Problem:
 Score : 100 points    Problem Statement You are given strings s and t .
Find one longest string that is a subsequence of both s and t .      Notes A subsequence of a string x is the string obtained by removing zero or more characters from x and concatenating the remaining characters without changing the order.      Constraints  s and t are strings consisting of lowercase English letters.  1 \leq |s|, |t| \leq 3000         Input Input is given from Standard Input in the following format:  s  t       Output Print one longest string that is a subsequence of both s and t .
If there are multiple such strings, any of them will be accepted.        Sample Input 1 axyb
abyxb      Sample Output 1 axb  The answer is axb or ayb ; either will be accepted.       Sample Input 2 aa
xayaz      Sample Output 2 aa       Sample Input 3 a
z      Sample Output 3   The answer is (an empty string).       Sample Input 4 abracadabra
avadakedavra      Sample Output 4 aaadara

Solution (Python):
def lcs(x, y):
    m, n = len(x), len(y)
    dp = [[-1] * (n+1) for _ in range(m+1)]

    for i in range(m+1):
        for j in range(n+1):
            if i == 0 or j == 0:
                dp[i][j] = 0
            elif x[i-1] == y[j-1]:
                dp[i][j] = 1 + dp[i-1][j-1]
            else:
                dp[i][j] = max(dp[i-1][j], dp[i][j-1])

    i, j = m, n
    idx = dp[m][n]
    seq = [''] * (idx + 1)

    while i > 0 and j > 0:
        if x[i-1] == y[j-1]:
            seq[idx-1] = x[i-1]
            i -= 1
            j -= 1
            idx -= 1
        elif dp[i-1][j] > dp[i][j-1]:
            i -= 1
        else:
            j -= 1

    return ''.join(seq)


def main():
    str1 = input()
    str2 = input()
    ans = lcs(str1, str2)
    print(ans)


if __name__ == "__main__":
    main()

Solution (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    
        
        
            
            
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    R = lambda: list(map(int, r().split()))
    Rmap = lambda: map(int, r().split())
    Rfloat = lambda: list(map(float, r().split()))
    Rtuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    

    S = r()
    T = r()

    dp = [[0]*(len(T)+1) for _ in range(len(S)+1)]
    
    for si, s in enumerate(S, start=1):
        for ti in range(1, len(T)+1):
            dp[si][ti] = max(dp[si-1][ti-1]+(S[si-1]==T[ti-1]), dp[si][ti-1], dp[si-1][ti])

    ti = len(T)
    si = len(S)
    ans = []
    while si and ti:
        if dp[si][ti] == dp[si-1][ti]:
            si -= 1
        elif dp[si][ti] == dp[si][ti-1]:
            ti -= 1
        else:
            ans.append(S[si-1])
            si = si-1
            ti = ti-1

    print(*ans[::-1], sep='')
    
    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Solution (Python):
import sys
input = lambda: sys.stdin.readline().rstrip()
tdlist = lambda i, j, value=0: [[value] * j for _ in range(i)]

s = input()
t = input()
n, m = len(s), len(t)
dp = tdlist(n+5, m+5)

for i in range(n):
    for j in range(m):
        dp[i+1][j+1] = dp[i][j] + 1 if s[i] == t[j] else max(dp[i+1][j], dp[i][j+1])

res = []
i, j = n, m
while i and j:
    if dp[i][j] == dp[i-1][j]: i -= 1
    elif dp[i][j] == dp[i][j-1]: j -= 1
    else:
        res.append(s[i-1])
        i -= 1; j -= 1

print("".join(res[::-1]))

Solution (Python):
s = input()
t = input()

s_len = len(s)
t_len = len(t)

dp = [[] * (t_len + 1)] * (s_len + 1)

