Go: package main

import "fmt"

func initialize_grid(width int,height int)[][]int{
	var grid [][]int
	for i:=0;i<height+1;i++{
		var grid_row  []int
		for j:=0;j<width+1;j++{
			grid_row = append(grid_row,0)
		}
		grid = append(grid,grid_row[:])
	}
	return grid
}

func ma(x int,y int)int{
	if x >= y{
		return x
	}else{
		return y
	}
}

func main()  {
	//Take input
	var num int
	var st1,st2 string
	var string_pairs [][]string
	fmt.Scan(&num)
	for i:=0;i<num;i++{
		var string_pair []string
		fmt.Scan(&st1)
		fmt.Scan(&st2)
		string_pair = append(string_pair,st1,st2)
		string_pairs = append(string_pairs,string_pair)
	}
	//DP
	//initialize grid
	for i:=0;i<num;i++{
		string_1 := string_pairs[i][0]
		string_2 := string_pairs[i][1]

		dp := initialize_grid(len(string_2),len(string_1))

		for j:=1;j<len(string_1)+1;j++{
			for k:=1;k<len(string_2)+1;k++{
				if string_1[j-1] == string_2[k-1]{
					dp[j][k] = dp[j-1][k-1] + 1
				}else{
					dp[j][k] = ma(dp[j-1][k],dp[j][k-1])
				}
			}
		}
		fmt.Println(dp[len(string_1)][len(string_2)])
	}
}

Python: def lcs(x, y):
    m, n = len(x), len(y)
    dp = [0] * (n+1)
    
    for xi in x:
        temp = dp[:]
        for j in range(n):
            if xi == y[j]:
                dp[j+1] = temp[j] + 1
            elif dp[j+1] < dp[j]:
                dp[j+1] = dp[j]
    
    return dp[-1]

N = int(input())
for _ in range(N):
    x = input()
    y = input()
    print(lcs(x, y))

Python: def lcs_len(x, y):
    indices = [0]
    for y_i in y:
        t_index = 0
        for i, index in enumerate(indices, 1):
            c_index = x.find(y_i, t_index) + 1
            if c_index:
                if i < len(indices):
                    t_index = indices[i]
                    indices[i] = min(c_index, t_index)
                else:
                    indices.append(c_index)
                    break
    print(len(indices) - 1)


def answer(X, Y):
    m, n = len(X), len(Y)
    C = [[0] * (n + 1) for _ in range(m + 1)]
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if X[i - 1] == Y[j - 1]:
                C[i][j] = C[i-1][j-1] + 1
            else:
                C[i][j] = max(C[i][j -1], C[i -1][j])
    return C[m][n]


if __name__ == '__main__':
    q = int(input())
    for _ in range(q):
        X = list(input())
        Y = list(input())
        print(lcs_len(X, Y))

Python: #dj 16D8101012J ito jun
n = int(input())
for _ in range(n):
    a = input()
    b = input()
    na=len(a)
    nb=len(b)
    array = [[0 for i in range(nb+1)] for j in range(na+1)]
    for i,x in enumerate(a,1):
        prerow=array[i-1]
        row=array[i]
        for j,y in enumerate(b,1):
            if x == y:
                row[j]=prerow[j-1]+1
            else:
                row[j] = max(prerow[j],row[j-1])
    print(array[na][nb])

Python: def LCS(str1,str2):
    A = [0 for _ in range(len(str2)+1)]
    for i in range(len(str1)):
        A_copy = A[:]
        for j in range(len(str2)):
            if(str1[i]==str2[j]):
                A[j+1] = A_copy[j]+1
            elif(A[j] > A[j+1]):
                A[j+1] = A[j]
    return A[-1]


m = int(input())
for i in range(m):
    str1 = input()
    str2 = input()
    print(LCS(str1,str2))

Python: q = int(input())

def lcs(X, Y):
    x_len = len(X)
    y_len = len(Y)
    dp = [[0 for _ in range(y_len+1)] for _ in range(x_len+1)]
    
    for i in range(1, x_len+1):
        for j in range(1, y_len+1):
            if X[i-1] == Y[j-1]:
                dp[i][j] = dp[i-1][j-1] + 1
            else:
                dp[i][j] = max(dp[i-1][j], dp[i][j-1])
                               
    return max(max(dp))
    
for _ in range(q):
    X = input()
    Y = input()
    print(lcs(X, Y))

