'''
Given two sequences, find the length of longest subsequence present in both of them. Both the strings are of uppercase.

Example 1:
Input:
A = 6, B = 6
str1 = ABCDGH
str2 = AEDFHR
Output: 3
Explanation: LCS for input Sequences
"ABCDGH" and "AEDFHR" is "ADH" of
length 3.

Example 2:
Input:
A = 3, B = 2
str1 = ABC
str2 = AC
Output: 2
Explanation: LCS of "ABC" and "AC" is
"AC" of length 2.

https://www.geeksforgeeks.org/longest-common-subsequence-dp-4/

using memoization --> https://www.geeksforgeeks.org/longest-common-subsequence-dp-using-memoization/

'''
def lcs(X , Y): 
    # find the length of the strings 
    m = len(X) 
    n = len(Y) 
  
    # declaring the array for storing the dp values 
    L = [[None]*(n+1) for i in range(m+1)] 
  
    """Following steps build L[m+1][n+1] in bottom up fashion 
    Note: L[i][j] contains length of LCS of X[0..i-1] 
    and Y[0..j-1]"""
    for i in range(m+1): 
        for j in range(n+1): 
            if i == 0 or j == 0 : 
                L[i][j] = 0
            elif X[i-1] == Y[j-1]: 
                L[i][j] = 1 + L[i-1][j-1]
            else: 
                L[i][j] = max(L[i-1][j] , L[i][j-1]) 
  
    # L[m][n] contains the length of LCS of X[0..n-1] & Y[0..m-1] 
    return L[m][n] 
#end of function lcs 
  
  
# Driver program to test the above function 
X = "AGGTAB"
Y = "GXTXAYB"
print(lcs(X, Y))