SetType | Topcoder Archive

Problem Statement

We would like to add some syntax to a programming language to make it easier to work with sets and pairs. To make this work though, we need to be able to define a type for everything, and so we will use the following simple grammar for our types:

<type> ::= set(<type>) | pair(<type₁>,<type₂>) | integer

If something has type set(<type>), it will be written as:

{e₀,e₁,...,e_n}

where each e_i has type <type> and e₀ exists.
If something has type pair(<type>₁,<type>₂), it will be written as:

(a,b)

where a has type <type>₁ and b has type <type>₂. Naturally, if something has type integer, it is an integer (which will be between 1 and 100 in this problem). You will be given a well-formed set, pair or integer as defined above, and you are to return the type of that expression.

Definition

Class:: SetType
Method:: type
Parameters:: String
Returns:: String
Method signature:: String type(String expression)
(be sure your method is public)

Constraints

expression will represent a well formed expression. All elements of a set will contain the same type, and all integers will be between 1 and 100 with no leading zeros. All sets will contain at least 1 element.
expression will contain between 1 and 50 characters, inclusive.

Examples

```
"100"
```
```
Returns: "integer"
```
```
"(1,2)"
```
```
Returns: "pair(integer,integer)"
```
```
"{1,2,3}"
```
```
Returns: "set(integer)"
```

"({1},2)"

Returns: "pair(set(integer),integer)"

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