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.Scanner;

public class Main {
	
	public static void main(String[] args) {
		
		Scanner input = new Scanner(System.in);
		
		//get first part of input
		int numOfDatasets = input.nextInt();
		String[] sequences = new String[numOfDatasets * 2];
		
		input.nextLine();
		
		//get sequences from input
		for(int i = 0; i < sequences.length; i++) {
			sequences[i] = input.nextLine();
		}
		
		for(int i = 0; i < sequences.length; i += 2) {
			
			//initialize matrix
			int[][] matrix = new int[sequences[i].length() + 1][sequences[i + 1].length() + 1];
			
			//set first row and column to all 0s
			for(int j = 0; j < matrix.length; j++) {
				matrix[j][0] = 0;	
			}
			for(int j = 1; j < matrix[0].length; j++) {
				matrix[0][j] = 0;
			}
			
			//complete the table
			for(int j = 0; j < matrix.length - 1; j++) {
				
				char rowChar = sequences[i].charAt(j);
				
				for(int k = 0; k < matrix[0].length - 1; k++) {
					
					char columnChar = sequences[i+1].charAt(k);
					
					if(rowChar == columnChar) {
						matrix[j+1][k+1] = matrix[j][k] + 1;
					}
					else {
						matrix[j+1][k+1] = java.lang.Math.max(matrix[j][k+1], matrix[j+1][k]);
					}
					
				}
				
			}
			
			System.out.println(matrix[matrix.length-1][matrix[0].length-1]);
			
		}
		
	}

}