Problem:
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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 <string.h>
char a[1100],b[1100];
int c[1100][1100];
int max(int a,int b){
    return a>b?a:b;
}
void lcs(char a[],char b[]){
    int alen,blen,i,j;
    alen=strlen(a),blen=strlen(b);
    for(i=0;i<alen;i++)c[i][0]=0;
    for(j=0;j<blen;j++)c[0][j]=0;
    for(i=1;i<alen;i++)
        for(j=1;j<blen;j++)
            if(a[i]==b[j])c[i][j]=c[i-1][j-1]+1;
            else c[i][j]=max(c[i-1][j],c[i][j-1]);
}
int main(){
    int t,alen,blen,i;
    scanf("%d",&t);
    while(t--){
        scanf("%s%s",a+1,b+1);//此?a[0]='\0'  b[0]='\0' 
        a[0]=' ',b[0]=' ';//?a[0]一直到a[]都有数据 ?次弄明白了a+1,b+1的移位?取了
        lcs(a,b); 
        printf("%d\n",c[strlen(a)-1][strlen(b)-1]);
    }
    return 0;
}