distance.py

import numpy

def EditDistance(s1, s2):
    """ Computes the edit distance of two strings
    (str, str) -> (int, 2D-array) """
    ln_s1 = len(s1)
    ln_s2 = len(s2)

    # Initializing the matrix
    Matrix = numpy.zeros((ln_s1+1 , ln_s2+1))
    for i in range(ln_s2+1):
        Matrix[0][i] = i

    for i in range(ln_s1+1):
        Matrix[i][0] = i

    # Filling the matrix
    for i in range(1, ln_s1+1):
        for j in range(1, ln_s2+1):
            insertion = Matrix[i][j-1]   + 1
            deletion  = Matrix[i-1][j]   + 1
            mismatch  = Matrix[i-1][j-1] + 1
            match     = Matrix[i-1][j-1]
            if s1[i-1] == s2[j-1]:
                Matrix[i][j] = min(insertion, deletion, match)
            if s1[i-1] != s2[j-1]:
                Matrix[i][j] = min(insertion, deletion, mismatch)

    return (int(Matrix[ln_s1][ln_s2]), Matrix)

def OptimalAlignment(Matrix, s1, s2, top, bottom, i, j):
    """ Finds the optimal alignment of two strings given the edit matrix
    (2D-array, str, str, str, str, int, int) -> (str, str) """

    if i == 0 and j == 0:
        return (' '.join(top[::-1]), ' '.join(bottom[::-1]))

    if i>0 and Matrix[i][j] == Matrix[i-1][j] + 1:
        top.append(f'|{s1[i-1]}|')
        bottom.append('|-|')
        return OptimalAlignment(Matrix, s1, s2, top, bottom, i-1, j)

    elif j>0 and Matrix[i][j] == Matrix[i][j-1] + 1:
        bottom.append(f'|{s2[j-1]}|')
        top.append('|-|')
        return OptimalAlignment(Matrix, s1, s2, top, bottom, i, j-1)

    else:
        top.append(f'|{s1[i-1]}|')
        bottom.append(f'|{s2[j-1]}|')
        return OptimalAlignment(Matrix, s1, s2, top, bottom, i-1, j-1)

if __name__ == '__main__':
    s1, s2 = input(), input()
    edit_distance, Matrix = EditDistance(s1, s2)
    top, bottom = OptimalAlignment(Matrix, s1, s2, [], [], len(s1), len(s2))

    print(f'Editing distance : {edit_distance}')
    print(f'Optimal alignment:\n{top}\n{bottom}')