[Feature] Added finding edit distance between 2 strings.

Author: exterkamp

README.md

@@ -85,4 +85,5 @@ Different algorithmic programs.  Grouped by general topic.
   * [Trie](algorithms/string/longest_common_prefix.py)
   * [Reduce](algorithms/string/longest_common_prefix.py)
 * [Finding Substring](algorithms/string/rabin_karp_substring_search.py)
-  * [Rabin-Karp](algorithms/string/rabin_karp_substring_search.py)
+  * [Rabin-Karp](algorithms/string/rabin_karp_substring_search.py)
+* [Calculate Edit Distance](algorithms/string/edit_distance.py)

algorithms/string/edit_distance.py

@@ -0,0 +1,88 @@
+def calculate_edit_distance(str1, str2):
+    '''
+    Calculate the edit distance between two strings.
+
+    An edit is defined as one of three actions, a deletion, 
+    a replacement, or an addition.
+
+    '''
+    
+
+    # operation enums
+    MATCH, INSERT, DELETE = 0, 1, 2
+
+    # three possible operations @ each point
+    opt = [0,0,0]
+
+    # 2D array to hold all edit distance data
+    distance = [[0] * (len(str1)+1) for _ in range(len(str2)+1)]
+    # 2D array to hold parent least cost relationships
+    parent = [[0] * (len(str1)+1) for _ in range(len(str2)+1)]
+
+    str1 = " " + str1
+    str2 = " " + str2
+
+    # initial values
+    for i in range(len(str2)):
+        distance[i][0] = i
+        parent[i][0] = DELETE
+
+
+    for j in range(len(str1)):
+        distance[0][j] = j
+        parent[0][j] = INSERT
+
+    distance[0][0] = 0
+    parent[0][0] = -1
+
+
+    # go through every letter combination
+    for i in range(1, len(str2)):
+        for j in range(1, len(str1)):
+            opt = [0,0,0]
+
+            # populate with edit data
+            if j > 0:
+                opt[INSERT] = distance[i][j-1] + 1 # indel
+            if i > 0:
+                opt[DELETE] = distance[i-1][j] + 1 # indel
+            if j > 0 and i > 0:
+                opt[MATCH] = distance[i-1][j-1] + (0 if str1[j] == str2[i] else 1) # match or substitution
+
+            # find min cost operation
+            lowest_cost = min(opt)
+            parent_opt = opt.index(lowest_cost)
+            # print(opt, lowest_cost, parent_opt)
+            distance[i][j] = lowest_cost
+            parent[i][j] = parent_opt
+    
+    # for i in range(len(distance)):
+    #     print(distance[i])
+    # print('-----')
+    # for i in range(len(parent)):
+    #     print(parent[i])
+    
+    # traceback
+    current_pos = (len(str2)-1, len(str1)-1)
+    D,I,M,S = 'Delete','Insert','M','Substitute'
+    trace_stack = []
+    while parent[current_pos[0]][current_pos[1]] != -1:
+        parent_val = parent[current_pos[0]][current_pos[1]]
+        if parent_val == 0:
+            if str2[current_pos[0]] == str1[current_pos[1]]:
+                # trace_stack.append(M)
+                pass
+            else:
+                trace_stack.append(S + ' ' + str1[current_pos[1]])
+
+            current_pos = (current_pos[0]-1, current_pos[1]-1)
+        elif parent_val == 1:
+            trace_stack.append(I + ' ' + str1[current_pos[1]])
+            current_pos = (current_pos[0], current_pos[1]-1)
+            
+        else:
+            trace_stack.append(D + ' ' + str2[current_pos[0]])
+            current_pos = (current_pos[0]-1, current_pos[1])
+            
+    return trace_stack[::-1]
+  

tests/test_edit_distance.py

@@ -0,0 +1,9 @@
+import unittest
+from algorithms.string.edit_distance import calculate_edit_distance
+
+class TestEditDistance(unittest.TestCase):
+
+    def test_edit_distance(self):
+
+        self.assertEqual(['Substitute h', 'Insert l', 'Substitute l'], calculate_edit_distance('hello','teio'))
+