feat: add Lucas numbers algorithm with doctests

Author: zhk319

maths/lucas_numbers.py

@@ -0,0 +1,39 @@
+def lucas_number(n: int) -> int:
+    """
+    Returns the n-th Lucas number using an iterative approach.
+    The Lucas numbers are an integer sequence where each term is the sum of the
+    two preceding terms, starting with 2 and 1.
+
+    Reference: https://en.wikipedia.org/wiki/Lucas_number
+
+    >>> lucas_number(0)
+    2
+    >>> lucas_number(1)
+    1
+    >>> lucas_number(5)
+    11
+    >>> lucas_number(10)
+    123
+    >>> lucas_number(-3)
+    Traceback (most recent call last):
+        ...
+    ValueError: n must be a non-negative integer.
+    """
+    if n < 0:
+        raise ValueError("n must be a non-negative integer.")
+
+    if n == 0:
+        return 2
+    if n == 1:
+        return 1
+
+    a, b = 2, 1
+    for _ in range(2, n + 1):
+        a, b = b, a + b
+    return b
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()