kmp in python

python/34_kmp/kmp.py

@@ -0,0 +1,45 @@
+"""
+    KMP algorithm
+
+    Author: Wenru Dong
+"""
+
+from typing import List
+
+def kmp(s: int, pattern: int) -> int:
+    m = len(pattern)
+    partial_match_table = _get_partial_match_table(pattern)
+    j = 0
+    for i in range(len(s)):
+        while j and s[i] != pattern[j]:
+            j = partial_match_table[j - 1] + 1
+        j += 1
+        if j == m:
+            return i - m + 1
+    return -1
+
+
+def _get_partial_match_table(pattern: int) -> List[int]:
+    # Denote pi^k(i) as pi applied to i for k times,
+    # i.e., pi^2(i) = pi(pi(i)).
+    # Then we have the result:
+    #    pi(i) = pi^k(i-1) + 1,
+    # where k is the smallest integer such that
+    # pattern[pi^k(i-1)+1] == pattern[i].
+    
+    m = len(pattern)
+    pi = [0] * m
+    pi[0] = k = -1  # We use k here to represent pi^k(i)
+    for i in range(1, m):
+        while k >= 0 and pattern[k + 1] != pattern[i]:
+            k = pi[k]
+        k += 1
+        pi[i] = k
+    return pi
+
+
+if __name__ == "__main__":
+
+    s = "abc abcdab abcdabcdabde"
+    pattern = "bcdabd"
+    print(kmp(s, pattern), s.find(pattern))