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CS Program 231 Fall 1989 Craig A. Rich
Add implementations of the operations in the following abstract data type to the digraph ADT module created in program 3. These operations read and operate on labeled digraphs of type LABELED DIGRAPH. digraph adt.pas [environment] module DIGRAPH ADT; const MAX VERTICES = 20; type VERTEX = 1..MAX VERTICES; VERTEX LABEL = varying [30] of CHAR; EDGE LABEL = INTEGER; LABELED ADJACENCY MATRIX = array [VERTEX,VERTEX] of EDGE LABEL; LABELED DIGRAPH = record N: 0..MAX VERTICES; V: array [VERTEX] of VERTEX LABEL; E: LABELED ADJACENCY MATRIX end; procedure READ LABELED DIGRAPH (var INFILE: TEXT; var G: LABELED DIGRAPH); ... procedure FLOYD (G: LABELED DIGRAPH; var LEAST: LABELED DIGRAPH; var THROUGH: LABELED DIGRAPH); ... procedure WRITE LEAST COST PATH (var OUTFILE: TEXT; I,J: VERTEX; THROUGH: LABELED DIGRAPH); ... end. Write a Pascal program which reads an adjacency lists representation of a labeled digraph from a le, asks the user to enter two vertices i and j, prints the cost of a least-cost path from i to j, and prints the labels of the vertices in such a path.
Digraph ADT Module Implementation Notes 1. READ LABELED DIGRAPH reads the labeled digraph G from the Pascal le INFILE. The input le will consist of 2*N linestwo for each vertex in the digraph. Line 2i 1 of the input le contains the label associated with vertex i, for 1 i N. The vertex label can be read directly into V[i] using READLN. Line 2i of the input le alternately contains numbers of vertices are which adjacent to vertex i and labels associated with those edges, for 1 i N. The labeled digraph is represented internally by the labeled adjacency matrix E. E[i,j] should contain MAXINT for any vertices i and j such that j is not adjacent to i. 2. FLOYD should compute LEAST to be the labeled reexive transitive closure of G, where the edge label LEAST.E[i,j] is the cost of a least-cost path from vertex i to vertex j, or MAXINT if no such path exits. FLOYD should compute THROUGH to be the labeled reexive transitive closure of G, where the edge label THROUGH.E[i,j] is the number of a vertex through which a least-cost path from vertex i to vertex j goes, or 0 if no such vertex exists. 3. WRITE LEAST COST PATH should take the labeled digraph THROUGH produced by FLOYD and print the labels of the vertices through which a least-cost path from vertex I to vertex J goes. Program 4 Implementation ...