fix bugs

Author: jerryderry

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))