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



for i in range(s_len):
  for j in range(t_len):
    if s[i] == t[j]:
      
      dp[i+1][j+1] = max(dp[i+1][j+1], dp[i][j] + 1)
    else:
      
      dp[i+1][j+1] = max(dp[i+1][j+1], dp[i][j+1])
      dp[i+1][j+1] = max(dp[i+1][j+1], dp[i+1][j])
    


ans = ''
i = s_len
j = t_len

while(i > 0 and j > 0):
    
  if dp[i][j] == dp[i-1][j]:
    i -= 1
  elif dp[i][j] == dp[i][j-1]:
    j -= 1
  else:
    ans = s[i-1] + ans
    i -= 1
    j -= 1
    

print(ans)

Solution (Python):
def main():
  import numpy as np

  s = np.array(list(input()), np.unicode)
  sl = len(s)
  t = np.array(list(input()), np.unicode)
  tl = len(t)
  equal = (s[:, None] == t[None, :])

  dp = [np.zeros(tl + 1, np.int32)]
  for i in range(sl):
    tmp = dp[-1].copy()
    np.maximum(tmp[1:], tmp[:-1] + equal[i], out=tmp[1:])
    np.maximum.accumulate(tmp, out=tmp)
    dp.append(tmp)

  answer = ''
  while sl > 0 and tl > 0:
    if s[sl - 1] == t[tl - 1]:
      sl -= 1
      tl -= 1
      answer += s[sl]
      continue

    if dp[sl - 1][tl] > dp[sl][tl - 1]:
      sl -= 1
    else:
      tl -= 1

  print(answer[::-1])

if __name__ == '__main__':
  main()

Solution (Python):
s = list(input())
t = list(input())
S = len(s)
T = len(t)

dp = [[0] * (S+1) for _ in range(T+1)]

for i in range(T):
    for j in range(S):
        if s[j] == t[i]:
            dp[i+1][j+1] = dp[i][j] + 1
        else:
            dp[i+1][j+1] = max(dp[i+1][j],dp[i][j+1])


ans = []

while T != 0 and  S != 0:
    if dp[T][S] != dp[T-1][S]:
        if dp[T][S] != dp[T][S-1]:
            ans.append(s[S-1])
            T -= 1
            S -= 1
        else:
            S -= 1
    else:
        T -= 1

    
print("".join(ans[::-1]))

Solution (Python):
s1 = input()
s2 = input()
dp = [[0 for i in range(len(s1) + 1)] for j in range(len(s2) + 1)]
for j in range(1, len(s1) + 1):
    for i in range(1, len(s2) + 1):
        if j == 0 or i == 0:
            dp[i][j] = 0
        elif s1[j-1] == s2[i-1]:
            dp[i][j] = dp[i - 1][j - 1] + 1
        else:
            dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
x, y = len(s2), len(s1)
ans = []
while x > 0 and y > 0:
    if dp[x][y] == dp[x - 1][y]:
        x = x - 1
    else:
        if dp[x][y] != dp[x][y-1]:
            ans.append(s2[x-1])
        y = y - 1
ans.reverse()
print("".join(ans))

Solution (Python):

s=input()
t=input()
n=len(s)
m=len(t)
dp=[[0 for _ in range(n+1)] for _ in range(m+1)]
for i in range(m):
    for j in range(n):
        if t[i] == s[j]:
            dp[i+1][j+1] = dp[i][j] + 1
        else:
            dp[i+1][j+1] = max(dp[i+1][j],dp[i][j+1])
r=m
c=n
ans=[]
while r !=0 and c!=0:
    
    if dp[r][c] != dp[r-1][c]:
        if dp[r][c] != dp[r][c-1]:
            ans.append(s[c-1])
            r-=1
            c-=1
        else:
            c-=1
    else:
        r-=1
print("".join(ans[::-1]))

Solution (Python):
import sys
sys.setrecursionlimit(10**5)
s = input()
t = input()



dp = [[0] * (len(t) + 1) for j in range(len(s) + 1)]
for i in range(1,len(s)+1):
    for j in range(1,len(t)+1):
        if s[i-1] == t[j-1]:
            x = 1
        else:
            x = 0
        dp[i][j] = max(dp[i-1][j-1] + x, dp[i-1][j], dp[i][j-1])


def make_ans(a, b):
    if a ==  0 or b == 0:
        return 
    if s[a-1] == t[b-1]:
        make_ans(a-1,b-1)
        ans.append(s[a-1])
    else:
        if a == 0:
            make_ans(a, b - 1)
        elif b == 0:
            make_ans(a - 1,b)
        else:
            if dp[a - 1][b] > dp[a][b - 1]:
                make_ans(a-1,b)
            else:
                make_ans(a,b-1)

ans = []
make_ans(len(s),len(t))
print("".join(ans))

