# Leetcode 1143 - Longest common subsequence

Note

• dp[i][j] means the max length of common subsequence between text1 [0, i-1] and text2 [0, j-1] (Doesn’t need to end with the cur char)
• Create an (text1.length+1) x (text1.length+1) dp array
• Initialize all elements as 0.
• To skip initializing first row/col manually, the techinique is to iterate from i=1 and j=1 but compare text1[i-1] and text2[j-1]. In this way, we will initialize the first row/col in our for loops.
• By checking the table we drew, it’s easier to find the deduction.
• When text1[i-1] === text2[j-1], dp[i][j] = dp[i-1][j-1] + 1.
• When text1[i-1] !== text2[j-1], dp[i][j] = Math.max(dp[i-1][j], dp[i][j-1]).

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