1143. Longest Common Subsequence

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

Given two strings text1 and text2, return the length of their longest common subsequence.

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. (eg, "ace" is a subsequence of "abcde" while "aec" is not). A common subsequence of two strings is a subsequence that is common to both strings.

 

If there is no common subsequence, return 0.

 

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 <= 1000
  • 1 <= text2.length <= 1000
  • The input strings consist of lowercase English characters only.
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Intuition
Nested loop on both strings
if chars match
    len of LCS = 1 + len of LCS of previous positions of both
else
    len of LCS = max(len of LCS ignoring char from S1, len of LCS ignoring char from S2) 

dp - init to size of S1, S2

Loop from 1 to = S.length()

if (char(i - 1) == char(j - 1)
    dp[i][j] = 1 + dp[i - 1][j - 1]
else
    dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])

return dp[S1.len()][S2.len()]
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Time - O(m * n)
Space - O(m * n)

Can optimize on space with 2 rows, and columns of smaller string
Time - O(m * n)
Space - O(min(m, n))
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