Solution (Python):
S = input()
T = input()
M = len(S)
N = len(T)

dp = [[0] * (N+1) for _ in range(M+1)]

for i, s in enumerate(S):
    for j, t in enumerate(T):
        if s == t:
            dp[i+1][j+1] = max(dp[i+1][j+1], dp[i][j] + 1)
        dp[i+1][j+1] = max(dp[i+1][j+1], dp[i+1][j], dp[i][j+1])

res = ""
while M > 0 and N > 0:
    if dp[M][N] == dp[M-1][N]:
        M -= 1
    elif dp[M][N] == dp[M][N-1]:
        N -= 1
    else:
        res = S[M-1] + res
        M -= 1
        N -= 1

print(res)

Solution (Python):
s = input()
t = input()

s_len = len(s)
t_len = len(t)

dp = [[0]*(t_len+1) for t_item in range(0, s_len+1)]


for i in range(1, s_len+1):
    for j in range(1, t_len+1):
        if (s[i-1] == t[j-1]):
            dp[i][j] = dp[i-1][j-1] + 1
        else :
            dp[i][j] = max(dp[i-1][j], dp[i][j-1])

N=dp[s_len][t_len]
y=s_len
x=t_len
H=[]
while N>0:
    if dp[y][x-1]-dp[y][x]==0:
        x-=1
        continue
    if dp[y-1][x]-dp[y][x]==0:
        y-=1
        continue
    H.append(t[x-1])
    N-=1
    y-=1
    x-=1
print(''.join(H[::-1]))

Solution (Python):
def main():
    X = input()
    Y = input()
    N = len(X)
    M = len(Y)
    dp = [[0]*(M+1) for _ in range(N+1)]
    for i, x in enumerate(X):
        for j, y in enumerate(Y):
            if x == y:
                dp[i+1][j+1] = dp[i][j] + 1
            else:
                dp[i+1][j+1] = max(dp[i][j+1], dp[i+1][j])
    res = ""
    while N > 0 and M > 0:
        if dp[N][M] == dp[N-1][M]:
            N -= 1
        elif dp[N][M] == dp[N][M-1]:
            M -= 1
        else:
            res = X[N-1] + res
            N -= 1
            M -= 1
    print(res)


if __name__ == "__main__":
    main()

Solution (Python):


s=list(input())
t=list(input())

dp=[[0]*(len(t)+1) for i in range(len(s)+1)]

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


ans=""
ns=len(s)
nt=len(t)

while ns>0 and nt>0:
    
    if s[ns-1]==t[nt-1]:
        ans+=s[ns-1]
        ns-=1
        nt-=1
    elif dp[ns][nt]==dp[ns-1][nt]:
        ns-=1
    else:
        nt-=1
        
print(ans[::-1])

Solution (Python):
s = input()
t = input()
n1, n2 = len(s), len(t)
dp = [[0] * (n2 + 1) for _ in range(n1 + 1)]
for i in range(1, n1 + 1):
	for j in range(1, n2 + 1):
		if s[i - 1] == t[j - 1]:
			dp[i][j] = dp[i - 1][j - 1] + 1
		else:
			dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
res = ''
i, j = n1 , n2
while i >= 1 and j >= 1:
	if s[i - 1] == t[j - 1]:
		res += s[i - 1]
		i -= 1
		j -= 1
	elif dp[i][j] == dp[i - 1][j]:
		i -= 1
	else:
		j -= 1
print(res[::-1])

