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};
import scala.annotation.tailrec;
object Main {
    def main(args: Array[String]): Unit = {
        (0 until readInt).foreach { i =>
            val y = readLine;
            val x = readLine;
            println(longestCommonSubsequence(y, x));
        }
    }
    def longestCommonSubsequence(strY: String, strX: String): Int = {
        val sizeX = strX.length;
        val sizeY = strY.length;
        val arr = Array.ofDim[Int](sizeY + 1, sizeX + 1);
        (1 to sizeY).foreach { y => (1 to sizeX).foreach { x => arr(y)(x) = -1}}
        def go(y: Int, x: Int): Int = arr(y)(x) match {
            case -1 => {
                val lcs1 = go(y - 1, x - 1);
                val lcs2 = go(y - 1, x);
                val lcs3 = go(y, x - 1);
                arr(y)(x) = if (strX(x - 1) == strY(y - 1)) {
                    max(lcs1 + 1, lcs2, lcs3);
                } else  {
                    max(lcs1, lcs2, lcs3);
                }
                arr(y)(x);
            }
            case lcs => lcs;
        }
        go(sizeY, sizeX);
    }

    def max(a: Int, b: Int, c: Int): Int = {
        if (a > b)
            if (a > c) a else c;
        else
            if (b > c) b else c;
    }
}