📓
Algorithms
  • Introduction to Data Structures & Algorithms with Leetcode
  • Strings
    • Dutch Flags Problem
      • List Partitoning
    • Counters
      • Majority Vote
      • Removing Parentheses
      • Remove Duplicates from Sorted Array
    • Maths
      • Lone Integer
      • Pigeonhole
      • Check If N and Its Double Exist
      • Find Numbers with Even Number of Digits
    • Two Pointers
      • Remove Element
      • Replace Elements with Greatest Element on Right Side
      • Valid Mountain Array
      • Sort Array by Parity
      • Squares of a Sorted Array
      • Max Consecutive Ones
    • Sliding Window
      • Max Consecutive Ones 3
    • Stacks
      • Balanced Brackets
    • General Strings & Arrays
      • Move Zeros
      • Unique Elements
      • Merge Sorted Array
    • Matrices
      • Valid Square
      • Matrix Search Sequel
  • Trees
    • Untitled
  • Recursion
    • Introduction
    • Backtracking
      • Permutations
  • Dynamic Programming
    • Introduction
    • Minimum (Maximum) Path to Reach a Target
      • Min Cost Climbing Stairs
      • Coin Change
      • Minimum Path Sum
      • Triangle
      • Minimum Cost to Move Chips to The Same Position
      • Consecutive Characters
      • Perfect Squares
    • Distinct Ways
      • Climbing Stairs
      • Unique Paths
      • Number of Dice Rolls with Target Sum
    • Merging Intervals
      • Minimum Cost Tree From Leaf Values
    • DP on Strings
      • Levenshtein Distance
      • Longest Common Subsequence
  • Binary Search
    • Introduction
      • First Bad Version
      • Sqrt(x)
      • Search Insert Position
    • Advanced
      • KoKo Eating Banana
      • Capacity to Ship Packages within D Days
      • Minimum Number of Days to Make m Bouquets
      • Split array largest sum
      • Minimum Number of Days to Make m Bouquets
      • Koko Eating Bananas
      • Find K-th Smallest Pair Distance
      • Ugly Number 3
      • Find the Smallest Divisor Given a Threshold
      • Kth smallest number in multiplication table
  • Graphs
    • Binary Trees
      • Merging Binary Trees
      • Binary Tree Preorder Traversal
      • Binary Tree Postorder Traversal
      • Binary Tree Level Order Traversal
      • Binary Tree Inorder Traversal
      • Symmetric Tree
      • Populating Next Right Pointers in Each Node
      • Populating Next Right Pointers in Each Node II
      • 106. Construct Binary Tree from Inorder and Postorder Traversal
      • Serialise and Deserialise a Linked List
      • Maximum Depth of Binary Tree
      • Lowest Common Ancestor of a Binary Tree
    • n-ary Trees
      • Untitled
      • Minimum Height Trees
    • Binary Search Trees
      • Counting Maximal Value Roots in Binary Tree
      • Count BST nodes in a range
      • Invert a Binary Tree
      • Maximum Difference Between Node and Ancestor
      • Binary Tree Tilt
  • Practice
  • Linked Lists
    • What is a Linked List?
    • Add Two Numbers
      • Add Two Numbers 2
    • Reverse a Linked List
    • Tortoise & Hare Algorithm
      • Middle of the Linked List
  • Bitshifting
    • Introduction
  • Not Done Yet
    • Uncompleted
    • Minimum Cost For Tickets
    • Minimum Falling Path Sum
Powered by GitBook
On this page

Was this helpful?

  1. Dynamic Programming
  2. DP on Strings

Longest Common Subsequence

PreviousLevenshtein DistanceNextIntroduction

Last updated 4 years ago

Was this helpful?

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.

Let's look at the base case here.

Per the question:

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.

It can be none.

That means for any 2 strings:

  • The minimum substring is 1.

We should keep track of the longest common substring for every possible combination.

Because we have empty strings, the values for each empty string is 0. If we are filling in (a, a) we ask ourselves if we have string "a" and "a" and nothing else, what will be the longest subsequence? The length of the common subsequence is 1 here. Note: When we read the top, we are reading it as ["a", "ab", "abc"].

With only the letter "a" we can only make at most 1 subsequence with all of them. Our third row now includes c as well as a for "ac".

We compare "abc" with "ac". Since 2 letters are the same our value is 2.

We choose the maximum of these 2 values. 2 is the maximum so we use it here.

Our value here is 3 + 1 which is 4.

And we are done!

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