Problem:
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Longest Common Subsequence

For given two sequences $X$ and $Y$, a sequence $Z$ is a common subsequence of $X$ and $Y$ if $Z$ is a subsequence of both $X$ and $Y$. For example, if $X = \{a,b,c,b,d,a,b\}$ and $Y = \{b,d,c,a,b,a\}$, the sequence $\{b,c,a\}$ is a common subsequence of both $X$ and $Y$. On the other hand, the sequence $\{b,c,a\}$ is not a longest common subsequence (LCS) of $X$ and $Y$, since it has length 3 and the sequence $\{b,c,b,a\}$, which is also common to both $X$ and $Y$, has length 4. The sequence $\{b,c,b,a\}$ is an LCS of $X$ and $Y$, since there is no common subsequence of length 5 or greater.

Write a program which finds the length of LCS of given two sequences $X$ and $Y$. The sequence consists of alphabetical characters.

Input

The input consists of multiple datasets. In the first line, an integer $q$ which is the number of datasets is given. In the following $2 \times q$ lines, each dataset which consists of the two sequences $X$ and $Y$ are given.

Output

For each dataset, print the length of LCS of $X$ and $Y$ in a line.

Constraints

$1 \leq q \leq 150$

$1 \leq$ length of $X$ and $Y$ $\leq 1,000$

$q \leq 20$ if the dataset includes a sequence whose length is more than 100

Sample Input 1

3
abcbdab
bdcaba
abc
abc
abc
bc

Sample Output 1

4
3
2

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in JAVA (judge verdict: Accepted)


import java.util.*;
public class Main {
	public static int LongestCommonSequence(String string1, String string2)
	{
		int max = 0;
		int len1 = string1.length() , len2 = string2.length();
		//table to find longest common sequence
		int[][] table = new int[len1 + 1][len2 + 1];
		//filling the table for max values
		for(int i = 1; i <= len1  ; i++)
		{
			for(int j = 1 ; j <= len2 ; j++)
			{
				if(string1.charAt(i-1) != string2.charAt(j-1))
				{
					table[i][j] = Math.max(table[i-1][j],table[i][j-1]);
				}
				if(string1.charAt(i-1) == (string2.charAt(j-1)))
				{
					table[i][j] = 1 + table[i-1][j-1];
				}
			}
		}
		max = table[len1][len2];
		return max;
	}
	
	public static void main(String args[])
	{
		Scanner in = new Scanner(System.in);
		int pairs = in.nextInt();
		for(int i = 0; i < pairs ; i ++)
		{
			String s1 = in.next();
			String s2 = in.next();
			int answer = LongestCommonSequence(s1,s2);
			System.out.println(answer);
		}
		
	}
}