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.*;

public class Main{
	public static int Length(String[] a, String[] b) {
		int table[][] = new int [a.length+1][b.length+1];
		
		for (int i=0; i < a.length+1;i++) {
			for (int j=0; j<b.length+1; j++) {
				if (i==0 || j==0) {
					table[i][j] =0;
					
				}
				else if(a[i-1].equals(b[j-1])) {
					table[i][j] = table[i-1][j-1]+1;
				}
				else {
					table[i][j] = maxNum(table[i-1][j], table[i][j-1]);
				}
			}
		}
	
		return table[a.length][b.length];
	}
	
	public static int maxNum(int a, int b) {
		if (a>b) return a;
		else return b;
	}
	public static int minNum(int a, int b) {
		if(a<b) return b;
		else return a;
	}
	
	public static void main(String[] args) {
		// storing input as arrays
		Scanner s = new Scanner(System.in);
		int numSets = Integer.parseInt(s.nextLine());
		int answer[] = new int[numSets];
		for(int i=0; i < numSets;i++) {
			String[] a = s.nextLine().split("");
			String[] b = s.nextLine().split("");
			answer[i] = Length(a,b);
		}
		for (int j =0; j<numSets; j++) {
			System.out.println(answer[j]);
		}
	}
}