Solution (Python):
S=input()
T=input()

dp=[[0]*(len(T)+1) for _ in range(len(S)+1)]

for i in range(1,len(S)+1):
    s=S[i-1]
    for j in range(1,len(T)+1):
        t=T[j-1]
        if s==t:
            dp[i][j]=dp[i-1][j-1]+1
        else:
            dp[i][j]=max(dp[i-1][j],dp[i][j-1])

ans=""
i=len(S)
j=len(T)
while i>0 and j>0:
    if dp[i][j]==dp[i-1][j]:
        i-=1
    elif dp[i][j]==dp[i][j-1]:
        j-=1
    elif dp[i][j]==dp[i-1][j-1]+1:
        ans+=S[i-1]
        i-=1
        j-=1
print("".join(reversed(list(ans))))

Solution (Python):
S = input()
T = input()
lens = len(S)
lent = len(T)

DP = [[0]*(lent+1) for _ in range(lens+1)]

for i in range(1,lens+1):
    for j in range(1,lent+1):
        if S[i-1] == T[j-1]:
            DP[i][j] = max(DP[i][j],DP[i-1][j-1]+1)
        DP[i][j] = max(DP[i][j],DP[i][j-1])
        DP[i][j] = max(DP[i][j],DP[i-1][j])
ans = ""
i = lens
j = lent
while i > 0 and j > 0:
    if DP[i][j] == DP[i-1][j]:
        i -= 1
    elif DP[i][j] == DP[i][j-1]:
        j -= 1
    else:
        ans += S[i-1]
        i -= 1
        j -= 1
print(ans[::-1])

Solution (Python):
s = input()
t = input()

ls = len(s)
lt = len(t)
dp = [[0 for _ in range(lt+1)] for _ in range(ls+1)]
for i in range(ls):
    for j in range(lt):
        dp[i+1][j+1] = max(dp[i+1][j], dp[i][j+1])
        if s[i] == t[j]:
            dp[i+1][j+1] = max(dp[i+1][j+1], dp[i][j] + 1)

ans = []
x = ls
y = lt
while x + y > 0:
    if dp[x][y] == dp[x-1][y] and x != 0:
        x -= 1
    elif dp[x][y] == dp[x][y-1] and y != 0:
        y -= 1
    else:
        ans.append(s[x-1])
        x -= 1
        y -= 1

print(''.join(reversed(ans)))

Solution (Python):
S, T = input(), input()
sLen, tLen = len(S), len(T)
dp = [[0 for _ in range(tLen+1)] for _ in range(sLen+1)]
for i in range(sLen):
    for j in range(tLen):
        if S[i] == T[j]:
            dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i][j] + 1)
        dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i + 1][j], dp[i][j + 1])
i, j = sLen, tLen
ans = ''
while i != 0 and j != 0:
    if dp[i][j] == dp[i-1][j]:
        i -= 1
    elif dp[i][j] == dp[i][j-1]:
        j -= 1
    else:
        ans = S[i-1] + ans
        i -= 1
        j -= 1
print(ans)

Solution (Python):

import sys

S = sys.stdin.readline().rstrip()
T = sys.stdin.readline().rstrip()
sn, tn = len(S), len(T)
dp = [[0 for j in range(tn)] for i in range(sn)]


for j in range(tn):
    dp[0][j] = dp[0][j-1]
    if S[0]==T[j]:
        dp[0][j] = 1
for i in range(sn):
    dp[i][0] = dp[i-1][0]
    if S[i]==T[0]:
        dp[i][0] = 1
        

for i in range(1, sn):
    for j in range(1, tn):
        if S[i] == T[j]:
            dp[i][j] = dp[i-1][j-1]+1
        else:
            dp[i][j] = max(dp[i-1][j], dp[i][j-1])



i,j= sn-1, tn-1
ans =''
while True:
    if i ==0:
        if dp[i][j]==1:
            ans+= S[0]
        print(ans[::-1])
        break
    if j ==0:
        if dp[i][j]==1:
            ans+= T[0]
        print(ans[::-1])
        break
    if dp[i-1][j] == dp[i][j]:
        i-=1
    elif dp[i][j-1] == dp[i][j]:
        j-=1
    elif dp[i-1][j-1] +1 == dp[i][j]:
        ans += S[i]
        i-=1
        j-=1

