Add Padovan Sequence Algorith

maths/padovan_sequence.py

@@ -0,0 +1,50 @@
+def padovan_sequence(n: int) -> int:
+    """
+    Return the n-th term of the Padovan Sequence.
+    The Padovan sequence is the sequence of integers P(n) defined by the initial values
+    P(0) = P(1) = P(2) = 1 and the recurrence relation P(n) = P(n-2) + P(n-3).
+
+    https://en.wikipedia.org/wiki/Padovan_sequence
+
+    :param n: The index of the term to return.
+    :return: The n-th term of the Padovan Sequence.
+
+    >>> padovan_sequence(0)
+    1
+    >>> padovan_sequence(1)
+    1
+    >>> padovan_sequence(2)
+    1
+    >>> padovan_sequence(3)
+    2
+    >>> padovan_sequence(4)
+    2
+    >>> padovan_sequence(5)
+    3
+    >>> padovan_sequence(10)
+    12
+    >>> padovan_sequence(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input must be a non-negative integer.
+    """
+    if not isinstance(n, int) or n < 0:
+        raise ValueError("Input must be a non-negative integer.")
+
+    if n <= 2:
+        return 1
+
+    p_prev_3, p_prev_2, p_prev_1 = 1, 1, 1
+
+    for _ in range(3, n + 1):
+        curr = p_prev_2 + p_prev_3
+        p_prev_3, p_prev_2, p_prev_1 = p_prev_2, p_prev_1, curr
+
+    return p_prev_1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print("Doctests passed!")