Question

Lottery’s Powerball game, each ticket costs $2 and consists of two parts:--> Five distinct integers (i.e., no duplicates) between 1-69, inclusive • One integer (the “Powerball number”) between 1-26, inclusive. The Powerball number may or may not coincide with one of the previously chosen numbers. A ticket wins the jackpot if all five distinct numbers plus the Powerball number match the randomly drawn numbers. The matching of the five distinct numbers is done without regard to order. For example, a ticket with 54, 49, 3, 18, and 20 matches drawn numbers of 3, 54, 18, 20, and 49. In math, the set of five distinct numbers chosen by the player is known as a combination. The number of possible combinations of k items chosen from a set of n items is usually written as (pronounced “n choose k”) and is computable using this formula:   This concept should be familiar; it was discussed in an earlier lab. As mentioned then, calculating the factorials directly is not an efficient way to find n choose k. This is because the terms in (n−k)! cancel some of the terms in n!, so there’s no need to compute those cancelled terms at all. A more efficient way to compute n choose k is this:      

The number of possible Powerball tickets can be computed by letting n = 69, k = 5, and multiplying the result of n choose k by 26 (the quantity of possible Powerball numbers):Number of possible tickets = 26   

plus one of m bonus numbers, we can compute the number of possible tickets like this. Number of possible tickets =   

The game settings (i.e., the values of k, n, and m above) can be chosen by the play.All of your code should be within a single class named Lottery.java.numPossibleTickets(int k, int n, int m-->This method should return the number of possible tickets in a lottery game that involves choosing k distinct integers from 1 to n (inclusive), plus one bonus integer from 1 to m (inclusive). Use equation (3) to compute this, and use the efficient technique of equation (2) when computing the value of n choose k. Because the number of tickets can be quite large, return it as a long value.getPlayerNumbers(int k, int n-->This method should get user input for k distinct integers between 1 and n (inclusive). The results should be returned in a 1D array of length k. Include input validation with loops to ensure that each input cannot be outside the range 1 to n, and also does not duplicate any previously entered value.getDrawnNumbers(int k, int n-->This method should simulate randomly drawing k distinct integers between 1 and n (inclusive). The results should be returned in a 1D array of length k. countMatches(int[] a, int[] b-->This method should return the number of elements in array a that also appear in array b. You may assume that both parameter arrays contain distinct elements. Here are some example arguments for this method and their expected return values:

a	b	Return Value
{1, 2, 3}	{3, 1}	2
{1, 2, 3}	{5, 7, -1}	0

5. The main method should tie everything together. Call your previously written methods as necessary. Here’s a summary of what the main method should do:Get user input for how to set up the lottery game (i.e., get values for k, n, and m). Include input validation with loops to ensure that k ≥ 1, n ≥ k, and m ≥ 1.Show how many possible tickets exist for that game, and a single ticket’s chance of winning the jackpot.Get user input for t, how many tickets to buy. Include input validation with a loop to ensure that t ≥ 1.For each ticket, get user input for the k distinct numbers to play and the corresponding bonus number. Include input validation with loops to ensure that all the numbers are valid. (The distinct numbers should already be validated from the method getPlayerNumbers.)Once all tickets have been entered, simulate the lottery drawing.Find and show the “best” ticket(s). The “best” ticket is the one that matches more of the k distinct numbers than any other ticket. Matching the bonus number is used as a tiebreaker. For example, in a game that involves selecting 3 distinct numbers, here’s a hierarchy of possible tickets from best to worst:
   • All 3 numbers match, plus the bonus number (this wins the jackpot)
   • All 3 numbers match, without the bonus number
   • 2 of 3 numbers match, plus the bonus number
   • 2 of 3 numbers match, without the bonus number
   • 1 of 3 numbers match, plus the bonus number
   • 1 of 3 numbers match, without the bonus number
   • 0 of 3 numbers match, and the bonus number matches
   • 0 of 3 numbers match, and the bonus number doesn’t match In case two or more tickets tie for “best,” show all of them.

