fix bugs

python/34_kmp/kmp.py

@@ -9,37 +9,54 @@
 def kmp(s: int, pattern: int) -> int:
     m = len(pattern)
     partial_match_table = _get_partial_match_table(pattern)
+    print(partial_match_table)
     j = 0
     for i in range(len(s)):
-        while j and s[i] != pattern[j]:
-            j = partial_match_table[j - 1] + 1
+        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 pi^k(i) as pi applied to i for k times,
-    # i.e., pi^2(i) = pi(pi(i)).
+    # Denote πᵏ(i) as π applied to i for k times,
+    # i.e., π²(i) = π(π(i)).
     # Then we have the result:
-    #    pi(i) = pi^k(i-1) + 1,
+    #    π(i) = πᵏ(i-1) + 1,
     # where k is the smallest integer such that
-    # pattern[pi^k(i-1)+1] == pattern[i].
+    # 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)
-    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]
+    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
-        pi[i] = k
-    return pi
+        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))