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"""

Given a function on floating number f(x) and two floating numbers ‘a’ and ‘b’ such that

f(a) * f(b) < 0 and f(x) is continuous in [a, b].

Here f(x) represents algebraic or transcendental equation.

Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0)

https://en.wikipedia.org/wiki/Bisection_method

"""

def equation(x: float) -> float:

"""

>>> equation(5)

-15

>>> equation(0)

10

>>> equation(-5)

-15

>>> equation(0.1)

9.99

>>> equation(-0.1)

9.99

"""

return 10 - x * x

def bisection(a: float, b: float) -> float:

"""

>>> bisection(-2, 5)

3.1611328125

>>> bisection(0, 6)

3.158203125

>>> bisection(2, 3)

Traceback (most recent call last):

...

ValueError: Wrong space!

"""

# Bolzano theory in order to find if there is a root between a and b

if equation(a) * equation(b) >= 0:

raise ValueError("Wrong space!")

c = a

while (b - a) >= 0.01:

# Find middle point

c = (a + b) / 2

# Check if middle point is root

if equation(c) == 0.0:

break

# Decide the side to repeat the steps

if equation(c) * equation(a) < 0:

b = c

else:

a = c

return c

if __name__ == "__main__":

import doctest

doctest.testmod()

print(bisection(-2, 5))

print(bisection(0, 6))