java 数据结构最短路径

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COMP3712/8712 GE    COMPUTER PROGRAMMING 3    ASSIGNMENT 2 
Assignment 2: Shortest Paths in Graphs 
 
Write a Java program that implements  Dijkstra's  algorithm to find shortest paths to all vertices  in a
directed weighted graph  from a given  starting vertex.  
As mentioned  in the lectures,  choosing an implementation  for the data structure  representing  a
graph  is highly dependent  on the sparsity of the graph. For dense graphs,  an adjacency matrix
representation  is preferable, but  for sparse graphs,  an adjacency list representation may be more
efficient. You are asked to implement  either  the adjacency  list or adjacency matrix representation
for graphs  in your program.   If you choose to extend you implementation  from Lab03 then  it will
need account for weighted edges.
Your program  should  (a) read in data defining  a graph  from a text  file, (b) build an adjacency list OR
matrix  representation  of the weighted graph and (c) use the graph  representation  to find shortest
paths from a specified vertex  in the graph  to all other vertices, using Dijkstra’s algorithm*. 
In addition,  you should  (d) provide documentation for your program describing  how to run  it, and
explaining  how the code works. You should also justify your choice of data structures*,  and details of
your code implementation,  in terms of space and  time efficiency. 
*(e) Use both a standard  List and Java’s builtin  PriorityQueue  for the storing  the list of distances
from the given  starting  vertex to other vertices compare the performance  (e.g. runtime, memory,
etc). 
(f) Implement  your own Priority Queue  class using  a Heap as described  in lectures and tutorials.
Compare your implementation  with the List and built-in PriorityQueue  compare.  Implementing  your
own priority queue  should allow you to make optimizations  specific to the Dijkstra’s Algorithm  (e.g.
not being generic)  that the Java PriorityQueue  must maintain  to be widely usable.
 
Marking Guide
It is expected  that all students  attempt parts (a)-(f).  All students  should be able to complete parts
(a)-(d) and most should be able to complete part  (e).  Part (f) is potentially more challenging.  The
table below gives an indication as to the distribution  of marks  to the parts of the assignment
described  above.
 
 
 
 
 
  
Part  Weight (100%)  Weight (15%)
a  5  2
b  20  3
c  25  3
d  20  3
e  20  3
f  10  2
Total  100  15 COMP3712/8712 GE    COMPUTER PROGRAMMING 3    ASSIGNMENT 2 
 
Data Format: There are five example  files (in Assignment02-data.zip) provided as example
input  files. Feel free to test your program with your own files as well. The data format is as follows:  
The first line  contains the number  of vertices.  
Every line after that represents  all edges going out from a particular vertex. The first number  on each
line is the number  of the vertex. After that,  there are a number  of pairs of integers. The first integer
is the index of a vertex connected to the first vertex in the line. The second integer  is the weight of
the edge  connecting  those two vertices.  
For example,  if the text file content  is: 
4 
1 2 18 3 12 
2 1 22 
3 2 16 4 14 4 1 31  
then  this means that there are 4 vertices, numbered  1 to 4. Vertex 1 has an edge to vertex 2, with
weight 18, and an edge  to vertex 3 with weight 12. Vertex 2 has an edge back to vertex 1, but its
weight  is 22 (because  this is a directed graph,  if there is an edge  from A to B, it doesn’t mean  that
there  is an edge from B to A, or if there  is, the weights don’t need to be the same).  
 
Output: The graph  in graphPosLittle.txt has size of 10 vertices. If coded correctly, a call to find
shortest paths from vertex 1 should produce  the following output:  
Shortest path to 1: 1: cost = 0 
Shortest path to 2: 1 2: cost = 6 
Shortest path to 3: 1 7 9 10 4 8 5 3: cost = 35 
Shortest path to 4: 1 7 9 10 4: cost = 21 
Shortest path to 5: 1 7 9 10 4 8 5: cost = 28 
Shortest path to 6: 1 7 9 10 4 8 5 3 6: cost = 37 
Shortest path to 7: 1 7: cost = 6 
Shortest path to 8: 1 7 9 10 4 8: cost = 25 
Shortest path to 9: 1 7 9: cost = 11 
Shortest path to 10: 1 7 9 10: cost = 15 
 
Submission of Assignment
Submission will be via FLO.  A single  zip file containing  all source code and required  documents.    If
there are any special requirements  for running  the program  these should be detailed  somewhere,
preferably  in separate document about running  your program.   Additional  documents  should be in
PDF format.  If you have utilised  additional data files for your assignment  and they are too large  to
upload  to FLO then provide a link in your documentation.