1143_Longest_Common_Subsequence.py

"""
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 1:

Input: text1 = "abcde", text2 = "ace" 
Output: 3  
Explanation: The longest common subsequence is "ace" and its length is 3.
Example 2:

Input: text1 = "abc", text2 = "abc"
Output: 3
Explanation: The longest common subsequence is "abc" and its length is 3.
Example 3:

Input: text1 = "abc", text2 = "def"
Output: 0
Explanation: There is no such common subsequence, so the result is 0.
 

Constraints:

1 <= text1.length, text2.length <= 1000
text1 and text2 consist of only lowercase English characters.
use two d grid. when the character is the same, move diaganal +1. otherwise take max( lower or right )
we start comparing the character from the last character of both string
"""

class Solution:
    def longestCommonSubsequence(self, text1: str, text2: str) -> int:
#2d grid
        dp = [[0 for j in range(len(text2)+1)] for i 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]:
                    dp[i][j] = 1+ dp[i+1][j+1] # diagnal 
                else:
                    dp[i][j] = max(dp[i][j+1], dp[i+1][j]) # max right or lower 
        return dp[0][0]