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Decode the Coding Interview in Java: Real-World Examples

Feature #7: Exponentiation for Mobile Devices

Explore how to add exponentiation support to mobile device calculators by implementing compiler features. Understand the recursive method quickPow that handles positive and negative powers efficiently. Learn the algorithm's step-by-step logic and analyze its O(log n) time and space complexities to optimize compiler performance for unsupported exponentiation operations.

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Description

Mobile phones are widely used in the whole world. They also provide basic functionalities, like calculators, to ease everyday tasks. However, most mobile devices do not provide all of the functionalities of a calculator, because their processor does not support them. This is where our compiler comes in. First, we will discuss one of those unsupported functions named exponentiation, which computes any integer number raised to a specific power. Then, we will implement compiler functionality that does exponentiation in software.

Let’s see the following illustration to understand what a power function does.

Solution

Whenever our compiler encounters an expression involving exponentiation, it replaces the exponentiation part of the expression with a method call that calculates the result.

Here is how we will implement this feature:

  1. We will call the quickPow() function and check if power is less than 0. If so, we will change the base value to 1 / base and the negative power to positive. Then, we will call the quickPowRec() method recursively.

  2. If the given value of the power is zero, then we will return 1. This case will also be true when the power value reaches zero on the last function call.

  3. We will ...