Go: package main

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

type Position struct {
	X int
	Y int
}

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	n, err := nextInt(sc)
	if err != nil {
		panic(err)
	}
	for i := 0; i < n; i++ {
		strX := nextText(sc)
		strY := nextText(sc)
		fmt.Println(calcLcs(strX, strY))
	}
}

func calcLcs(strX, strY string) int {
	return lcs(strX, strY, Position{0, 0}, make(map[Position]int))
}

func lcs(strX string, strY string, position Position, memo map[Position]int) int {
	if position.X >= len(strX) || position.Y >= len(strY) {
		return 0
	}
	if v, ok := memo[position]; ok {
		return v
	}
	if strX[position.X] == strY[position.Y] {
		result := lcs(strX, strY, Position{position.X + 1, position.Y + 1}, memo)
		memo[position] = result + 1
		return memo[position]
	} else {
		result1 := lcs(strX, strY, Position{position.X + 1, position.Y}, memo)
		result2 := lcs(strX, strY, Position{position.X, position.Y + 1}, memo)
		var result int
		if result1 > result2 {
			result = result1
		} else {
			result = result2
		}
		memo[position] = result
		return result
	}
}

func nextInt(sc *bufio.Scanner) (int, error) {
	sc.Scan()
	return strconv.Atoi(sc.Text())
}

func nextText(sc *bufio.Scanner) string {
	sc.Scan()
	return sc.Text()
}

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

????????±?????¨??????
"""
# 4/5??§Time Limit Exceeded 5.52s ????????????5s??\???????????????????????????

c = []
def prep_array(X, Y):
    """ ??????0???2?¬???????????????¨??????????????????????????\????????????????????§??????????????????????¨?(1000+1)??\???????????? """
    c = [[0]*1001 for _ in range(1001)]
    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_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_lcs5(X, Y)

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

Python: n=int(input())

for i in range(n):
    a=list(input())
    b=list(input())
    x=len(a)+1
    y=len(b)+1

    r=[[0 for j in range(y)]for i in range(x)]

    for j in range(1,x):
        for k in range(1,y):
            c=max(r[j-1][k-1],r[j-1][k],r[j][k-1])
            if a[j-1]==b[k-1]:
                c=max(r[j-1][k-1]+1,r[j-1][k],r[j][k-1])
            
            r[j][k]=c    
    print(r[x-1][y-1])

Python: def lcs(x, y):
    lx = len(x)
    ly = len(y)
    pcsl = [[0 for i in range(ly + 1)] for j in range(lx + 1)]
    for i in range(lx):
        for j in range(ly):
            if x[i] == y[j]:
                pcsl[i][j] = pcsl[i - 1][j - 1] + 1
            elif pcsl[i - 1][j] > pcsl[i][j - 1]:
                pcsl[i][j] = pcsl[i - 1][j]
            else:
                pcsl[i][j] = pcsl[i][j - 1]
    print(pcsl[i][j])


q = int(input())

for i in range(q):
    ax = input()
    ay = input()
    lcs(ax, ay)

Python: DP_MAX = 1000
dp = [0] * (DP_MAX + 1)

for i in range(DP_MAX + 1):
  dp[i] = [0] * (DP_MAX + 1)

def lcs(s, t):
  slen = len(s)
  tlen = len(t)

  dp_i = dp[0]
  for i in range(1, slen + 1):
    dp_i_1 = dp_i
    dp_i   = dp[i]
    for j in range(1, tlen + 1):
      if s[i-1] == t[j-1]:
        dp_i[j] = dp_i_1[j-1] + 1
      else:
        dp_i[j] = max(dp_i[j-1], dp_i_1[j])

  return dp[slen][tlen]

n = int(raw_input())

for i in range(n):
  x = raw_input()
  y = raw_input()
  print(lcs(x, y))

Python: q = int(input())
for _ in [0]*q:
    s1, s2 = input(), input()
    l1, l2 = len(s1), len(s2)

    dp = [[0]*(l2+1) for _ in [0]*(l1+1)]
    for i, c1 in enumerate(s1, start=1):
        for j, c2 in enumerate(s2, start=1):
            dp[i][j] = max(dp[i][j], dp[i-1][j], dp[i][j-1], dp[i-1][j-1]+(c1==c2))

    print(dp[-1][-1])