CS412-Applied-Algorithms/Palindrome-Partitioning/cs412_palindrome_dynamic.py

"""
name: Nicholas Tamassia

Honor Code and Acknowledgments:

        This work complies with the JMU Honor Code.

       Runtime: O(n^2).
"""

# Analysis:
# The loop on line 28 iterates n times where n is the length of the input string.
# The loop on line 32 iterates n - i times, which despite being practically fewer
# steps on average than the line 28 loop, still scales linearly with the size of
# the input string. Because both loops are O(n) and the second is nested in the
# first, the overall runtime complexity is O(n^2).


def palindrome_partitions(s: str) -> int:

    n: int = len(s)
    memo: list[int] = [0] * (n + 1)
    memo[n] = 1

    def is_palindrome(start: int, end: int) -> bool:
        return s[start:end] == s[start:end][::-1]

    for i in range(n - 1, -1, -1):

        sum = 0

        for j in range(i + 1, n + 1):
            if is_palindrome(i, j):
                sum += memo[j]

        memo[i] = sum

    return memo[0]


# All modules for CS 412 must include a main method that allows it
# to imported and invoked from other python scripts
def main():
    n: int = int(input())

    for _ in range(0, n):
        in_str = input().strip()
        print(palindrome_partitions(in_str))


if __name__ == "__main__":
    main()