Binary search on a real-valued answer

Binary search on a real-valued answer

When needed

Used when the desired answer is a real number, for example:

• length;
• time;
• probability;
• area.

Idea

For real numbers, you cannot correctly use the condition l < r, because numbers can be divided infinitely many times.
Therefore, one of two approaches is used:

• perform a fixed number of iterations;
• perform the search until the error becomes small enough.

Template

The number of iterations is chosen to ensure the required accuracy of the result (usually $60–100$ iterations are more than enough).