description.md

Dynamic Programming

Click here to go back to the notes page.

Leetcode Problem

Medium 1143

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

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

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

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

Key Idea

For any two strings text1 and text2, suppose we know the longest common subsequence between the string text1[:i] and text2[:j].

Now if:

• text1[i] == text2[j], then the longest common subsequence could be
  • 1 + longest common subsequence of text1[:i] and text2[:j].
  • or two options below
• text1[i] != text2[j], then the longest common subsequence could be
  • longest common subsequence of text1[:i + 1] and text2[:j]
  • longest common subsequence of text1[:i] and text2[:j + 1]

Complexity Analysis

• Runtime Complexity: O(nm)
• Space Complexity: O(nm)

Solution:

• C++