Question

X266: Recursion Programming Exercise: log For function log, write the missing base case condition and the recursive call This function computes the log of n to the base b.As an example: log 8 to the base 2 equals 3 since 8 = 2*2*2. We can find this by dividing 8 by 2 until we reach 1, and we count the number of divisions we make. You should assume that n is exactly b to some integer power. Examples: log(2, 4) -> 2 Log(10, 100) -> 2 1 public int log(int b, int n) { 2 if <cMissing base case condition>> ( return 0; } else { return <Missing a Recursive case action>> Check my answer! Reset MacBook Pro

Answer 1

Note: The code is implemented in Java language.

The required method is as follows:

    // Define the method log().

    public int log(int b, int n)

    {

        // Return 0 if the value of n is equal to 1.

        if (n == 1)

        {

            return 0;

        }

        // Else, call the method recursively with

        // the division of n by b.

        // Add 1 to this result and return the

        // computed value.

        else

        {

            return 1 + log(b, n/b);

        }

    }

The complete program to test the above method for different test cases is as follows:

Program screenshots:

// Define the class Main. class Main { // Define the method log(). public int log(int b, int n) { // Return 0 if the value of n is equal to 1. if (n == 1) return 0; // Else, call the method recursively with // the division of n by b. // Add 1 to this result and return the // computed value. else return 1 + log(b, n/b); // Define the main() method. public static void main(String[] args) // Create an object of the class Main. Main main = new Main(); // Call the method and display the result. System.out.println("log(2, 4) ->" + main.log(2, 4)); System.out.println("log(10, 100) -> " + main.log(10, 100)); System.out.println("log(3, 27) ->" + main.log(3, 27)); System.out.println("log(10, 100000) ->" + main.log(10, 100000)); System.out.println("log(2, 64) ->" + main.log(2, 64));

Sample output:

log (2, 4) -> 2 log(10, 100) -> 2 log (3, 27) -> 3 log(10, 100000) -> 5 log (2, 64) -> 6

Code to copy:

// Define the class Main.

class Main

{

    // Define the method log().

    public int log(int b, int n)

    {

        // Return 0 if the value of n is equal to 1.

        if (n == 1)

        {

            return 0;

        }

        // Else, call the method recursively with

        // the division of n by b.

        // Add 1 to this result and return the

        // computed value.

        else

        {

            return 1 + log(b, n/b);

        }

    }

    // Define the main() method.

    public static void main(String[] args)

    {

        // Create an object of the class Main.

        Main main = new Main();

        // Call the method and display the result.

        System.out.println("log(2, 4) -> " + main.log(2, 4));

        System.out.println("log(10, 100) -> " + main.log(10, 100));

        System.out.println("log(3, 27) -> " + main.log(3, 27));

        System.out.println("log(10, 100000) -> " + main.log(10, 100000));

        System.out.println("log(2, 64) -> " + main.log(2, 64));

    }

}