minimum edit distance in python

python/42_dynamic_programming/min_edit_dist.py

@@ -0,0 +1,31 @@
+"""
+    Author: Wenru Dong
+"""
+
+def levenshtein_dp(s: str, t: str) -> int:
+    m, n = len(s), len(t)
+    table = [[0] * (n + 1) for _ in range(m + 1)]
+    table[0] = [j for j in range(m + 1)]
+    for i in range(m + 1):
+        table[i][0] = i
+    for i in range(1, m + 1):
+        for j in range(1, n + 1):
+            table[i][j] = min(1 + table[i - 1][j], 1 + table[i][j - 1], int(s[i - 1] != t[j - 1]) + table[i - 1][j - 1])
+    return table[-1][-1]
+
+
+def common_substring_dp(s: str, t: str) -> int:
+    m, n = len(s), len(t)
+    table = [[0] * (n + 1) for _ in range(m + 1)]
+    for i in range(1, m + 1):
+        for j in range(1, n + 1):
+            table[i][j] = max(table[i - 1][j], table[i][j - 1], int(s[i - 1] == t[j - 1]) + table[i - 1][j - 1])
+    return table[-1][-1]
+
+
+if __name__ == "__main__":
+    s = "mitcmu"
+    t = "mtacnu"
+
+    print(levenshtein_dp(s, t))
+    print(common_substring_dp(s, t))