added horner's method (#1360)

maths/polynomial_evaluation.py

@@ -1,25 +1,53 @@
-def evaluate_poly(poly, x):
-    """
-        Objective: Computes the polynomial function for a given value x. 
-                Returns that value. 
-        Input Prams: 
-            poly: tuple of numbers - value of cofficients
-            x: value for x in f(x)
-        Return: value of f(x)
+from typing import Sequence
 
-        >>> evaluate_poly((0.0, 0.0, 5.0, 9.3, 7.0), 10)
-        79800.0
-    """
 
+def evaluate_poly(poly: Sequence[float], x: float) -> float:
+    """Evaluate a polynomial f(x) at specified point x and return the value.
+
+    Arguments:
+    poly -- the coeffiecients of a polynomial as an iterable in order of
+            ascending degree
+    x -- the point at which to evaluate the polynomial
+
+    >>> evaluate_poly((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)
+    79800.0
+    """
     return sum(c * (x ** i) for i, c in enumerate(poly))
 
 
+def horner(poly: Sequence[float], x: float) -> float:
+    """Evaluate a polynomial at specified point using Horner's method.
+
+    In terms of computational complexity, Horner's method is an efficient method
+    of evaluating a polynomial. It avoids the use of expensive exponentiation,
+    and instead uses only multiplication and addition to evaluate the polynomial
+    in O(n), where n is the degree of the polynomial.
+
+    https://en.wikipedia.org/wiki/Horner's_method
+
+    Arguments:
+    poly -- the coeffiecients of a polynomial as an iterable in order of
+            ascending degree
+    x -- the point at which to evaluate the polynomial
+
+    >>> horner((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)
+    79800.0
+    """
+    result = 0.0
+    for coeff in reversed(poly):
+        result = result * x + coeff
+    return result
+
+
 if __name__ == "__main__":
     """
-        Example: poly = (0.0, 0.0, 5.0, 9.3, 7.0)  # f(x) = 7.0x^4 + 9.3x^3 + 5.0x^2 
-                 x = -13
-                 print (evaluate_poly(poly, x))  # f(-13) = 7.0(-13)^4 + 9.3(-13)^3 + 5.0(-13)^2 = 180339.9
+    Example:
+    >>> poly = (0.0, 0.0, 5.0, 9.3, 7.0)  # f(x) = 7.0x^4 + 9.3x^3 + 5.0x^2
+    >>> x = -13.0
+    >>> print(evaluate_poly(poly, x))  # f(-13) = 7.0(-13)^4 + 9.3(-13)^3 + 5.0(-13)^2 = 180339.9
+    180339.9
     """
     poly = (0.0, 0.0, 5.0, 9.3, 7.0)
-    x = 10
+    x = 10.0
     print(evaluate_poly(poly, x))
+    print(horner(poly, x))