Longest Common Subsequence

Problem

https://leetcode.com/problems/longest-common-subsequence/

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.

Pattern

String, Dynamic Programming

Approaches

Dynamic Programming

Code

def longestCommonSubsequence(text1: str, text2: str) -> int:
    M = len(text1)
    N = len(text2)
    lcs = [[0 for _ in range(N + 1)] for _ in range(M + 1)]

    for i in range(1, M + 1):
        for j in range(1, N + 1):
            if text1[i - 1] == text2[j - 1]:
                lcs[i][j] = lcs[i - 1][j - 1] + 1
            else:
                lcs[i][j] = max(lcs[i - 1][j], lcs[i][j - 1])

    return lcs[-1][-1]

Test

>>> from longest_common_subsequence__dynamic_programming import longestCommonSubsequence
>>> longestCommonSubsequence("abcde", "ace")
3
>>> longestCommonSubsequence("abc", "abc")
3
>>> longestCommonSubsequence("abc", "def")
0

longest_common_subsequence__dynamic_programming.longestCommonSubsequence(text1: str, text2: str) → int