%% Introduction to Artificial Intelligence
%% Homework 3 starter program for completion by Oct 18, 2000
%% Look for the pattern 
%%
%% **************************************************
%% YOU COMPLETE THIS
%% **************************************************
%%
%% to find the places where your definitions should go.

:- use_module(library(heaps)).

%% This material defines a relation
%%
%% segment(Start, End, Direction, Distance, Name)
%%
%% for ways to get around Busch campus by walking.

basicSegment(johnson, russell, south, 100, s1).
basicSegment(russell, nelson, south, 100, s2).
basicSegment(nelson, lsm, south-west, 80, s3).
basicSegment(lsm, psych, east, 130, s4).
basicSegment(nelson, psych, south, 100, s5).
basicSegment(psych, arc, east, 20, s6).
basicSegment(arc, physics, east, 100, s7).
basicSegment(physics, chemistry, north, 80, s8).
basicSegment(nelson,chemistry, east, 120, s9).
basicSegment(russell,packaging, east, 110, s10).
basicSegment(packaging,doolittle, east, 90, s11).
basicSegment(chemistry,doolittle, north-east, 70, s12).
basicSegment(chemistry,optics, east, 80, s13).
basicSegment(physics, serc, east, 50, s14).
basicSegment(serc, hill, east, 40, s15).
basicSegment(hill, engineering, north, 50, s16).
basicSegment(hill, core, east, 30, s17).
basicSegment(core, werblin, south, 120, s18).
basicSegment(core, winlab, east, 140, s19).
basicSegment(winlab, werblin, south-west, 100, s20).
basicSegment(engineering, optics, north, 60, s21).
basicSegment(optics, sc, east, 40, s22).
basicSegment(optics, robeson, north-east, 50, s23).
basicSegment(sc, robeson, north-west, 30, s24).
basciSegment(doolittle, robeson, east, 90, s25).
basicSegment(doolittle, dorms, north-east, 160, s26).
basicSegment(robeson, dorms, north, 120, s27).

oppDir(south,north).
oppDir(east,west).

inverse(A,B) :- 
        oppDir(A,B).
inverse(A,B) :- 
        oppDir(B,A).
inverse(A-B,C-D) :-
        inverse(A,C),
        inverse(B,D).

segment(S, E, D, L, N) :-
        basicSegment(S, E, D, L, N).

segment(S, E, D, L, N) :-
        basicSegment(E, S, OD, L, N),
        inverse(D, OD).

%% **************************************************
%% YOU COMPLETE THIS
%% **************************************************
%%
%% First part, predicates:
%%
%% reaches(Node,Endpoint)
%%    true if the path represented by Node ends at 
%%    location Endpoint.
%%
%% cost(Node,Amount)
%%    true if the distance traveled in the path represented
%%    by Node is Amount.
%%
%% describe_path(Node)
%%    always true, but as a side-effect prints out the 
%%    directions corresponding to path Node.

%% **************************************************
%% YOU COMPLETE THIS
%% **************************************************
%%
%% Second part, predicate:
%%
%% neighbor(Node,Neighbor)
%%    true if node Neighbor can be reached in one step from Node.


%% Given: predicate 
%%
%%    neighbors(Node,Neighbors)
%%
%% This uses a Prolog builtin findall
%% to go from the neighbor relation you write to
%% the neighbors relation that the CI-style search
%% function needs.

neighbors(Node, Nodes) :- 
	findall(Neighbor, neighbor(Node,Neighbor), Nodes).

%% **************************************************
%% YOU COMPLETE THIS
%% **************************************************
%%
%% Third part, predicates:
%%
%% select(N,F1,F2)
%% add_to_frontier(Neighbors,F1,F2)
%%    with interpretation as in Computational Intelligence
%%    (and in class), using heaps to implement
%%    lowest-cost-first search.

%% Given: predicate
%%
%% find(F, G, P)
%%    true if node P is path that reaches location G and 
%%    which is accessible from frontier F.

find(F, G, P) :-
	select(P, F, _),
	reaches(P, G).

find(F, G, P) :-
	select(N, F, F2),
	neighbors(N, NN),
	add_to_frontier(NN, F2, F3),
	find(F3, G, P).

%% **************************************************
%% YOU COMPLETE THIS
%% **************************************************
%%
%% Fourth and final part, predicate:
%%
%% go(S,E)
%%    use lowest-cost-first search to compute whether
%%    there is a path between S and E and which, as 
%%    a side effect of proof, describes this path 
%%    to the user.