added type hints and doctests to arithmetic_analysis/intersection.py (T…

…heAlgorithms#2242)

continuing TheAlgorithms#2128

arithmetic_analysis/intersection.py

@@ -1,15 +1,38 @@
 import math
+from typing import Callable
 
 
-def intersection(function, x0, x1):
+def intersection(function: Callable[[float], float], x0: float, x1: float) -> float:
     """
     function is the f we want to find its root
     x0 and x1 are two random starting points
+    >>> intersection(lambda x: x ** 3 - 1, -5, 5)
+    0.9999999999954654
+    >>> intersection(lambda x: x ** 3 - 1, 5, 5)
+    Traceback (most recent call last):
+    ...
+    ZeroDivisionError: float division by zero, could not find root
+    >>> intersection(lambda x: x ** 3 - 1, 100, 200)
+    1.0000000000003888
+    >>> intersection(lambda x: x ** 2 - 4 * x + 3, 0, 2)
+    0.9999999998088019
+    >>> intersection(lambda x: x ** 2 - 4 * x + 3, 2, 4)
+    2.9999999998088023
+    >>> intersection(lambda x: x ** 2 - 4 * x + 3, 4, 1000)
+    3.0000000001786042
+    >>> intersection(math.sin, -math.pi, math.pi)
+    0.0
+    >>> intersection(math.cos, -math.pi, math.pi)
+    Traceback (most recent call last):
+    ...
+    ZeroDivisionError: float division by zero, could not find root
     """
-    x_n = x0
-    x_n1 = x1
+    x_n: float = x0
+    x_n1: float = x1
     while True:
-        x_n2 = x_n1 - (
+        if x_n == x_n1 or function(x_n1) == function(x_n):
+            raise ZeroDivisionError("float division by zero, could not find root")
+        x_n2: float = x_n1 - (
             function(x_n1) / ((function(x_n1) - function(x_n)) / (x_n1 - x_n))
         )
         if abs(x_n2 - x_n1) < 10 ** -5:
@@ -18,7 +41,7 @@ def intersection(function, x0, x1):
         x_n1 = x_n2
 
 
-def f(x):
+def f(x: float) -> float:
     return math.pow(x, 3) - (2 * x) - 5