Solution (Python):
"""
【最長共通部分列問題】
2つの文字列s,tが与えられたときの2つの共通部分文字列の長さの最大値とその文字列
!!制約!!
1<=n,m<=1000
"""



s=input()
t=input()
n=len(s)
m=len(t)
dp=[[0 for i in range(m+1)] for j in range(n+1)]






for i in range(n):
    for j in range(m):
        if s[i]==t[j]:
            dp[i+1][j+1]=dp[i][j]+1 
        else:
            dp[i+1][j+1]=max(dp[i][j+1],dp[i+1][j])



ans = ''
while(dp[n][m]>0):
  if dp[n][m] == dp[n-1][m-1] +1 and dp[n][m] == dp[n-1][m] +1 and dp[n][m] == dp[n][m-1] +1:
    ans += s[n-1]
    n -= 1
    m -= 1
  elif dp[n-1][m] > dp[n][m-1]:
    n -= 1
  else:
    m -= 1
print(''.join(reversed(list(ans))))

Solution (Python):
s=input()
t=input()
n=len(s)
m=len(t)
dp=[[0 for i in range(m+1)] for j in range(n+1)]
for i in range(n):
    for j in range(m):
        if s[i]==t[j]:
            dp[i+1][j+1]=dp[i][j]+1
        else:
            dp[i+1][j+1]=max(dp[i][j+1],dp[i+1][j])
ans = ''
while(dp[n][m]>0):
  if dp[n][m] == dp[n-1][m-1] +1 and dp[n][m] == dp[n-1][m] +1 and dp[n][m] == dp[n][m-1] +1:
    ans = ''.join([s[n-1],ans])
    n -= 1
    m -= 1
  elif dp[n-1][m] > dp[n][m-1]:
    n -= 1
  else:
    m -= 1
print(ans)

Solution (Python):
s = input()
t = input()

dp = [[0] * (len(t) + 1) for _ in range(len(s) + 1)]

for i in range(len(s)):
    for j in range(len(t)):
        if s[i] == t[j]:
            dp[i + 1][j + 1] = dp[i][j] + 1
        dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i][j + 1], dp[i + 1][j])


i, j = len(s), len(t)

ans = []
while i > 0 and j > 0:
    if s[i - 1] == t[j - 1] and dp[i][j] == dp[i - 1][j - 1] + 1:
        ans.append(s[i - 1])
        i -= 1
        j -= 1
    else:
        if dp[i - 1][j] == dp[i][j]:
            i -= 1
        else:
            j -= 1
print(*reversed(ans), sep='')

Solution (Python):
s = input()
t = input()

dp = [[0 for j in range(len(t)+1)] for i in range(len(s)+1)]
dp[0][0] = 0

for i in range(len(s)):
    for j in range(len(t)):
        if s[i] == t[j]:
            dp[i+1][j+1] = max(dp[i][j+1],dp[i+1][j],dp[i][j]+1)
        else:
            dp[i+1][j+1] = max(dp[i][j+1],dp[i+1][j])

ans = ''
i,j = len(s),len(t)

while i>0 and j>0:
    if dp[i][j] == dp[i-1][j]:
        i -= 1
    elif dp[i][j] == dp[i][j-1]:
        j -= 1
    else:
        ans = s[i-1]+ans
        i -= 1
        j -= 1
        
print(ans)

Solution (Python):
def LCS(s,t): 
    global dp,ns,nt
    ns=len(s)
    nt=len(t)
    dp=[[0 for _ in range(nt+1)] for _ in range(ns+1)]
    for i in range(1,ns+1):
        for j in range(1,nt+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] )
    

def recovery(s,t): 
    LCS(s,t)
    x=ns
    y=nt
    ans=[]
    while x>0 and y>0:
        if dp[x][y]==dp[x][y-1]:
            y-=1
        elif dp[x][y]==dp[x-1][y]:
            x-=1
        else:
            x-=1
            y-=1
            ans.append(s[x])
    ans.reverse()
    print(''.join(ans))
    
def main():
    s=list(input())
    t=list(input())
    recovery(s,t)
    
if __name__ == "__main__":
    main()