• For the best ticket(s), show how many of the k distinct numbers match the drawn numbers, whether the bonus number matches, and whether the jackpot was won. To win the jackpot, all k distinct numbers and the bonus number must match the drawn numbers.The next pages have examples of how your completed program might look when running.Example program run (underlined parts indicate what the user enters) --> First, let’s set up the game!How many distinct numbers should the player pick? 4 OK. Each of those 4 numbers should range from 1 to what? 3Error - range must be at least 1 to 4 to have a valid game. Please try again: 4OK. And finally, the bonus number should range from 1 to what? 2-->There are 2 possible tickets in this game. Each ticket has a 50.0% chance of winning the jackpot. Let’s play, good luck!How many tickets would you like to buy? Error - must buy at least 1 ticket! Please try again: 1* Ticket #1 of 1 *Pick your 4 distinct numbers!Enter number 1 (must be 1-4, cannot repeat): 1Enter number 2 (must be 1-4, cannot repeat): 2 Enter number 3 (must be 1-4, cannot repeat): 1Error - you’ve already entered 1. Please try again.Enter number 3 (must be 1-4, cannot repeat): 3Enter number 4 (must be 1-4, cannot repeat): 1Error - you’ve already entered 1. Please try again.Enter number 4 (must be 1-4, cannot repeat):4Now pick your bonus number (must be 1-2): 3Error - number must be between 1 and 2. Please try again: 2Your tickets so far: --------------------

1               2              3              4              ||              Bonus: 2

The moment of truth has arrived! Here are the drawn numbers:

4               2              1              3              ||              Bonus: 2

Your best ticket(s):

1               2              3              4              ||              Bonus: 2

You matched 4/4 drawn numbers.You did match the bonus number.WOOHOO, JACKPOT!!

Example program run (underlined parts indicate what the user enters)First, let’s set up the game!How many distinct numbers should the player pick? 5OK. Each of those 5 numbers should range from 1 to what? 69OK. And finally, the bonus number should range from 1 to what? -1Error - range must be at least 1 to 1 to have a valid game. Please try again: 26There are 292201338 possible tickets in this game. Each ticket has a3.4222978130237034E-7% chance of winning the jackpot. Let’s play, good luck!How many tickets would you like to buy? -22Error - must buy at least 1 ticket! Please try again: 3* Ticket #1 of 3 *Pick your 5 distinct numbers!Enter number 1 (must be 1-69, cannot repeat): 77Error - number must be between 1 and 69. Please try again.Enter number 1 (must be 1-69, cannot repeat): 1Enter number 2 (must be 1-69, cannot repeat): 2Enter number 3 (must be 1-69, cannot repeat): 3Enter number 4 (must be 1-69, cannot repeat): 4Enter number 5 (must be 1-69, cannot repeat): 5Now pick your bonus number (must be 1-26): 22Your tickets so far: --------------------

1               2              3              4              5               ||              Bonus: 22

* Ticket #2 of 3 *Pick your 5 distinct numbers!Enter number 1 (must be 1-69, cannot repeat): 55Enter number 2 (must be 1-69, cannot repeat): 22Enter number 3 (must be 1-69, cannot repeat): 33Enter number 4 (must be 1-69, cannot repeat): 44Enter number 5 (must be 1-69, cannot repeat): 22Error - you’ve already entered 22. Please try again.Enter number 5 (must be 1-69, cannot repeat): 11Now pick your bonus number (must be 1-26): 19

Your tickets so far: --------------------

1               2              3              4              5               ||              Bonus: 22

55             22             33            44            11             ||              Bonus: 19

* Ticket #3 of 3 *Pick your 5 distinct numbers!Enter number 1 (must be 1-69, cannot repeat): 8Enter number 2 (must be 1-69, cannot repeat): 13 Enter number 3 (must be 1-69, cannot repeat): 2Enter number 4 (must be 1-69, cannot repeat): 17Enter number 5 (must be 1-69, cannot repeat): 29Now pick your bonus number (must be 1-26): 4

Your tickets so far: --------------------

1               2              3              4              5               ||              Bonus: 22

55        22        33        44        11        ||        Bonus: 19 8     13        2          17        29        ||        Bonus: 4

*****

The moment of truth has arrived! Here are the drawn numbers:

43            3               22            36            51             ||              Bonus: 4

Your best ticket(s):

1              2              3              4              5               ||              Bonus: 22

55            22             33            44            11             ||              Bonus: 19

You matched 1/5 drawn numbers. You did not match the bonus number.

Sorry, no jackpot this time. Really, did you expect anything else?

Try may be next time!!!!

