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 {
	
	int findLCS(char[] X, char[] Y, int lenX, int lenY) {
		int[][] chart = new int[lenX+1][lenY+1];
		for(int i = 0; i <= lenX; i++) {
			for(int j = 0; j <= lenY; j++) {
				if(i == 0 || j == 0) {
					chart[i][j] = 0;
				}
				else if (X[i-1] == Y[j-1]) {
					chart[i][j] = chart[i-1][j-1] + 1;
				}else {
					chart[i][j] = higherOfTwo(chart[i-1][j], chart[i][j-1]);
				}
			}
		}
		return chart[lenX][lenY];
	}
	int higherOfTwo(int top, int left) {
		return (top > left)? top : left; 
	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner input = new Scanner(System.in);
		int q = input.nextInt();
		Main test = new Main();
		input.nextLine();
		for(int i = 0 ; i < q; i++) {
			String str1 = input.nextLine();
			String str2 = input.nextLine();
			char[] X = str1.toCharArray();
			char[] Y = str2.toCharArray();
			int lenX = X.length;
			//System.out.println(lenX);
			int lenY = Y.length;
			//System.out.println(lenY);
			int ans = test.findLCS(X, Y, lenX, lenY);
			System.out.println(ans);
		}
		input.close();	
	}
}