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")
    [x]
"""
if not pattern or not text:
    return [x]

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(x)

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

[algorithms-keeper]

Closing this pull request as invalid

@signore662-beep, this pull request is being closed as the files submitted contains an invalid extension. This repository only accepts Python algorithms. Please read the Contributing guidelines first.

Invalid files in this pull request: z_algorithm.py.