Go: package main

import (
	"fmt"
	"os"
	"strconv"
	"bufio"
	"strings"
	"sort"
)

// define
var (
	sc = bufio.NewScanner(os.Stdin)
)

func bordersInt(in_map [][]int, invalid int) [][]int{
	H, W := len(in_map), len(in_map[0])
	out_map := make([][]int, H+2)
	for h:=0; h<H+2; h++ {
		out_map[h] = make([]int, W+2)
		for w:=0; w<W+2; w++ {
			out_map[h][w] = invalid
		}
	}
	for h:=0; h<H; h++{
		for w:=0; w<W; w++{
			out_map[h+1][w+1] = in_map[h][w] 
		}
	}
	return out_map
}

func bordersString(in_map [][]string, invalid string) [][]string{
	H, W := len(in_map), len(in_map[0])
	out_map := make([][]string, H+2)
	for h:=0; h<H+2; h++ {
		out_map[h] = make([]string, W+2)
		for w:=0; w<W+2; w++ {
			out_map[h][w] = invalid
		}
	}
	for h:=0; h<H; h++{
		for w:=0; w<W; w++{
			out_map[h+1][w+1] = in_map[h][w] 
		}
	}
	return out_map
}

func scanIntLine(len int) []int{
	arr := make([]int, len)
	for i:=0; i<len; i++{
		sc.Scan()
		tmp, err := strconv.Atoi(sc.Text())
		if err == nil{
			arr[i] = tmp
		}
	}
	return arr
}

func scanStringLine(len int) []string{
	arr := make([]string, len)
	for i:=0; i<len; i++{
		sc.Scan()
		arr[i] = sc.Text()
	}
	return arr
}

func scanIntSplit(len int) []int{
	arr := make([]int, len)
	sc.Scan()
	for i, v := range strings.Split(sc.Text(), " "){
		tmp, err := strconv.Atoi(v)
		if err == nil{
			arr[i] = tmp
		}
	}
	return arr
}

func maxInt(args... int) int{
	sort.Ints(args)
	return args[len(args)-1]
}

func main(){
	buf := make([]byte, 0)
    sc.Buffer(buf, 1000000009)
	var n int 
	fmt.Scan(&n)
	dp := make([][]int, 1003)
	for i:=0; i<1003; i++ {
		dp[i] = make([]int, 1003)
	}
	input_lines := scanStringLine(2*n)
	for i:=0; i<n; i++ {
		S, T := input_lines[2*i], input_lines[2*i+1]
		lenS, lenT := len(S), len(T)
		for i:=1; i<lenS+1; i++ {
			for j:=1; j<lenT+1; j++ {
				if S[i-1] == T[j-1] {
					dp[i][j] = maxInt(dp[i-1][j-1]+1, dp[i-1][j], dp[i][j-1])
				} else {
					dp[i][j] = maxInt(dp[i-1][j], dp[i][j-1])
				}
			}
		}
		fmt.Println(dp[lenS][lenT])
	}
}

Python: # -*- coding: utf-8 -*-
"""
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_10_C

????????±?????¨??????
"""
# 4/5??§Time Limit Exceeded 5.20s ????????????5s??\???????????????????????????

# c = []  # global?????????????????????????
def prep_array(X, Y):
    """ ??????0???2?¬???????????????¨??????????????????????????\????????????????????§??????????????????????¨?(1000+1)??\???????????? """
    from array import array
    c = [[0]*1024 for _ in range(1024)]
    # c = [array('I', [0] * 1024) for _ in range(1024)]
    return c


def check_max(array):
    """ 2?¬????????????????????????§??????????????? """
    max_lcs = 0
    for row in array:
        temp_max = max(row)
        if temp_max > max_lcs:
            max_lcs = temp_max
    return max_lcs


def calc_lcs4(X, Y, c):
    """
    Y[j]?????¢???????????????????????´
    ???????????????????????°???????????????????????´
    4/5 ?????????????????????????????¨????????????????????????????????°??§6.0?§?
    """
    X = ' ' + X
    Y = ' ' + Y
    m = len(X)
    n = len(Y)
    max_lcs = 0

    pre_row = c[0]
    for i in range(1, m):
        row = c[i]
        XX = X[i]
        for j, YY in enumerate(Y):
            if XX == YY:
                pr_j1 = pre_row[j - 1]
                cv = pr_j1 + 1
                row[j] = cv
                if cv > max_lcs:
                    max_lcs = cv
            else:
                pr_j = pre_row[j]
                r_j1 = row[j-1]
                if pr_j >= r_j1:
                    row[j]= pr_j
                else:
                    row[j] = r_j1
        pre_row = row
    return max_lcs



