Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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 {

    static Scanner sc = new Scanner(System.in);
    static int[][] dp = new int[1005][1005];
    static String x, y;

    public static void main(String[] args) {
        int N = sc.nextInt();
        for (int i = 0; i < N; i++) {
            read();
            clear();
            System.out.println(lcs(0, 0));
        }
    }

    public static void read() {
        x = sc.next();
        y = sc.next();
    }

    public static int lcs(int i, int j) {
        if (dp[i][j] >= 0) {
            return dp[i][j];
        } else if (x.length() == i || y.length() == j) {
            return dp[i][j] = 0;
        } else if (x.charAt(i) == y.charAt(j)) {
            return dp[i][j] = lcs(i + 1, j + 1) + 1;
        } else {
            return dp[i][j] = Math.max(lcs(i + 1, j), lcs(i, j + 1));
        }
    }

    public static void clear() {
        for (int i = 0; i < 1005; i++) {
            for (int j = 0; j < 1005; j++) {
                dp[i][j] = -1;
            }
        }
    }
}