The goal of this experiment is to gain experience in using the technique of dynamic programming on problems.

Tasks

Write a program to find the length of the longest common subsequence $($LCS$)$ present in the given two sequences. A subsequence is a subset of elements in the sequence taken in order.

For example, "bcba" and "bdab" are subsequences of $x=$ "ABCBDAB" and $Y=$ "BDCABA".

Analyze the time complexity of solving LCS using dynamic programming.

Fill out the report sheet.

Submit both the report sheet and the source files to Canvas.

Sample Input $1$ :

$x=$ "ACADB" and $Y=$ "CBDA"

Output: $2("$CA$")$

Sample Input $2$:

$x=$ BACDB and $Y=BDCB$

Output: $3("$BCB$"$ OR $"$BDB$")$