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.



Sample input:
3
abcbdab
bdcaba
abc
abc
abc
bc


Sample output:
4
3
2

Submission status: Runtime Error

Solution code:
def Ics(x, y):
    a = len(x)
    b = len(y)
    c1 = [0] * (b + 1)

    for i in range(a):
        d = x[i]
        c2 = c1[:]
        for j in range(n):
            if d == y[j]:
                c1[j + 1] = c2[j] + 1
            elif c1[j + 1] < c1[j]:
                c1[j + 1] = c1[j]
    return c1[-1]

q = int(input().rstrip())
r = []
for k in range(q):
    s1 = input().rstrip()
    s2 = input().rstrip()
    r.append(Ics(s1, s2))

print(*r, sep = "/n")

Submission status: Runtime Error

Solution code:
q = int(input())
t = []
for i in range(q):
    X = input()
    Y = input()
    m = len(X)
    n = len(Y)
    c1 = [0] * (n + 1)
    for i in range(m):
        d = X[i]
        c2 = c1[:]
        for j in range(n):
            if (d == Y[j]):
                c1[j + 1] = c2[j] + 1
            elif (c1[j + 1] < c1[j]):
                c1[j + 1] = c1[j]
    return (c1[-1])
    print(Ics(s1, s2))

Submission status: Runtime Error

Solution code:
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))

Submission status: Runtime Error

Solution code:
import sys
import functools as ft
sys.setrecursionlimit(10000)

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

def print_memo() :
    for x in range(len(X)):
        print(ft.reduce(lambda x,y: x + str(y) + "\t" ,memo[x], ""))

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

Submission status: Runtime Error

Solution code:
from collections import defaultdict
q = int(input())
for _ in range(q):
    x = input()
    y = input()
    len_x = len(x)
    len_y = len(y)
    if len_x < len_y:
        len_x, len_y = len_y, len_x
        x, y = y, x
    c = defaultdict(list)
    for i, s in enumerate(x):
        c[s].append(i)
    ans = 0
    def g(li, a):
        for i in li:
            if i >= a:
                return i
        return -1
    def f(x_i, y_i, cnt):
        if x_i >= len_x or y_i >= len_y:
            global ans
            if ans < cnt:
                ans = cnt
            return
        f(x_i, y_i + 1, cnt)
        s = g(c[y[y_i]], x_i)
        if s != -1:
            f(s + 1, y_i + 1, cnt + 1)
    f(0, 0, 0)
    print(ans)

Submission status: Runtime Error

Solution code:
import sys
sys.setrecursionlimit(200000)
from collections import defaultdict
from bisect import bisect_left, bisect, insort_left, insort
q = int(input())
for _ in range(q):
    x = input()
    y = input()
    len_x = len(x)
    len_y = len(y)
    if len_x < len_y:
        len_x, len_y = len_y, len_x
        x, y = y, x
    c = defaultdict(list)
    for i, s in enumerate(x):
        c[s].append(i)
    ans = 0
    @lru_cache(maxsize=1000)
    def f(x_i, y_i, cnt):
        if x_i >= len_x or y_i >= len_y:
            global ans
            if ans < cnt:
                ans = cnt
            return
        f(x_i, y_i + 1, cnt)
        s = bisect_left(c[y[y_i]], x_i)
        if s < len(c[y[y_i]]) and c[y[y_i]][s] < len_x:
            f(c[y[y_i]][s] + 1, y_i + 1, cnt + 1)
    f(0, 0, 0)
    print(ans)

Submission status: Runtime Error

Solution code:
a=[]
for _ in[0]*int(input()):
 X,z=input(),[]
 for y in input():
  s=i=0
  for k in z:
   t=X.find(y,s)+1
   if t<1:break
   if t<k:z[i]=t
   s=k;i+=1
  else:
   t=X.find(y,s)+1
   if t:z+=[t]
 a+=[len(z)]
print('\n'.join(a))

Submission status: Runtime Error

Solution code:
i=input
for _ in[0]*int(i()):
 X,z=i(),[]
 for y in i():
  s=i=0
  for k in z:
   t=X.find(y,s)+1
   if t<1:break
   if t<k:z[i]=t
   s=k;i+=1
  else:
   t=X.find(y,s)+1
   if t:z+=[t]
 print(len(z))

Submission status: Runtime Error

Solution code:
def solver(str_1 ,str_2):
  dp = [[0] * (len(str_2) + 1) for i in range(len(str_1) + 1)]
  for r in range(len(str_2)):
    for c in range(len(str_1)):
      if str_2[r] == str_1[c]:
        dp[r + 1][c + 1] = dp[r][c] + 1
      else:
        dp[r + 1][c + 1] = max(dp[r + 1][c], dp[r][c + 1])
  return dp[len(str_2)][len(str_1)]

n = int(input())
for _ in range(n):
  str_1 = input()
  str_2 = input()
  print(solver(str_1, str_2))

