Solution: Longest Common Subsequence

Explore how to find the longest common subsequence between two strings by applying dynamic programming techniques in C++. Understand the naive recursive method, its limitations, and how memoization optimizes the solution. Learn to implement a 2D table to store intermediate results, reducing time complexity to O(m×n) and managing space complexity effectively.

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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 ...