Description
Task 1:A complex number is a number in the form a + bi, where a and b are real numbers and i
is 2-1. The numbers a and b are known as the real part and imaginary part of the complex
number, respectively. You can perform addition, subtraction, multiplication, and division for
complex numbers using the following formulas:
You can also obtain the absolute value for a complex number using the following formula:
JAC – 444 Winter 2019
(A complex number can be interpreted as a point on a plane by identifying the (a,b) values as
the coordinates of the point. The absolute value of the complex number corresponds to the
distance of the point to the origin, as shown in Figure)
Design a class named Complex for representing complex numbers.
The methods
o add,
o subtract,
o multiply,
o divide, and
o abs
for performing complexnumber operations.
Override toString method for returning a string representation for a complex number.
(The toString method returns (a + bi) as a string. If b is 0, it simply returns a. )
Your Complex class should also implement the Cloneable interface.
Provide three constructors
o Complex(a, b),
o Complex(a), and
o Complex().
Complex() creates a Complex object for number 0 and Complex(a) creates a Complex object
with 0 for b. Also provide the getRealPart() and getImaginaryPart() methods for returning the
real and imaginary part of the complex number, respectively.
Write a test program that prompts the user to enter two complex numbers and displays the
result of their addition, subtraction, multiplication, division, and absolute value. Here is a
sample run:
JAC – 444 Winter 2019
Task 2:
Banks lend money to each other. In tough economic times, if a bank goes bankrupt, it
may not be able to pay back the loan. A bank’s total assets are its current balance plus
its loans to other banks. The diagram below shows five banks. The banks’ current
balances are 25, 125, 175, 75, and 181 million dollars, respectively. The directed edge
from node 1 to node 2 indicates that bank 1 lends 40 million dollars to bank 2.
If a bank’s total assets are under a certain limit, the bank is unsafe. The money it borrowed
cannot be returned to the lender, and the lender cannot count the loan in its total assets.
Consequently, the lender may also be unsafe, if its total assets are under the limit.
Write a program to find all the unsafe banks. Your program reads the input as follows.
1. It first reads two integers n and limit, where n indicates the number of banks and
limit is the minimum total assets for keeping a bank safe.
2. It then reads n lines that describe the information for n banks with IDs from 0 to n-1.
The first number in the line is the bank’s balance, the second number indicates the number
of banks that borrowed money from the bank, and the rest are pairs of two numbers. Each
pair describes a borrower. The first number in the pair is the borrower’s ID and the second
is the amount borrowed. For example, the input for the five banks in above picture is as
follows (note that the limit is 201):
Number of banks: 5
Minimum asset limit: 201
Bank # 0 Balance: 25 Number of banks Loaned: 2 Bank ID: 1 Amount: 100.5
Bank ID: 4 Amount: 320.5
Bank # 1 Balance: 125 Number of banks Loaned: 2 Bank ID: 2 Amount: 40
Bank ID: 3 Amount: 85
Bank # 2 Balance: 175 Number of banks Loaned: 2 Bank ID: 0 Amount: 125
Bank ID: 3 Amount: 75
Bank # 3 Balance: 75 Number of banks Loaned: 1 Bank ID: 0 Amount: 125
Bank # 4 Balance: 181 Number of banks Loaned: 1 Bank ID: 2 Amount: 125
JAC – 444 Winter 2019
The total assets of bank 3 are (75 + 125), which is under 201, so bank 3 is unsafe. After bank
3 becomes unsafe, the total assets of bank 1 fall below (125 + 40). Thus, bank 1 is also
unsafe.
Note: Program should take inputs from the user like Number of banks, Minimum asset
limit and then all other inputs
The output of the program should be
Unsafe banks are 3 and Bank 1
Task 3.
Design an interface named Colorable with a void method named howToColor(). Every class
of a colorable object must implement the Colorable interface.
Design a class named Square that extends GeometricObject and implements Colorable.
Implement howToColor to display the message Color all four sides.
Write a test program that creates an array of five GeometricObjects. For each object in the
array, display its area and invoke its howToColor method if it is colorable.
