# CS 280 Data Structures - PowerPoint PPT Presentation

CS 280 Data Structures

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CS 280 Data Structures

## CS 280 Data Structures

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##### Presentation Transcript

1. CS 280Data Structures Professor John Peterson

2. Project “Tree 1” Questions? Must be in by Wednesday – solutions will be posted after class Tree 2 is almost ready – there’s some simple stuff to do in the wiki already.

3. Parse Trees One of the big deals in computer science is context free languages – we use these to create recursive structures (trees) from linear ones (strings or sequences). There is a whole lot of theory underneath – we’ll skip most of it and concentrate on the practical stuff.

4. Example: English

5. The Problem Given: • A sequence of tokens • A grammar that gives structure to these tokens Produce: • A parse tree that covers the sequence

6. Grammars • Names: the left side of a production is a name – this name can be used in other productions • Constants: specific pieces of the underlying token-level language • Sequence: x y means that y follows x • Choice: (x | y) means either x or y may appear here • Optionals: [x] means x may appear here • Repetition: (x)* means that an arbitrary number of x’s are repeated

7. Example: Java Tokens: a = a + b * c; Grammar: statement = assignment assignment = var‘=‘addexp ‘;’ addexp = mulexp (‘+’mulexp)* mulexp = aexp (‘*’aexp)* aexp = var | num | ‘(‘addexp‘)’

8. How Does this Work? You need to know where to start (“statement”) This grammar is constructed so that you can always decide what to do based on the next token (peek). When you have a choice, always go as far as possible. If you get to a place where the current token doesn’t fit into the grammar, you have a “parse error”.

9. Parsing Theory Not all grammars are “easy” to parse Grammars can handle things like operator precedence Grammars can be ambiguous – we’ll avoid these The grammar “inverts” the recursive “print” for a datatype. There are other ways to represent the same thing – railroad diagrams.