Solution (Python):
def main():
    s = input()
    t = input()
    v = [0] * (len(t) + 1)
    dp = [v]
    for i, si in enumerate(s, 1):
        u, v = v, v.copy()
        dp.append(v)
        ll, ul = 0, 0
        for j, ti in enumerate(t, 1):
            uu = u[j]
            if si == ti:
                v[j] = ll = ul + 1
            else:
                if ll > uu:
                    v[j] = ll
                else:
                    ll = uu
            ul = uu
    k = dp[i][j]
    r = ''
    while k:
        if dp[i - 1][j] == k:
            i -= 1
        elif dp[i][j - 1] == k:
            j -= 1
        else:
            k -= 1
            i -= 1
            j -= 1
            r += s[i]
    print(r[::-1])

main()

Solution (Python):
import numpy as np

s = np.array(list(input()), np.unicode)
sl = len(s)
t = np.array(list(input()), np.unicode)
tl = len(t)
equal = (s[:, None] == t[None, :])

dp = [np.zeros(tl + 1, np.int32)]
for i in range(sl):
    tmp = dp[-1].copy()
    np.maximum(tmp[1:], tmp[:-1] + equal[i], out=tmp[1:])
    np.maximum.accumulate(tmp, out=tmp)
    dp.append(tmp)

answer = ''
while sl > 0 and tl > 0:
    if s[sl - 1] == t[tl - 1]:
        sl -= 1
        tl -= 1
        answer += s[sl]
        continue

    if dp[sl - 1][tl] > dp[sl][tl - 1]:
        sl -= 1
    else:
        tl -= 1

print(answer[::-1])

Solution (Python):
s=input()
t=input()
ma=0
a=[0,0]
dp=[[0 for i in range(len(t)+1)] for j in range(len(s)+1)]
for i in range(1,len(s)+1):
    for j in range(1,len(t)+1):
        dp[i][j]=max(dp[i-1][j],dp[i][j-1])
        if s[i-1]==t[j-1]:
            dp[i][j]=max(dp[i][j],1+dp[i-1][j-1])
i=len(s)
j=len(t)

ss=""
while i and j:
    if dp[i][j]==dp[i-1][j]:
        i-=1
    elif dp[i][j]==dp[i][j-1]:
        j-=1
    else:
        ss+=s[i-1]
        i-=1
        j-=1
ss=ss[-1::-1]
print(ss)

Solution (Python):
s = input()
t = input()

dp = [[0]*(len(t)+1) for _ in range(len(s)+1)]

for i in range(len(s)):
    for j in range(len(t)):
        if (s[i]==t[j]):
            dp[i+1][j+1] = dp[i][j]+1
        else:
            dp[i+1][j+1] = max(dp[i+1][j],dp[i][j+1])
        
i = len(s)
j = len(t)
ans = ''
while i>0 and j>0:
    if (dp[i-1][j] == dp[i][j]):
        i -= 1
    elif (dp[i][j-1] == dp[i][j]):
        j -= 1
    else:
        ans = s[i-1]+ans
        i -= 1
        j -= 1

print(ans)

Solution (Python):
import sys
input = sys.stdin.readline


def main():
    s = input()[:-1]
    t = input()[:-1]

    S = len(s)
    T = len(t)
    dp = [[0]*(T+1) for _ in range(S+1)]
    for i in range(S):
        for j in range(T):
            if s[i:i+1] == t[j:j+1]:
                dp[i+1][j+1] = max(dp[i+1][j+1], dp[i][j] + 1)
            dp[i+1][j+1] = max(dp[i+1][j+1], dp[i+1][j])
            dp[i+1][j+1] = max(dp[i+1][j+1], dp[i][j+1])
    
    ans = ""
    i = S
    j = T
    while i>0 and j>0:
        if dp[i][j] == dp[i-1][j]:
            i -= 1
        elif dp[i][j] == dp[i][j-1]:
            j -= 1
        else:
            ans = s[i-1:i] + ans
            i -= 1
            j -= 1
    
    
    
    print(ans)


if __name__ == '__main__':
    main()