Binary Search on

Question

I am trying to apply a binary search on the following:

### START FUNCTION
def binary_search(f,domain, MAX = 1000):

### END FUNCTION
f = lambda x:(np.sin(x)**2)*(x**2)-2
domain = (0,2)
x=binary_search(f,domain)
x

1.43 Expected output

binary_search(lambda x:(np.sin(x)**2)*(x**2)-2,(0,2))==1.43

How do I apply a binary search to the above?

Answer 1

Assuming that you're looking for f(x) == 0, you use the same method as for any binary search:

• Examine the midpoint of the domain
• If f(x) is zero, you have found x
  • In your case: if you have done MAX iterations, take x as your approximation
• Otherwise, halve the domain and search again in the appropriate half depending on whether f(x) is negative or positive