Python: n = int(input())
for _ in range(n):
    a, b = input(), input()
    indices = []
    for cb in b:
        bgn_idx = 0
        for i, cur_idx in enumerate(indices):
            chr_idx = a.find(cb, bgn_idx) + 1
            if not chr_idx:
                break
            if chr_idx < cur_idx:
                indices[i] = chr_idx
            bgn_idx = cur_idx
        else:
            chr_idx = a.find(cb, bgn_idx) + 1
            if chr_idx:
                indices.append(chr_idx)
    print(len(indices))

Python: import sys
sys.setrecursionlimit(20000)

q = int(input())
X = ""
Y = ""
memo = [[]]

def LCS(x, y):
    if (x < 0) or (y < 0):
        return 0
    elif memo[x][y] != -1:
        return memo[x][y]
    else:
        memo[x][y] = max(LCS(x-1,y), LCS(x,y-1), LCS(x-1, y-1)+int(X[x] == Y[y]))
        return memo[x][y]

for c in range(q):
    X = input()
    Y = input()
    memo = [[-1 for j in range(len(Y))] for i in range(len(X))]
    print(LCS(len(X)-1, len(Y)-1))

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

Python: def num_substr(s, t):
    sl = len(s)
    tl = len(t)
    dp = {}
    for i in range(sl + 1):
        dp[i] = {0: 0}
    for j in range(st + 1):
        dp[0][j] = 0
     
    for i in range(1,sl+1):
        si_1 = s[i-1]
        dpi = dp[i]
        dpi_1 = dp[i-1]
        for j in range(1,tl+1):
            d=1 if si_1 == t[j-1] and dpi_1[j-1] == dpi[j-1] else 0
            dpi[j] = max(dpi_1[j] ,
                           dpi[j-1] +d)
    return dp[len(s)][len(t)]
 
n = int(input())
for i in range(n):
    s = input()
    t = input()
    print(num_substr(s,t))

Python: q = int(input())
for i in range(q):
    x = input().rstrip()
    y = input().rstrip()
    n = len(x)
    m = len(y)
    d = [[0 for _ in range(m+1)] for _ in range(n+1)]
    for i in range(n):
        for j in range(m):
            if x[i] == y[j]:
                d[i+1][j+1] = d[i][j]+1
            else:
                d[i+1][j+1] = max(d[i+1][j],d[i][j+1])
    print(d[n][m])

Python: def lcs(s1, s2):
    dp = []
    for s2_k in s2:
        bgn_idx = 0
        for i, cur_idx in enumerate(dp):
            chr_idx = s1.find(s2_k, bgn_idx) + 1
            if not chr_idx:
                break
            dp[i] = min(cur_idx, chr_idx)
            bgn_idx = cur_idx
        else:
            chr_idx = s1.find(s2_k, bgn_idx) + 1
            if chr_idx:
                dp.append(chr_idx)
    return len(dp)

def solve():
    N = int(input())
    for _ in range(N):
        x = input()
        y = input()
        print(lcs(x, y))

if __name__ == '__main__':
    solve()

Python: """
problem statment url: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_10_C
"""

from __future__ import division
from sys import stdin, maxint

def lcs(s1, s2):
	dp = [[0 for _ in range(len(s2) + 1)] for _ in range(len(s1) + 1)]

	for i in range(1, len(s1) + 1):
		for j in range(1, len(s2) + 1):
			if s1[i - 1] == s2[j - 1]:
				dp[i][j] = dp[i - 1][j - 1] + 1
			else:
				dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])

	return dp[len(s1)][len(s2)]

if __name__ == '__main__':
	tc = int(stdin.readline())
	for _ in range(tc):
		sa = stdin.readline().strip()
		sb = stdin.readline().strip()
		print(lcs(sa, sb))

Python: import numpy as np
def f(i,j):
    if i == 0 or j == 0:
        if s1[i] == s2[j]:
            x[i][j] = 1
        else:
            if i == 0:
                x[i][j] = x[i][j-1]
            else:
                x[i][j] = x[i-1][j]
    elif s1[i] == s2[j]:
        x[i][j] = max(x[i-1][j-1]+1,x[i][j-1],x[i-1][j])
    else:
        x[i][j] = max(x[i-1][j-1],x[i][j-1],x[i-1][j])

n = int(input())
for i in range(n):
    s1 = input()
    s2 = input()
    x = np.zeros((len(s1),len(s2)))
    for j in range(len(s1)):
        for k in range(len(s2)):
            f(j,k)
            
    print(x[len(s1)-1][len(s2)-1])
#print(*x)