LC1143 - Longest Common Subsequence

Problem

Given two strings text1 and text2, return the length of their longest common subsequence. If there is no common subsequence, return 0.

A subsequence of a string is a new string generated from the original string with some characters (can be none) deleted without changing the relative order of the remaining characters.

• For example, "ace" is a subsequence of "abcde".

A common subsequence of two strings is a subsequence that is common to both strings.

Example

Input: text1 = "abcde", text2 = "ace"

Output: 3

Explanation: The longest common subsequence is "ace" and its length is 3.

Solution

2D Dynamic Programming

Lay the words against each other on a 2D grid and fill in values of the path. Time and space complexity is $O(m\cdot n)$, where $m$ is the length of text1 and $n$ is the length of text2.

def longestCommonSubsequence(self, text1: str, text2: str) -> int:
	# Allocate empty matrix
	arr = [[0 for _ in range(len(text2) + 1)] for _ in range(len(text1) + 1)]
	
	for i in range(len(text1)-1, -1, -1):
		for j in range(len(text2)-1, -1, -1):
			if text1[i] == text2[j]:
				arr[i][j] = 1 + arr[i+1][j+1]
			else:
				arr[i][j] = max(arr[i][j+1], arr[i+1][j])
	
	return arr[0][0]