manacher.py

# calculate palindromic length from center with incrementing difference
def palindromic_length(center, diff, string):
    if (
        center - diff == -1
        or center + diff == len(string)
        or string[center - diff] != string[center + diff]
    ):
        return 0
    return 1 + palindromic_length(center, diff + 1, string)


def palindromic_string(input_string):
    """
    Manacher’s algorithm which finds Longest Palindromic Substring in linear time.

    1. first this conver input_string("xyx") into new_string("x|y|x") where odd positions are actual input
        characters.
    2. for each character in new_string it find corresponding length and store,
        a. max_length
        b. max_length's center
    3. return output_string from center - max_length to center + max_length and remove all "|"   
    """
    max_length = 0

    # if input_string is "aba" than new_input_string become "a|b|a"
    new_input_string = ""
    output_string = ""

    # append each character + "|" in new_string for range(0, length-1)
    for i in input_string[: len(input_string) - 1]:
        new_input_string += i + "|"
    # append last character
    new_input_string += input_string[-1]

    # for each character in new_string find corresponding palindromic string
    for i in range(len(new_input_string)):

        # get palindromic length from ith position
        length = palindromic_length(i, 1, new_input_string)

        # update max_length and start position
        if max_length < length:
            max_length = length
            start = i

    # create that string
    for i in new_input_string[start - max_length : start + max_length + 1]:
        if i != "|":
            output_string += i

    return output_string


if __name__ == "__main__":
    n = input()
    print(palindromic_string(n))