[Leetcode] Longest Common Subsequence
Classic two dimensional dp problem.
Description
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.
Examples
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.Solution
Imagine a matrix where char of text1 filled in top of each row, and char of text2 filled in top of each col.
# abcde
# ^
# ace
# ^
# X A C E [0 0 0 0]
# A [0 1 1 1]
# B [0 1 1 1]
# C [0 1 2 2]
# D [0 1 2 2]
# E [0 1 2 3]dp[i][j] represents lcs for text1[:i] & text2[:j]
When forwarding new, inherit value from up left / up / left. When new common char founded, use up left (exclude new for both) and increment 1 as this new common enable two to increase lcs of 1 len. When not common char, use up and left (respectively one with new and one without new) and inherit the larger one. e.g. [5][1] lcs(ABCDE, A) = 1 with [4][2] lcs(ABCD, AC) = 2 -> [5][2] lcs(ABCDE, AC) = 2
- code
