Bratko, Chapter 9: Operations on Data Structures

9.1 Representing and sorting lists
- lists are merely structures
  - not required to stick with []/nil notation
- bubblesort (p213)
  - note use of cut, i.e., swap in only one way
- insertsort (p214)
- quicksort (p215, fig9.2)
  - quicksort with list difference-pair representation (p216, fig9.3)

9.2 Representing sets by binary trees
- binary tree
  - t( Left, Root, Right)
  - 'nil' indicates empty tree
  - inefficient searches for elements in lower right or not in tree
- binary dictionary (binary search tree)
  - for every tree and subtree t(L,X,R), elements(L) < X < elements(R)
  - in( X, Tree) (p221, fig9.7)

9.3 Insertion and deletion in binary dictionary
- addleaf( Tree, X, NewTree) [p224, fig9.10]
- del( Tree, X, NewTree) [p226, fig9.13]
- add(Tree,X,NewTree) / addroot(Tree,X,NewTree) [p228, fig9.15]
  - nondeterministic binary dictionary add
  - deletion doesn't work

9.4 Displaying trees
- show(Tree) [p230, fig9.17]

9.5 Graphs
- representation
  - facts
    - connected(Node1,Node2)  % undirected
    - arc(Node1,Node2,Label)  % directed, labeled
  - structures: graph(Node,Edges), digraph(Nodes,Edges)
    - graph([a,b,c],[e(a,b),e(b,c)])
    - digraph([s,t,u],[a(s,t,5),a(t,u,10)])
  - adjacency list
    - G1 = [ a -> [b], b -> [a,c], c -> [b] ]
    - G2 = [ s -> [t/5], t -> [s/3, u/10] ]
  - choice depends on application
- finding a path
  - acyclic paths [p234, fig9.20]
  - hamiltonian paths [p234]
    - not(node(N,Graph),not member(N,Path)
  - acyclic paths with costs [p235, fig9.21]
    - minimum cost path [p235]
      - path(...Cost...), not (path(...Cost2...), Cost2 < Cost).
- finding a spanning tree
  - algorithmic program [p237, fig9.22]
    - add one edge at a time
  - declarative program [p238, fig9.23]
    - try subsets of edges, inefficient
    - includes power set code !!!

Examples
- write a Prolog program for interactive binary dictionary manipulation
- define 'less than' for atoms

Other Procedures
- load_files(List)
- @<, @>, @=, compare(Order,Term1,Term2)
- format(Control,ArgList)
  -      C-like
HW
- Exercise 9.15, page 238