Comp 388-005 Week 5

Lewis Tower 415, 4:15-8:15

Welcome

Readings:

 

Traversing a Tree

Some ways to traverse a tree: traversers.cs

Alternative stack-based traverser

Queue-based traverser


Hash statistics

    How many buckets can we expect to use?
    If hashtable array size is M and there are N things inserted, the fill ratio is λ = N/M
    Poisson distribution: fraction of buckets with k items is λke-λ/k!
    k=0: e-λ
    k=1: λe-λ

Suppose λ=2, so the average bucket has 2 items. Then we expect this:

k     fraction
0 13.5%
1 27%
2 27%
3 18%
4 9%
5 3.6%
6 1.2%

Compiler

    parsing: a, b, c, d, e are specific symbols, A, B, C are higher-level constructs
        A ::= a A | b B
        B ::= c C { c e C }
        C ::= d [ e C ]

        We can parse this language with
        parseA: if (token=A) {accept(a); parseA();}
                     else {accept(b); parseB();}
        parseB: accept(c); parseC(); while (token==c) {accept(c); accept(e); parseC();}
        parseC: accept(d); if (token==e) {accept(e); parseC();}

    machine code
    recursive-descent compilation
        expressions
        if and while
        global and local variables; stack frames
        recursion