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Longest Common Subsequence

Medium
dynamic-programming

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.

Recurrence Relation:

  • If text1[i] == text2[j]: dp[i][j] = dp[i-1][j-1] + 1
  • Else: dp[i][j] = max(dp[i-1][j], dp[i][j-1])

This is a fundamental 2D DP problem that introduces comparing two sequences.

Example 1

Input: text1 = "abcde", text2 = "ace"
Output: 3
Explanation: The longest common subsequence is "ace" with length 3.

Example 2

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

Example 3

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

Constraints

  • •1 <= text1.length, text2.length <= 1000
  • •text1 and text2 consist of only lowercase English characters.
Show Hints (4)
Hint 1: Build a 2D table where dp[i][j] represents the LCS of text1[0..i-1] and text2[0..j-1].
Hint 2: If the current characters match, extend the LCS by 1.
Hint 3: If they do not match, take the maximum of excluding either character.
Hint 4: The answer is in dp[m][n] where m and n are the lengths of the strings.
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