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 Scala (judge verdict: Accepted)

import scala.io.StdIn.{readInt, readLine};

object Main {
    def main(args: Array[String]): Unit = {
        val n = readInt;
        for (i <- (0 until n)) {
            val a = readLine;
            val b = readLine;
            println(lcs(a, b).length);
        }
    }
    def lcs(a: String, b: String): String = {
        val arr = Array.ofDim[String](a.length + 1, b.length + 1);
        for (i <- (0 to a.length)) { arr(i)(0) = ""};
        for (i <- (0 to b.length)) { arr(0)(i) = "" };
        def go(row: Int, col: Int): String = {
            if (arr(row)(col) != null) {
                arr(row)(col)
            } else {
                val c1 = go(row - 1, col);
                val c2 = go(row, col - 1);
                val c3 = go(row - 1, col - 1);
                arr(row)(col) = if (a(row - 1) == b(col - 1)) {
                    max(c1, c2, c3 + a(row - 1));
                } else {
                    max(c1, c2, c3);
                }
                arr(row)(col); 
            }
        }
        go(a.length, b.length);
    }
    
    def max(a: String, b: String, c: String): String = {
        val lenA = a.length; val lenB = b.length; val lenC = c.length;
        if (lenA > lenB) {
            if (lenC > lenA) c else a;
        } else {
            if (lenC > lenB) c else b;
        }
    }
}