Merge pull request #186 from jerryderry/kmp-python

kmp in python

Author: wangzheng0822

python/34_kmp/kmp.py

@@ -0,0 +1,61 @@
+"""
+    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 >= 0 and s[i] != pattern[j]:
+            j = partial_match_table[j]
+        j += 1
+        if j == m:
+            return i - m + 1
+    return -1
+
+
+def _get_partial_match_table(pattern: int) -> List[int]:
+    # Denote πᵏ(i) as π applied to i for k times,
+    # i.e., π²(i) = π(π(i)).
+    # Then we have the result:
+    #    π(i) = πᵏ(i-1) + 1,
+    # where k is the smallest integer such that
+    # pattern[πᵏ(i-1)+1] == pattern[i].
+
+    # The value of π means the maximum length
+    # of proper prefix/suffix.
+    # The index of π means the length of the prefix
+    # considered for pattern.
+    # For example, π[2] means we are considering the first 2 characters
+    # of the pattern.
+    # If π[2] == 1, it means for the prefix of the pattern, P[0]P[1],
+    # it has a maximum length proper prefix of 1, which is also the
+    # suffix of P[0]P[1].
+    # We also add a π[0] == -1 for easier handling of boundary
+    # condition.
+    
+    m = len(pattern)
+    π = [0] * (m + 1)
+    π[0] = k = -1  # We use k here to represent πᵏ(i)
+    for i in range(1, m + 1):
+        while k >= 0 and pattern[k] != pattern[i - 1]:
+            k = π[k]
+        k += 1
+        π[i] = k
+    return π
+
+
+if __name__ == "__main__":
+
+    s = "abc abcdab abcdabcdabde"
+    pattern = "bcdabd"
+    print(kmp(s, pattern), s.find(pattern))
+
+    s = "hello"
+    pattern = "ll"
+    print(kmp(s, pattern), s.find(pattern))