Java program

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Mario and Luigi's Super Italian Bistro is looking to drum up more business during week nights. The brothers propose to attract more customers by offering special discounts on Monday to Thursday night. They have several menu items on which they can offer a discount or simply deduct some money from the overall bill of their customers. This leads to 5 total specials the brothers could offer.

10 Coins Off

Crushed Turtle

Firey Flower Pasta

Mushroom Veal

Stewed Goomba

The brothers are not sure what the most effective order of specials would be to boost business so begin discussing the possible orderings. The brothers would like to offer some sort of special from Monday to Thursday, on 4 nights. This leads to several possible orderings of the specials. For example, one ordering of specials from Monday to Thursday is:

Crushed Turtle

Firey Flower Pasta

Mushroom Veal

10 Coins Off

Note that the special Stewed Goomba does not get used in this ordering.

Initially the brothers see no reason that specials cannot repeat, so another possible ordering is the following.

Firey Flower Pasta

Crushed Turtle

Firey Flower Pasta

Crushed Turtle

3 All Possible Orderings with Replacement

The brothers become curious how many arrangements of the specials there are. While Mario begins busily writing out orders by hand, Luigi fires up his computer to write some code for the problem. (Before the brothers started their bistro, Mario spent quite a bit of time punching bricks, eating mushrooms, and chasing princesses while Luigi always seemed to be second choice, giving him time to pursue more intellectual topics).

After reviewing recursion, Luigi produces the following code which will list all possible orderings with replacement.

// Produce all possible orders of specials with replacement;

// currentOrder is the current order of specials and maxSize is

// the maximum length desired. allOrderings accumulates string

// results as they are found.

public static void orders(ArrayList<String> specials,

                       ArrayList<String> currentOrder,

                       int maxSize,

                       ArrayList<String> allOrders){

  // If currentOrder contains enough specials, add it to the list of

  // allOrders that have been found

  if(currentOrder.size() == maxSize){

    allOrders.add(currentOrder.toString());

    return;

  }

  // Haven't reached maxSize so add each possible special to the

  // end of allOrders and recurse down to continue the

  // search. Remove the special after finishing the recursive call

  // to replace it with another special.

  for(String special : specials){

    currentOrder.add(special);

    orders(specials, currentOrder, maxSize, allOrders);

    currentOrder.remove( currentOrder.size()-1 );

  }

  return;

}

Note: this function is included in the lab code pack in Orders.java. You will need to understand it and create several variants.

Luigi is quite proud of this method as it will work for not just 4 nights of specials, but any number of nights of specials. He simply needs to change the maxSize parameter which controls how long the currentOrder should be before adding it to the result list ofallOrders.

Luigi codes a short main() method and is a bit shocked when it produces 625 possible orderings of the specials.

> javac Orders.java

> java Orders

625 orders

[10 Coins Off, 10 Coins Off, 10 Coins Off, 10 Coins Off]

[10 Coins Off, 10 Coins Off, 10 Coins Off, Crushed Turtle]

[10 Coins Off, 10 Coins Off, 10 Coins Off, Firey Flower Pasta]

[10 Coins Off, 10 Coins Off, 10 Coins Off, Mushroom Veal]

...

[Stewed Goomba, Mushroom Veal, Firey Flower Pasta, Crushed Turtle]

The brothers agree this is far too many orderings to try. They disagree as to how to limit the possibilities to try though. Mario thinks that they should consider all orders with no adjacent repeats while Luigi feels they should use all orders with no repeats. The brothers are struggling to adapt their code to solve these problems so they turn to a talented young computer scientist for help.

4 All Orders No Adjacent Repeats

In the class Orders.java write the following method.

// Produce all possible orders of specials with replacement but

// ensure that no adjacent specials are identical (no adjacent

// repeats).

public static void ordersNoAdj(ArrayList<String> specials,

                            ArrayList<String> currentOrder,

                            int maxSize,

                            ArrayList<String> allOrders)

This method determines all orders of the elements in specials with replacement except those that contain adjacent elements that are identical. The results are stored in allOrders and each result order is maxSize elements long. For example, if maxSize=4, the following is a possible ordering: though it contains repeats, the repeated items are not adjacent.

Firey Flower Pasta

Crushed Turtle

Firey Flower Pasta

Crushed Turtle

However, the following order would not be accepted as it contains adjacent equal items.

Crushed Turtle

10 Coins Off

10 Coins Off

Mushroom Veal

The ordering need not contain any repeats so the following is also a viable order.

Crushed Turtle

Firey Flower Pasta

Mushroom Veal

Stewed Goomba

Keep the following in mind as you code this method.

• Start with the definition of orders() which is provided. This is very close to what you need but will require some tweaks to exclude adjacent repeats.
• The currentOrder parameter is a list that can have items added to it. If items are added at the end via the add() method, one can prevent adjacent items from being equal by not adding items that are equal to the last element in the list.
• Make sure while checking the last element that it exists: currentOrder might be empty.
• At the end of the method execution, the allOrders list should contain string representations of all possible orders without replacement.

5 All Orders No Repeats

In the class Orders.java write the following method.

// Produce all possible orders of specials WITHOUT replacement: each

// special in an order in allOrders should be unique.

public static void ordersNoRepeats(ArrayList<String> specials,

                               ArrayList<String> currentOrder,

                               int maxSize,

                               ArrayList<String> allOrders)

This method determines all orderings of items in specials which do not contain any repeats. Each order is maxSize long and the results are stored as strings in allOrders.

These orders are NOT allowed this time, as they contain repeated elements.

Firey Flower Pasta

Crushed Turtle

Firey Flower Pasta

Crushed Turtle

10 Coins Off

Crushed Turtle

Mushroom Veal

10 Coins Off

Crushed Turtle

Crushed Turtle

Mushroom Veal

Stewed Goomba

The following orders ARE allowed, as they contain no repeats.

Crushed Turtle

Firey Flower Pasta

Mushroom Veal

Stewed Goomba

Crushed Turtle

10 Coins Off

Firey Flower Pasta

Mushroom Veal

Stewed Goomba

Firey Flower Pasta

Mushroom Veal

Crushed Turtle

Keep the following in mind as you code this method:

• Again, start with the definition of orders() which is provided. This is very close to what you need but will require some tweaks to exclude duplicates.
• The currentOrder list contains a list that can have items added to it. Before adding a new item, check if currentOrder already contains that item. There may be some methods of ArrayList which make this a trivial task.