1143. 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 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.

Solve¶

A dynamic program problem, which leverage the information of pre-solve value

class Solution:
    def longestCommonSubsequence(self, text1: str, text2: str) -> int:
        dp = [[0]*len(text2) for _ in text1]

        for i, c1 in enumerate(text1):
            for j, c2 in enumerate(text2):
                possible_answer = []

                if i > 0:
                    possible_answer.append(dp[i-1][j])
                if j > 0:
                    possible_answer.append(dp[i][j-1])

                if c1 == c2:
                    if i > 0 and j > 0:
                        possible_answer.append(dp[i-1][j-1] + 1)
                    else:
                        possible_answer.append(1)
                if len(possible_answer) > 0:
                    dp[i][j] = max(possible_answer)

        return dp[len(text1)-1][len(text2)-1]