Solution: Longest Common Subsequence

Explore how to solve the longest common subsequence problem by applying a top-down dynamic programming technique. Understand the use of memoization and a 2D table to optimize recursive solutions, improving performance by avoiding redundant calculations. This lesson helps you implement and analyze the algorithm's time and space complexities for coding interview success.

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Statement
Solution
- Naive approach
- Optimized approach using dynamic programming

Statement

Suppose you are given two strings. You need to find the length of the longest common subsequence between these two strings.

A subsequence is a string formed by removing some characters from the original string while maintaining the relative position of the remaining characters. For example, “abd” is a subsequence of “abcd”, where the removed character is “c”.

If there is no common subsequence, then return 0.

Constraints:

$1 \leq$ str1.length $\leq 500$
$1 \leq$ str2.length $\leq 500$
str1 and str2 contain only lowercase English characters.

Solution

So far, you’ve probably brainstormed some approaches and have an idea of how to solve this problem. Let’s explore some of these approaches and figure out which one to follow based on considerations such as time complexity and any implementation constraints.

Naive approach

A naive approach would be to compare the characters of both strings based on the following rules:

If the current characters of both strings ...