DessertMaker | Topcoder Archive

Problem Statement

You have a number of tasty ingredients and you want to know how many different banana split desserts you could make using those ingredients. In order for something to count as a banana split, it must have at least one "banana", at least one "ice cream", and at least one other ingredient (i.e., at least one ingredient that is not a "banana" or an "ice cream"). Ingredients with the same name are not distinguishable, and it doesn't matter what order the items are added to the dessert. For example, suppose you had the following 5 ingredients:

"ice cream","banana","chocolate","chocolate","peanuts"

You could make a total of 5 different banana splits, as shown below:

"ice cream","banana","chocolate","chocolate","peanuts"
"ice cream","banana","chocolate","peanuts"
"ice cream","banana","chocolate","chocolate"
"ice cream","banana","chocolate"
"ice cream","banana","peanuts"

Note that if you would have had 2 bananas, you would have had 10 possibilities - as adding a banana to each combination above makes a new dessert. Return the number of distinct banana splits you could create using the items given in ingredients.

Definition

Class:: DessertMaker
Method:: countBananaSplits
Parameters:: String[]
Returns:: int
Method signature:: int countBananaSplits(String[] ingredients)
(be sure your method is public)

Constraints

ingredients will contain between 1 and 30 elements, inclusive.
Each element of ingredients will contain between 1 and 50 characters, inclusive.
Each element of ingredients will contain only lowercase letters and spaces ('a'-'z',' ').

Examples

{"ice cream","banana","chocolate","chocolate","peanuts"}

Returns: 5

The example from the problem statement.

```
{"banana", "banana", "chocolate", "strawberries", 
"pineapple", "pineapple", "rice cream"}
```
```
Returns: 0
```
To make a banana split, you need "ice cream", "banana", and at least one other ingredient. We have a "banana" and plenty of other ingredients, but we don't have an "ice cream" so we have zero possibilities.
```
{"ice cream", "ice cream", "banana", "banana", "chocolate",
 "chocolate"}
```
```
Returns: 8
```
To see the 8 possibilities, note that you can pick either one or two "ice cream"s, one or two "banana"s and one or two "chocolate"s (and 2*2*2=8). You cannot have no ice cream or no bananas - and we need to have at least one other ingredient so we need at least one chocolate. Note that {"ice cream","banana","chocolate"} counts as a different dessert than {"ice cream","ice cream","banana","banana","chocolate","chocolate"} because the ingredient list is not identical.

{"foam", "apple", "whipped cream", "apple", "mushroom", 
"apple core", "ice cream", "ice cream", "banana", "giraffe", 
"mushroom", "spare tire", "ice cream", "banana", "foam", 
"wrench", "paper", "cherry", "alarm clock", "football" ,"apple", 
"apple"}

Returns: 138234

You don't know if it'll be good until you try it.

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