def calc_lcs3(X, Y, c):
    """
    X[i]???for j?????????????????????????????°????????????????????§???
    4/5 ?????????????????????????????¨????????????????????????????????°??§7.1?§?
    """
    m = len(X)
    n = len(Y)
    X = ' ' + X
    Y = ' ' + Y

    pre_row = c[0]
    for i in range(1, m+1):
        row = c[i]
        XX = X[i]
        for j in range(1, n+1):
            if XX == Y[j]:
                row[j] = pre_row[j - 1] + 1
            elif pre_row[j] >= row[j - 1]:
                row[j] = pre_row[j]
            else:
                row[j] = row[j - 1]
        pre_row = row
    return check_max(c)



def calc_lcs2(X, Y, c):
    """
    c[i][j]????????¢????????????????????????????????§?????????????????¨?????????????????°??????????????????????????£??????????????§???
    4/5 ?????????????????????????????¨????????????????????????????????°??§8.2?§?
    """
    m = len(X)
    n = len(Y)
    X = ' ' + X
    Y = ' ' + Y

    pre_row = c[0]
    for i in range(1, m+1):
        row = c[i]
        for j in range(1, n+1):
            if X[i] == Y[j]:
                row[j] = pre_row[j - 1] + 1
            elif pre_row[j] >= row[j - 1]:
                row[j] = pre_row[j]
            else:
                row[j] = row[j - 1]
        pre_row = row
    return check_max(c)


def calc_lcs1(X, Y):
    """
    array?????????????????¨???byte???????????¨????????¨????§??????????????????????????????????????????§?????¨???????????£?????????int???????????¨???
    4/5 ?????????????????????????????¨????????????????????????????????°??§19.3?§?
    """
    from array import array
    m = len(X)
    n = len(Y)
    X = ' ' + X
    Y = ' ' + Y
    c = array('i', [0] * (1024 * 1024))
    for i in range(1, m+1):
        for j in range(1, n+1):
            if X[i] == Y[j]:
                c[i*1024 + j] = c[(i-1)*1024 + j - 1] + 1
            elif c[(i-1)*1024 + j] >= c[i*1024 + j - 1]:
                c[i*1024 + j] = c[(i-1)*1024 + j]
            else:
                c[i*1024 + j] = c[i*1024 + j - 1]
    return max(c)


def calc_lcs1_1(X, Y):
    """

    4/5 ?????????????????????????????¨????????????????????????????????°??§7.1?§?
    """
    from array import array
    X = ' ' + X
    Y = ' ' + Y
    m = len(X)
    n = len(Y)
    max_lcs = 0
    C = [array('I', [0] * n) for _ in range(m)]

    pre_row = C[0]
    for i in range(1, m):
        row = C[i]
        XX = X[i]
        for j, YY in enumerate(Y[1:]):
            if XX == YY:
                pr_j1 = pre_row[j-1]
                row[j] = pr_j1 + 1
                if row[j] > max_lcs:
                    max_lcs = pr_j1 + 1
            else:
                pr_j = pre_row[j]
                r_j1 = row[j-1]
                if pr_j >= r_j1:
                    row[j] = pr_j
                else:
                    row[j]= r_j1
        pre_row = row
    return max_lcs


def calc_lcs(X, Y, c):
    """
    ??????????????¢?????´????????????????????????????£?????????????
    4/5 ?????????????????????????????¨????????????????????????????????°??§12.5?§?
    """
    m = len(X)
    n = len(Y)
    X = ' ' + X
    Y = ' ' + Y

    for i in range(1, m+1):
        for j in range(1, n+1):
            if X[i] == Y[j]:
                c[i][j] = c[i - 1][j - 1] + 1
            elif c[i - 1][j] >= c[i][j - 1]:
                c[i][j] = c[i - 1][j]
            else:
                c[i][j] = c[i][j - 1]
    return check_max(c)


if __name__ == '__main__':
    # ??????????????\???
    num = int(input())
    # f = open('input.txt')
    # num = int(f.readline())

    for _ in range(num):
        X = input()
        Y = input()
        # X = f.readline().strip()
        # Y = f.readline().strip()

        # ???????????????
        result = calc_lcs4(X, Y, prep_array(X, Y))
        # result = calc_lcs1_1(X, Y)

        # ???????????¨???
        print(result)

Python: q = int(input())
for i in range(q):
    X = input()
    Y = input()

    m, n = len(X), len(Y)
    c = [[0 for i in range(n+1)] for j in range(m+1)]

    for i in range(1, m+1):
        for j in range(1, n+1):
            x, y = X[i-1], Y[j-1]
            if x == y:
                c[i][j] = c[i-1][j-1] + 1
            else:
                c[i][j] = max(c[i-1][j], c[i][j-1])

    print(c[m][n])