Create z_algorithm.py.

[signore662-beep]

"""
The Z-algorithm finds all occurrences of a pattern in a text in linear time O(n + m).
Reference: https://en.wikipedia.org/wiki/Z_algorithm
"""

from future import annotations

def z_algorithm(text: str, pattern: str) -> list[int]:
"""
Finds all starting indices of a pattern in a text using the Z-array.

Args:
    text: The string to be searched.
    pattern: The string to search for.

Returns:
    A list of indices where the pattern starts.

Examples:
    >>> z_algorithm("ababa", "aba")
    [0, 2]
    >>> z_algorithm("aaaaa", "aa")
    [0, 1, 2, 3]
    >>> z_algorithm("abcde", "f")
    []
"""
if not pattern or not text:
    return []

concat = f"{pattern}${text}"
z_array = calculate_z_array(concat)
pattern_len = len(pattern)

# Indices in the z_array correspond to matches in the original text
return [
    i - (pattern_len + 1)
    for i, val in enumerate(z_array)
    if val == pattern_len
]

def calculate_z_array(s: str) -> list[int]:
"""
Calculates the Z-array for a given string.
Z[i] is the length of the longest common prefix between s and s[i:].
"""
n = len(s)
z = [0] * n
left, right = 0, 0

for i in range(1, n):
    if i <= right:
        z[i] = min(right - i + 1, z[i - left])
    while i + z[i] < n and s[z[i]] == s[i + z[i]]:
        z[i] += 1
    if i + z[i] - 1 > right:
        left, right = i, i + z[i] - 1
return z

if name == "main":
import doctest

doctest.testmod()

# Manual test case
TEXT = "baabaa"
PATTERN = "aab"
print(f"Pattern found at indices: {z_algorithm(TEXT, PATTERN)}")

[algorithms-keeper]

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