Submission status: Runtime Error

Solution code:
n = int(input())

c = [[0, 0]for i in range(n)]

def lcs(x, y):
    xlen = len(x)
    ylen = len(y)
    if xlen == 0 or ylen == 0:
        return 0
    elif x[xlen-1] == y[ylen-1]:
        return lcs(x[:-1], y[:-1]) + 1
    else:
        return max(lcs(x, y[:-1]), lcs(x[:-1], y))

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

Submission status: Runtime Error

Solution code:
n = int(input())

def lcs(x, y):
    xlen = len(x)
    ylen = len(y)
    if xlen == 0 or ylen == 0:
        return 0
    elif x[xlen-1] == y[ylen-1]:
        return lcs(x[:-1], y[:-1]) + 1
    else:
        return max(lcs(x, y[:-1]), lcs(x[:-1], y))

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

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Fri May  4 20:33:37 2018
ALDS1_10_C
@author: maezawa
"""

def longest(x, y):
    m = len(x)
    n = len(y)
    c = [[0 for _ in range(m+1)] for _ in range(n+1)]
    for i in range(m):
        for j in range(n):
            print(i,j)
            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 c[m-1][n-1]
                
    

q = int(input())

for i in range(q):
    x = input()
    y = input()
    
    print(longest(x, y))

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Fri May  4 20:33:37 2018
ALDS1_10_C
@author: maezawa
"""

def longest(x, y):
    m = len(x)
    n = len(y)
    c = [[0 for _ in range(m+1)] for _ in range(n+1)]
    for i in range(m):
        for j in range(n):
            #print(i,j)
            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 c[m-1][n-1]
                
    

q = int(input())

for i in range(q):
    x = input()
    y = input()
    
    print(longest(x, y))

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Fri May  4 20:33:37 2018
ALDS1_10_C Using Numpy
@author: maezawa
"""

import numpy as np

def longest(x, y):
    m = len(x)
    n = len(y)
    maxl = 0
    c = np.zeros((m+1, n+1), dtype=int)
    for i in range(m):
        for j in range(n):
            #print(i,j)
            if x[i] == y[j]:
                c[i, j] = c[i-1, j-1] + 1
            else:
                c[i, j] = max(c[i-1, j], c[i, j-1])
            maxl = max(maxl, c[i, j])
    return maxl

q = int(input())
for i in range(q):
    x = input()
    y = input()
    print(longest(x, y))

Submission status: Runtime Error

Solution code:
def lcs(s1,s2):    
    if len(str_a) == 0 or len(str_b) == 0:
        return 0
    dp = [[0 for _ in range(len(str_b) + 1)] for _ in range(len(str_a) + 1)]
    for i in range(1, len(str_a) + 1):
        for j in range(1, len(str_b) + 1):
            if str_a[i-1] == str_b[j-1]:
                dp[i][j] = dp[i-1][j-1] + 1
            else:
                dp[i][j] = max([dp[i-1][j], dp[i][j-1]])
  #print ("length of LCS is :",dp[len(str_a)][len(str_b)])
  return dp[len(str_a)][len(str_b)]


#print (find_lcseque('abdfg','abcdfg')  )
n=int(input())
for i in range(n):
    s1=input()
    s2=input()
    #rt=find_lcseque(s1,s2)
    rt=lcs(s1,s2)
    print(rt)

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-
import numpy as np

def lcs_sol(x, y):
    n = len(x)
    m = len(y)
    dp = np.zeros((n + 1) * (m + 1)).reshape(n + 1, m + 1)

    for i in range(1, n + 1):
        for j in range(1, m + 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 dp[n][m]


if __name__ == '__main__':
    import sys
    q = int(sys.stdin.readline().strip())
    for i in range(q):
        x = sys.stdin.readline().strip()
        y = sys.stdin.readline().strip()
        print(lcs_sol(x, y))

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-
import numpy as np

def lcs_sol(x, y):
    n = len(x)
    m = len(y)
    dp = np.zeros((n + 1) * (m + 1), dtype=int).reshape(n + 1, m + 1)

    for i in range(1, n + 1):
        for j in range(1, m + 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 dp[n][m]


if __name__ == '__main__':
    import sys
    q = int(sys.stdin.readline().strip())
    for i in range(q):
        x = sys.stdin.readline().strip()
        y = sys.stdin.readline().strip()
        print(lcs_sol(x, y))

Submission status: Runtime Error

Solution code:
import numpy as np

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-
import functools


def lcs(x, y):
    n = len(x)
    m = len(y)
    return rec(x, y, n, m)


@functools.lru_cache(maxsize=None)
def rec(x, y, i, j):
    if i == 0 or j == 0:
        return 0
    elif x[i - 1] == y[j - 1]:
        return rec(x, y, i - 1, j - 1) + 1
    else:
        return max(rec(x, y, i, j - 1), rec(x, y, i - 1, j))


if __name__ == '__main__':
    import sys
    q = int(sys.stdin.readline().strip())
    for i in range(q):
        x = sys.stdin.readline().strip()
        y = sys.stdin.readline().strip()
        print(lcs(x, y))

