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 C (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#define N 1001
 
void count(char *A,char *B){
  int i,j,x[N][N];
 
  for(i=0; i<N; i++){
    for(j=0; j<N; j++){
      x[i][j]=0;
    }
  }
  for(i=0; i<strlen(A); i++){
    for(j=0; j<strlen(B); j++){
      if(A[i]==B[j])x[i+1][j+1]=x[i][j]+1;
      else if(x[i][j+1]>x[i+1][j]) x[i+1][j+1]=x[i][j+1];
      else x[i+1][j+1]=x[i+1][j];
    }
  }
  printf("%d\n",x[strlen(A)][strlen(B)]);
}
 
int main(){
  int n,i,j;
  char A[N],B[N];
  scanf("%d",&n);
 
  for(i=0;i<n;i++){
    scanf("%s",A);
    scanf("%s",B);
    count(A,B);
  }
 
  return 0; 
}