Leetcode #1940: Longest Common Subsequence Between Sorted Arrays
In this guide, we solve Leetcode #1940 Longest Common Subsequence Between Sorted Arrays in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given an array of integer arrays arrays where each arrays[i] is sorted in strictly increasing order, return an integer array representing the longest common subsequence among all the arrays. A subsequence is a sequence that can be derived from another sequence by deleting some elements (possibly none) without changing the order of the remaining elements.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Array, Hash Table, Counting
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: arrays = [[1,3,4],
[1,4,7,9]]
Output: [1,4]
Explanation: The longest common subsequence in the two arrays is [1,4].
Python Solution
class Solution:
def longestCommonSubsequence(self, arrays: List[List[int]]) -> List[int]:
cnt = [0] * 101
for row in arrays:
for x in row:
cnt[x] += 1
return [x for x, v in enumerate(cnt) if v == len(arrays)]
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.