Skill Builder 3 - Loopy Loops

This Skill Builder will require you to write several functions in which loops are the focus. So, let's get started!

The class called SkillBuilder3 includes a set of skeleton methods. The requirements for each method are provided below.

String Multiplication

Implement the method with the following signature.

public static String repeat(String s, int numOfTimesToRepeat)

The method returns a string consisting of the character represented by the parameter ch repeated numOfTimesToRepeat.

Since Java does not have string arithmatic as in Python, we are forced to write a method to simulate string arithmatic.

For example, invoking the method as,

skillBuilder3.repeat("*", 8);

results in a string, "********", consisting of eight asterisks.

Invoking the method,

skillBuilder3.repeat("%", 10);

results in a string, "%%%%%%%%%%", consisting of ten percent (%) characters.

Invoking the method,

skillBuilder3.repeat("Hi", 3);

results in a string, "HiHiHi", consisting of a string that repeats "Hi" three times.

Left Triangle

Implement the method with the following signature.

public static String leftRightTriangle(int height)

The method returns a string consisting of asterisks in a left-right triangle pattern with a height given by the parameter height. When the method is invoked as follows:

SkillBuilder3.leftRightTriangle(5);

the result is a string that is equivalent to the following:

*\n**\n***\n****\n*****\n

If printed,

System.out.println(SkillBuilder3.leftRightTriangle(5));

The result is:

*
**
***
****
*****

Invoking the method with a different argument,

SkillBuilder3.leftRightTriangle(3)

results in,

*\n**\n***\n

and if printed,

System.out.println(SkillBuilder6.leftRightTriangle(3));

results in,

*
**
***

NOTE: you must use the repeat method in your implementation of this method.

Right Triangle

Implement the method with the following signature.

public static String rightRightTriangle(int height)

The method returns a string consisting of asterisks in a right-right triangle pattern with a height given by the parameter height. When the method is invoked as follows:

skillBuilder3.rightRightTriangle(5);

the result is a string that is equivalent to the following:

    *\n   **\n  ***\n ****\n*****\n

If printed,

System.out.println(recitation7.rightRightTriangle(5));

The result is:

    *
   **
  ***
 ****
*****

Invoking the method with a different argument,

skillBuilder3.rightRightTriangle(3)

results in,

  *\n **\n***\n

and if printed,

System.out.println(skillBuilder3.rightRightTriangle(3));

results in

  *
 **
***

NOTE: you must use the repeat method in your implementation of this method.

Let's Draw a Circle - Yay!

Implement the method with the following signature.

public static String circle(int radius)

The method returns a string of asterisks representing a circle pattern with a radius given by the parameter radius. When the method is invoked as follows:

skillBuilder3.circle(5)

the result is a string as follows,

  ******\n ********\n ********\n ********\n**********\n ********\n ********\n ********\n  ******

If printed,

System.out.println(recitation7.circle(5))

the result is,

  ******
 ********
 ********
 ********
**********
 ********
 ********
 ********
  ******

Invoking the method with a different argument,

skillBuilder3.circle(8)

the result is a string as follows,

"     ******\n   **********\n  ************\n  ************\n **************\n **************\n **************\n****************\n **************\n **************\n **************\n  ************\n  ************\n   **********\n     ******\n"

If printed,

System.out.println(skillBuilder3.circle(8))

the result is,

     ******
   **********
  ************
  ************
 **************
 **************
 **************
****************
 **************
 **************
 **************
  ************
  ************
   **********
     ******

An explanation of how to calculate the number of asterisks to print on each line is provided in the illustration below.

Note that you do not need to calculate $x$ for $y = r$ or for $y = -r$ since for both these values, $x = 0$. So, you can use a for-loop that goes from radius-1 to -radius+1, inclusively or radius-1 to -radius, not including -radius.

NOTE: you must use the repeat method in your implementation of this method.

Sum of All Divisors of a Number

Implement the method with the following signature.

public static long sumOfDivisors(long number)

The method returns a long integer that is the sum of all the divisors of the parameter number but does not include number.

For example, invoking the method as follows,

skillBuilder3.sumOfDivisors(10)

results in,

8

because the divisors of 10 (not including 10) are 1, 2, 5, and their sum is 1 + 2 + 5 = 8.

Another example,

skillBuilder3.sumOfDivisors(56)

results in,

64

because the divisors of 56 (not including 56) are 1, 2, 4, 7, 8, 14, 28 and their sum is 1 + 2 + 4 + 7 + 8 + 14 + 28 = 64.

NOTE: you must implement this method using a for loop!

Perfect Numbers

Let's use the method designed above (sumOfAllDivisors) to determine if a number is perfect. A perfect number is a positive integer equal to the sum of its positive divisors, not including the number itself.

Implement the method with the following signature.

public static boolean isPerfect(long number)

The method returns true if the parameter number is a perfect number; otherwise false.

For example, invoking the method as follows,

skillBuilder3.isPerfect(10)

results in, false because the divisors of 10 (not including 10) are 1, 2, 5, and their sum is 1 + 2 + 5 = 8 is not equal to 10.

Another example,

skillBuilder3.sumOfDivisors(6)

results in true because the divisors of 6 (not including 6) are 1, 2, 3, and their sum is 1 + 2 + 3 = 6 is equal to 6.

Sum of All Divisors of a Number Using a While loop

Implement the sumOfDivsors method using a while loop. Implement this requirement in the method with the following signature,

public static long sumOfDivisorsUsingWhile(long number)

NOTE: you must implement this method using a while loop!