A collection of string matching algorithms taken from chapter 32 of CSLR.

string_matching.py

from functools import reduce
from string import ascii_lowercase

def naive_string_matching(T, P):
    """Computes all the occurrences of P in T.

    Cost of this procedure is O(n-m+1 * m)
    where n, m are the length of T and of P
    respectively.

    Args:
        T: text into which find occurrences.
        P: substring to search in T.

    Returns:
        A list containing the indexes at which
        the occurrences of P in T start. The actual
        substrings can be derived via mapping
        each element x of the returned list to T[x:x+len(P)].
    """

    shifts = []
    s, n, m = 0, len(T), len(P)
    assert m <= n, 'substring is longer than string'
    while s < n-m+1:
        if T[s] != P[0]: s += 1; continue
        j = 1
        while j < m:
            if T[s+j] != P[j]: break
            j += 1
        if j == m: shifts.append(s)
        s += 1

    return shifts

def rabin_karp_matching(T, P, q=997):
    """Computes all the occurrences of P in T.

    Cost of this procedure is O(n-m+1 * m)
    where n, m are the length of T and of P
    respectively.

    The idea behind Rabin-Karp is to leverage
    comparisons between computer WORD's that
    are supposed to happen in constant time.
    Thus a numeric fingerprint is computed
    for the pattern P and for each substring
    of T of length m. In case fingerprints
    match, the original pattern and the substring
    of T that generated one of the fingerprints
    are compared byte by byte.

    Assuming comparison of two strings happen in O(m),
    the worst case running time is computed assuming
    that for each substring of T of length m (i.e.
    n-m+1 substrings) a match of fingerprints will
    happen, forcing a O(m) comparison n-m+1 times.
    """

    T, P = T.encode('ASCII'), P.encode('ASCII')
    n, m = len(T), len(P)
    valid_shifts = []

    p = reduce(lambda ac, x, q=q: (ac*128 + x) % q, P)
    t_list = [reduce(lambda ac, x, q=q: (ac*128 + x) % q, T[:m])]
    for s in range(n-m):
        t = (t_list[-1]*128 + T[m+s] - pow(128, m, q) * T[s]) % q
        t_list.append(t)

    for s, t in enumerate(t_list):
        if t == p and T[s:s+m] == P:
            valid_shifts.append(s)

    return valid_shifts

def is_suffix(a, b):
    """Computes whethere a is suffix of b"""
    n = len(b)
    return a == b[n-len(a):]

def build_delta(P, sigma=ascii_lowercase):
    """Build the transition function 𝛿 for the DFA of P.

    𝛿(q, a) tells you the maximum number of characters
    that can act as a suffix for P[:q]+a.
    """
    delta, m = {}, len(P)
    for q in range(m+1):
        for a in sigma:
            k = min(m, q+1)
            while not is_suffix(P[:k], P[:q]+a):
                k = k - 1
            delta[(q, a)] = k
    return lambda q, a, delta=delta: delta[(q, a)]

def dfa_matching(T, P):
    """Computes all the occurrences of P in T."""
    delta = build_delta(P)
    valid_shifts, q, m = [], 0, len(P)
    for i, c in enumerate(T):
        q = delta(q, c)
        if q == m: valid_shifts.append(i-m+1)
    return valid_shifts

def build_pi(P):
    """Build the prefix function π, as described in CSLR.

    π(q) tells you the maximum number of characters
    that can act as a *proper* suffix for P[:q].
    """
    pi, m = [None], len(P)
    for q in range(1, m+1):
        k = q-1
        while not is_suffix(P[:k], P[:q]):
            k -= 1
        pi.append(k)
    return lambda q, pi=pi: pi[q]

def kmp_matching(T, P):
    """Computes all the occurrences of P in T."""
    pi, n, m, q = build_pi(P), len(T), len(P), 0
    valid_shifts = []
    for i in range(n):
        while q > 0 and P[q] != T[i]:
            q = pi(q)

        if P[q] == T[i]:
            q += 1

        if q == m:
            valid_shifts.append(i+1-m)
            q = pi(m)

    return valid_shifts