Question

Write a function integerPower(base, exponemt) that returns the value of base \(^{exponent}\) For example, integerPower \((3,4)=3: 3\) is 3 . Assume that exponent is a positive, nonzero integer and that base is an integer. Do not use any math library functions.

Short answer

The function integerPower computes the value of base raised to the power exponent by initializing result to 1 and repeatedly multiplying it by base in a loop that iterates exponent times.

Step-by-step solution

Understand the Problem

We need to create a function called integerPower that takes two arguments, base and exponent, where 'base' is an integer and 'exponent' is a positive, nonzero integer. The function should compute the power of the base raised to the exponent without using library functions.

Initializing the Result

Start by initializing a variable called result to 1. This variable will hold the result of the base raised to the power of the exponent as the calculation proceeds.

Compute the Power

Using a loop that runs from 1 to the value of exponent (inclusive), multiply the result by the base each time. This loop effectively performs the multiplication of the base, exponent number of times.

Return the Result

After the loop has finished executing, the variable result contains the final calculated value of base raised to the power of exponent. Return the result from the function.

Function Definition

Define the function integerPower with the given parameters, encapsulate steps 2 through 4 inside the function body, and ensure it returns the appropriate value.

Key concepts

Exponentiation Logic in C++

Exponentiation is the operation of raising one number, the base, to the power of another number, the exponent. In C++, we can create a simple algorithm to mimic this operation without the help of any built-in math library functions. The basic idea is to multiply the base by itself, exponent number of times. For example, to calculate the power of 3 raised to 4 (\(3^4\)), we multiply 3 by itself 4 times: \(3 \times 3 \times 3 \times 3 = 81\).

To translate this into C++ code, you initialize a result variable to 1, because multiplying by 1 does not change the value. Then, you use a loop to go through the multiplication process. Each iteration of the loop represents one multiplication by the base value, and after the loop finishes, the result variable holds the final answer. It is critical to remember that we are considering integer powers, which implies a positive, nonzero exponent and integer values throughout the entire operation. This provides an efficient and straightforward way to carry out exponentiation using only basic arithmetic operations and control structures available in C++.

Looping Structures in C++

Looping structures in C++, such as 'for', 'while', and 'do-while' loops, are powerful tools that allow a block of code to be executed repeatedly based on a condition. For the task of integer exponentiation, a 'for' loop is particularly useful because it allows us to specify three important components: initialization, condition, and incrementation – all in one line.

In our exponentiation function, the 'for' loop starts with the initialization of a counter variable, which is typically set to 1 since we want to start multiplying from the first power. The condition specifies that the loop should continue as long as the counter does not exceed the exponent. With each iteration, the counter is incremented by 1, indicating the completion of one multiplication cycle. The loop's body contains the critical multiplication operation, updating the result variable with the product of itself and the base. By understanding and using looping structures effectively, we can solve a range of problems, including exponentiation, with precision and clarity.

Function Implementation in C++

Implementing functions in C++ encapsulates a piece of code that performs a specific task into a block that can be called from various parts of a program. When it comes to writing our integer exponentiation function, the advantage of a function is that it makes the code reusable and easier to read.

A well-defined function has a name that clearly identifies what it does, in this case, 'integerPower'. It takes parameters, the 'base' and 'exponent', which are the inputs we need to perform exponentiation. Inside the function, the initialized result and the loop for the exponentiation logic are encapsulated. After the calculations, the function ends with a 'return' statement that outputs the final calculated power.

Function Signature

The function signature consists of the return type, the name of the function, and parameters with their types, syntax looking something like:
code{int integerPower(int base, int exponent)}. This outlines the function's interface with the rest of the program, indicating that it returns an int and takes two int parameters. Using this encapsulation concept in C++, we make our code modular and maintainable, greatly aiding in complex software development.