diff --git a/Levenshtein_Edit_Distance.py b/Levenshtein_Edit_Distance.py
index 1d98ac6..b076a99 100644
--- a/Levenshtein_Edit_Distance.py
+++ b/Levenshtein_Edit_Distance.py
@@ -11,4 +11,14 @@ def edit_distance(str1, str2): #input is 2 strings that we will be comparing
   for j in range(len(str2)+1):
     D[0][j] = j
 
-  # Fill in rest of matrix with recursive case
+  #fill in rest of matrix with recursive case
+  for i in range(1, len(str1)+1):
+    for j in range(1, len(str2)+1):
+      if str1[i-1] == str2[j-1]:
+        cost = 0  #match: no operation needed
+      else:
+        cost = 1  #no match: substitution
+      D[i][j] = min(D[i-1][j] + 1, D[i][j-1] + 1,D[i-1][j-1] + cost)
+
+    return D[len(str1)][len(str2)] #last cell of matrix contains optimal solution
+