there is a common subpath of a given length using rolling hash.
2Step 2: Use binary search on the length of the subpath from 0 to the length of the shortest path.
3Step 3: For each mid value in binary search, check if there is a common subpath of that length.

solution.py23 lines

1def longestCommonSubpath(n, paths):
2    def check_length(length):
3        seen = set()
4        base = 10**5 + 7
5        mod = 2**63 - 1
6        for path in paths:
7            current_hash = 0
8            for i in range(length):
9                current_hash = (current_hash * base + path[i]) % mod
10            seen.add(current_hash)
11            for i in range(length, len(path)):
12                current_hash = (current_hash * base - path[i - length] * (base ** length) % mod + path[i]) % mod
13                seen.add(current_hash)
14        return len(seen) > 1
15
16    left, right = 0, min(len(path) for path in paths)
17    while left < right:
18        mid = (left + right + 1) // 2
19        if check_length(mid):
20            left = mid
21        else:
22            right = mid - 1
23    return left

ℹ

Complexity note: The time complexity is O(n log m) due to binary search over the length of the subpath and checking each length using rolling hash, where m is the number of paths.

1Using binary search reduces the number of checks needed to find the longest common subpath.
2Rolling hash allows for efficient substring comparison, avoiding the need for nested loops.

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