Answer 1

Main.java

import java.util.Scanner;

public class Main {
    private static Scanner scanner = new Scanner(System.in);

    public static void main(String[] args) {
        LotteryGame game = new LotteryGame(6, 1, 49);
        System.out.println(game.getExplanationString());
        boolean run = true;
        while (run) {
            game.play();
            System.out.print("Continue (Y / N): ");
            System.out.flush();
            run = scanner.nextLine().equalsIgnoreCase("Y");
            System.out.println();
        }
    }   
}

LotteryGame.java

import java.util.Scanner;

public class LotteryGame {
    private Scanner scanner = new Scanner(System.in);

    private final int drawSize;
    private final int drawLowerLimit;
    private final int drawUpperLimit;

    public LotteryGame(int drawSize, int drawLowerLimit, int drawUpperLimit) {
        this.drawSize = drawSize;
        this.drawLowerLimit = drawLowerLimit;
        this.drawUpperLimit = drawUpperLimit;
    }

    public void play() {
        // generate new random draw
        Draw draw = Draw.generateRandomDraw(drawSize, drawLowerLimit, drawUpperLimit);

        // let the user guess
        Draw userDraw = guess();

       // compare the draws and print result
        int rightNumbers = draw.compare(userDraw);
        System.out.println("Your guess: " + userDraw.getStringRepresentation());
        System.out.println("Draw:       " + draw.getStringRepresentation());
        System.out.println("You guessed " + rightNumbers + " right!");
        System.out.println();
    }

    public Draw guess() {
        int numbers[] = new int[drawSize];
        while (true) {
            try {
                for (int i = 0; i < drawSize; i++) {
                    numbers[i] = HelpfulFunctions.saveIntInput("Number " + (i+1) + ": ");
                }
                System.out.println();
                return new Draw(numbers);
            } catch (IllegalArgumentException e) {
                System.out.println("The numbers have to be unique\n");
            }
        }
    }

    public String getExplanationString() {
        StringBuilder sb = new StringBuilder();
        sb.append("You have to guess the numbers of a lottery draw.\n");
        sb.append("A draw consists of 6 different numbers.\n");
        sb.append("Each number is in a range between 1 and 49.\n");
        sb.append("The more numbers you guess right, the luckier you can be!\n");
        return sb.toString();

}

}

HelpfulFunctions.java

import java.util.Scanner;

public class HelpfulFunctions {
    private static Scanner scanner = new Scanner(System.in);

    public static int saveIntInput(String message) {
        while (true) {
            try {
                System.out.print(message);
                System.out.flush();
                return Integer.valueOf(scanner.nextLine());
            } catch (NumberFormatException e) {
                System.out.println("Not a valid number.");
            }
        }
    }

Draw.java

import java.util.List;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;

public class Draw {
    public int[] numbers;

    public Draw(int[] numbers) throws IllegalArgumentException {
        // check if all numbers are unique
        for (int i = 0; i < numbers.length; i++) {
            for (int j = 0; j < numbers.length; j++) {
                if (i == j) continue;
                if (numbers[i] == numbers[j]) {
                    throw new IllegalArgumentException("All numbers have to be unique.");
                }
            }
        }

        this.numbers = numbers;
    }

    public static Draw generateRandomDraw(int numberOfEntries, int lowerLimit, int upperLimit) {
        // generate list that contains possible values
        List<Integer> possibleValues = new ArrayList<>();
        for (int i = lowerLimit; i <= upperLimit; i++) {
            possibleValues.add(i);
        }

        // fill draw with randomly picked values
        int[] numbers = new int[numberOfEntries];
        Random random = new Random();
        for (int i = 0; i < numberOfEntries; i++) {
            int randomIndex = random.nextInt(possibleValues.size());
            Integer pickedValue = possibleValues.get(randomIndex);
            possibleValues.remove(pickedValue);
            numbers[i] = pickedValue;
        }

        Arrays.sort(numbers);

        return new Draw(numbers);
    }
    // returns count of equal numbers
    public int compare(Draw draw) throws IllegalArgumentException {
        if (draw.numbers.length != numbers.length) {
            throw new IllegalArgumentException("The draws dont have the same length.");
        }

        int count = 0;
        for (int i = 0; i < numbers.length; i++) {
            for (int j = 0; j < numbers.length; j++) {
                if (numbers[i] == draw.numbers[j]) {
                    count++;
                }
            }
        }

        return count;
    }

    public String getStringRepresentation() {
        StringBuilder sb = new StringBuilder();
        sb.append("[" + numbers[0]);
        for (int i = 1; i < numbers.length; i++) {
            sb.append(", " + numbers[i]);
        }
        sb.append("]");
        return sb.toString();
    }
}