Longest Common Subsequence (LCS) and Dynamic Programming

These flashcards review key concepts and definitions related to the longest common subsequence (LCS) and dynamic programming based on the provided notes.

What is the purpose of dynamic programming in finding the longest common subsequence (LCS)?

Dynamic programming helps to break the problem into simpler subproblems, enabling efficient computation of the LCS.

How do you denote the length of an LCS for s[i, j]?

Let c[i, j] denote the length of the longest common subsequence for the prefixes ending at the i-th character of the first string and the j-th character of the second.

What happens if the ith character of the first string coincides with the jth character of the second string?

If they coincide, then c[i, j] = c[i-1, j-1] + 1.

What is the base case for computing c[i, j]?

The base case is c[i, 0] = c[0, j] = 0, which means if either string is empty, the length of the LCS is zero.

What is a palindrome?

A palindrome is a sequence that reads the same forwards and backwards.

What problem related to palindromes is presented for homework?

Find the longest palindromic subsequence of a given sequence.

What is the general approach to solving the quiz problem on LCS?

Determine the longest common subsequence of two sequences using dynamic programming techniques.

How is the recursion defined for c[i, j] when characters are different?

If the characters are different, then c[i, j] = max{c[i-1, j], c[i, j-1]}.

What does the quiz problem on LCS output for the sequences 010101 and 10010100?

The output is an optimal LCS of length 6: 010101.

What is the notation for referencing the longest common subsequence subproblems?

The notation is s[ij] where i and j represent the lengths of the prefixes of the strings being compared.