feat: add minimum edit distance implementation

Python_codes/Minimum Edit Distance/minimum_edit_distance.py

@@ -0,0 +1,149 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+#
+# Copyright 2021 Jude Michael Teves
+#
+# My implementation of Minimum Edit (Levenshtein) Distance.
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, see <http://www.gnu.org/licenses/>.
+
+def minimum_edit_distance(X, Y):
+  '''
+  This function calculates the distance matrix of 2 strings.
+
+  Parameters
+  ---
+  X : str
+    source string
+  Y: str
+    target string
+
+  Returns
+  ---
+  D : matrix (list of lists, numpy array, etc.)
+    D is the distance matrix and has a dimension of MxN, 
+    where: 
+      M = len(X)+1
+      N = len(Y)+1
+
+  Examples
+  ---
+  >>> X, Y = ('ant', 'at')
+  >>> D = minimum_edit_distance(X, Y)
+  >>> D
+  array([[0, 1, 2],
+       [1, 0, 1],
+       [2, 1, 2],
+       [3, 2, 1]])
+
+  '''
+
+  # Get length of each input
+  n = len(X)+1
+  m = len(Y)+1
+
+  D = np.zeros((n, m), dtype=int) # Create a maxtrix / table of size (n,m) of all zeros
+  # Initialize
+  D[0, 1:] = range(1, m)
+  D[1:, 0] =  range(1, n)
+
+  for i in range(1,n):
+    for j in range(1,m):
+      diagonal = D[i-1,j-1] + (2 if X[i-1] != Y[j-1] else 0)
+      up = D[i,j-1] + 1
+      left = D[i-1,j] + 1
+
+      D[i,j] = min(diagonal, up, left)
+
+  return D
+
+def backtrace(D, X, Y):
+  '''
+  This function does the back alignment. 
+  The priority is the operation that has the lowest cost.
+  If the same, then do insertion > deletion > substitution.
+
+  Parameters
+  ---
+  D: matrix (list of lists, numpy array, etc.)
+    D is the distance matrix and has a dimension of MxN, 
+    where: 
+      M = len(X)+1
+      N = len(Y)+1
+  X : str
+    source string
+  Y: str
+    target string
+
+  Returns
+  ---
+  operations : list of lists
+    operations is a list of operations(list), 
+    wherein the inner list has the following format:
+      [<source character>, <operation>, <target character>]
+
+    The symbol for each operation is as follows:
+      | => no change
+      D => deletion
+      I => insertion 
+      S => substitution
+
+    The operation starts at the last character of the string 
+    and ends with the first character.
+
+  Examples
+  ---
+  >>> X, Y = ('ant', 'at')
+  >>> D = minimum_edit_distance(X, Y)
+  >>> operations = backtrace(D, X, Y)
+  >>> operations
+  [['t', '|', 't'], ['n', 'D', '-'], ['a', '|', 'a']]
+
+  '''
+
+  i = D.shape[0] - 1
+  j = D.shape[1] - 1
+  # print("String1: %s; String2: %s" % (i,j))
+
+  operations = []
+  while i != 0 or j != 0:
+    diagonal = D[i-1,j-1]	# Match	
+    up = D[i-1,j]			  # Delete
+    left = D[i,j-1]			    # Insert
+
+    if up < left and up < diagonal:	# highest priority, insertion
+      operations.append([X[i-1], "D", "-"])
+      i -= 1
+    elif left < diagonal: # highest priority, insertion
+      operations.append(["-", "I", Y[j-1]])
+      j -= 1
+    else:
+      if X[i-1] == Y[j-1]:
+        operations.append([X[i-1], "|", Y[j-1]])
+      else:  
+        operations.append([X[i-1], "S", Y[j-1]])
+      i -= 1
+      j -= 1
+
+  return operations
+
+def format_backtrace(operations):
+  operations = operations[::-1] # reverse
+  source = ''.join([o[0] for o in operations])
+  operation = ''.join([o[1] for o in operations])
+  target = ''.join([o[2] for o in operations])
+
+  output = '\n'.join([source, operation, target])
+
+  return output