Lavenshtein minimum edit distance algorithm

__init__.py

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+__author__ = 'tg'

text/__init__.py

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+__author__ = 'tg'

text/edit_distance.py

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+
+__author__ = 'tg'
+
+from util.arrays import format_2d_array
+import sys
+
+
+
+def min_lavenshtein_distance(s1, s2):
+    '''
+    Computes Minimum Lavenshtein Distance between two strings
+    :param s1: string 1
+    :param s2: string 2
+    :return: minimum edit distance
+    '''
+
+
+    s1 = '#' + s1  # An empty space is added to make space for base case
+    s2 = '#' + s2  # An empty space is added to make space for base case
+    n = len(s1)
+    m = len(s2)
+
+    # declaring an empty array
+    matrix = [[0 for i in range(m)] for i in range(n)]
+
+    for i in range(n):
+        for j in range(m):
+
+            if i == 0:          # base case 1
+                distance = j
+            elif j == 0:        # base case 2
+                distance = i
+            else:              # general case
+                distance = sys.maxint  # use this as reference to find minimum distance
+                if matrix[i-1][j] + 1 < distance:  #horizontal move, insert s2 char
+                    distance = matrix[i-1][j] + 1
+                if matrix[i][j-1] + 1 < distance:   #vertical move, insert a char from s1
+                    distance = matrix[i][j-1] + 1
+
+                # diagonal move :
+                # the distance increases if the characters are different (substitution)
+                # the distance remains same if characters are same
+                diagonal_dist = matrix[i-1][j-1]  + (0 if s1[i] == s2[j] else 2)
+                if diagonal_dist < distance:
+                    distance = diagonal_dist
+            matrix[i][j] = distance
+
+    print format_2d_array(matrix, s1, s2)
+
+    return matrix[n-1][m-1]
+
+if __name__ == '__main__':
+    s1 = 'intention'
+    s2 = 'execution'
+    min_edit_distance = min_lavenshtein_distance(s1, s2)
+    print min_edit_distance

util/__init__.py

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+__author__ = 'tg'

util/arrays.py

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+__author__ = 'tg'
+
+def format_2d_array(arr, col_head, row_head):
+    '''
+    Formats a 2d array (list of lists) into a matrix like rows x columns representation
+    :param arr:  The array to be formatted
+    :param col_head:  the header for each column
+    :param row_head: the header for each row
+    :return: the string created by formatting the contents of array with headers
+    '''
+    res = '*'
+    for i in col_head:  ## adding the header to columns
+        res += '\t' + str(i)
+    res += '\n'
+
+    for row_idx in range(0, len(row_head)):
+        res += row_head[row_idx] # row head
+        for j in arr[row_idx]:
+            res += '\t' + str(j)
+        res += '\n'
+    return res
+
+if __name__ == '__main__':
+    arr = [[i for i in range(4)] for j in range(5)]
+    res = format_2d_array(arr, 'abcd', 'xyzf')
+    print res
+
+