longest-common-subsequence.py

# Dynamic Programming implementation of LCS problem


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 0 in (i, j):
                L[i][j] = 0
            elif X[i - 1] == Y[j - 1]:
                L[i][j] = L[i - 1][j - 1] + 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


def print_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 0 in (i, j):
                L[i][j] = 0
            elif X[i - 1] == Y[j - 1]:
                L[i][j] = L[i - 1][j - 1] + 1
            else:
                L[i][j] = max(L[i - 1][j], L[i][j - 1])
    index = L[m][n]
    lcs = [""] * (index + 1)
    lcs[index] = ""

    # Start from the right-most-bottom-most corner and
    # one by one store characters in lcs[]
    i = m
    j = n
    while i > 0 and j > 0:

        # If current character in X[] and Y are same, then
        # current character is part of LCS
        if X[i - 1] == Y[j - 1]:
            lcs[index - 1] = X[i - 1]
            i -= 1
            j -= 1
            index -= 1

        # If not same, then find the larger of two and
        # go in the direction of larger value
        elif L[i - 1][j] > L[i][j - 1]:
            i -= 1
        else:
            j -= 1

    print("LCS of " + X + " and " + Y + " is " + "".join(lcs))


# Driver program to test the above function
X = "AGGTAB"
Y = "GXTXAYB"
print("Length of LCS is ", lcs(X, Y))
print_lcs(X, Y)