Submission status: Runtime Error

Solution code:
def lcs(str1,str2):
    c=[[0 for _ in range(100)] for _ in range(100)]
    m=len(str1)
    n=len(str2)
    maxl=0
    str1=" "+str1
    str2=" "+str2

    i=1
    j=1
    while(i<=m):
        while(j<=n):
            if(str1[i]==str2[j]):
                c[i][j]=c[i-1][j-1]+1
              #  print(c[i][j])
            else:
                c[i][j]=max(c[i-1][j],c[i][j-1])
            maxl=max(maxl,c[i][j])
            j+=1
        i+=1
        j=0

    return maxl

def main():
    n=int(input())
    i=0
    while(i<n):
        str1=str(input())
        str2=str(input())
        print(int(lcs(str1,str2)))
        i+=1

main()

Submission status: Runtime Error

Solution code:
def lcs(str1,str2):
    c=[[0 for _ in range(1000)] for _ in range(1000)]
    m=len(str1)
    n=len(str2)
    maxl=0
    str1=" "+str1
    str2=" "+str2

    i=1
    j=1
    while(i<=m):
        while(j<=n):
            if(str1[i]==str2[j]):
                c[i][j]=c[i-1][j-1]+1
              #  print(c[i][j])
            else:
                c[i][j]=max(c[i-1][j],c[i][j-1])
            maxl=max(maxl,c[i][j])
            j+=1
        i+=1
        j=0

    return maxl

def main():
    n=int(input())
    i=0
    while(i<n):
        str1=str(input())
        str2=str(input())
        print(int(lcs(str1,str2)))
        i+=1

main()

Submission status: Runtime Error

Solution code:
#coding:utf-8
from copy import deepcopy
import numpy as np
n = int(input())

def lcs(X,Y):
    m = len(X)
    n = len(Y)
    c = [[False for i in range(n+1)] for j in range(m+1)]
    for i in range(m+1):
        c[i][0] = 0
    for i in range(n+1):
        c[0][i] = 0
    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
            elif c[i-1][j] >= c[i][j-1]:
                c[i][j] = c[i-1][j]
            else:
                c[i][j] = c[i][j-1]
    c = np.array(c)
    return c[m][n]
                            
        
for  i in range(n):
    A = input()
    B = input()
    a = lcs(A,B)
    print(a)

Submission status: Runtime Error

Solution code:
#coding:utf-8
from copy import deepcopy
import numpy as np
n = int(input())

def lcs(X,Y):
    m = len(X)
    n = len(Y)
    c = [[False for i in range(n+1)] for j in range(m+1)]
    for i in range(m+1):
        c[i][0] = 0
    for i in range(n+1):
        c[0][i] = 0
    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
            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 c[m][n]
                            
        
for  i in range(n):
    A = input()
    B = input()
    a = lcs(A,B)
    print(a)

Submission status: Runtime Error

Solution code:
import sys

def longestcommonsubsequence(seq1, seq2):
    a,b = len(seq1)+1, len(seq2)+1
    length = [[0 for i in range(b)] for j in range(a)]

    for i in range(a):
        e1=seq[i-1]
        for j in range(b):
            if i==0 or j==0:
                length[i][j]=0
            else:
                if e1 == seq2[j-1]:
                    length[i][j] = length[i-1][j-1] + 1
                else:
                    length[i][j] = max(length[i-1][j], length[i][j-1])
    return length[a-1][b-1]

n = input()
for i2 in range(n):
    seq1 = raw_input()
    seq2 = raw_input()

    print longestcommonsubsequence(seq1, seq2)

Submission status: Runtime Error

Solution code:
import sys

def longestcommonsubsequence():
    seq1 = raw_input()
    seq2 = raw_input()

    a,b = len(seq1), len(seq2)
    x1 = [0 for i in range(b+1)]
    for i in range(a+1):
        e1 = seq[i]
        x2 = x1
        x1 = [0 for i2 in range(b+1)]
        tmp = 0
        for j in range(b):
            if e1 == seq2[j]:
                tmp = x2[j] + 1
            else:
                tmp = max(x2[j+1], tmp)
            x1[j+1] = tmp
    return x1[-1]

n = input()
for i2 in range(n):

    print longestcommonsubsequence()

Submission status: Runtime Error

Solution code:
import sys

def longestcommonsubsequence():
    seq1 = raw_input()
    seq2 = raw_input()

    a,b = len(seq1), len(seq2)
    x1 = [0 for i in range(b+1)]
    for i in range(a+1):
        e1 = seq1[i]
        x2 = x1
        x1 = [0 for i2 in range(b+1)]
        tmp = 0
        for j in range(b):
            if e1 == seq2[j]:
                tmp = x2[j] + 1
            else:
                tmp = max(x2[j+1], tmp)
            x1[j+1] = tmp
    return x1[-1]

n = input()
for i2 in range(n):

    print longestcommonsubsequence()