使用C++ 代写 graph search algorithm
Overview
This assignment involves graphs, and using several different data structures together in order to
implement a class graph search algorithm.
Dijkastra’s Shortest Path Algorithm
Dijkstra's algorithm is an algorithm for finding the shortest paths between nodes in a graph, which may
represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956
and published three years later.
The algorithm exists in many variants; Dijkstra's original variant found the shortest path between two
nodes, but a more common variant fixes a single node as the "source" node and finds shortest paths from
the source to all other nodes in the graph, producing a shortest-path tree.
For a given source node in the graph, the algorithm finds the shortest path between that node and every
other.It can also be used for finding the shortest paths from a single node to a single destination node by
stopping the algorithm once the shortest path to the destination node has been determined. For example, if
the nodes of the graph represent cities and edge path costs represent driving distances between pairs of
cities connected by a direct road, Dijkstra's algorithm can be used to find the shortest route between one
city and all other cities
Source:
Heap
A heap is an ADT that is very similar to the priority-queue from the last assignment. A heap is called a
min-heap or a max-heap based on whether smaller or larger values determine the priority of a value. For
this assignment, we will be using a min-heap to determine which vertices we want to visit next. You will
be using the values in the distance array (see pseudocode) as the priority of a vertex. The min-heap will
automatically keep its heap structure when new values are inserted or the min value is extracted from the
top.
Resources
A visual goes a long way in explaining complex algorithms. This video goes through the entire process of
Dijkstra’s algorithm on the graph that is provided to you in the graph text files.
Source:
Take note of the process and how it related to the pseudocode below.
Pseudocode
Graph represents the adjacency matrix of a graph. You can determine all of the edges and vertex in the
graph just with the adjacency matrix. Source and target are both vertices from the graph, and simply
indices from the adjacency matrix.
CMPSC 122.2
April 12, 2018 Homework 5
Due: Refer to last
page for due dates
Distance is an array that is used to keep track of the shortest path between source and all of the other
vertices in the graph. The previous array is used to keep track of the vertices with the shortest path that
leads to each vertex.
This pseudocode is modified version of the code from here:
https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#Using_a_priority_queue
function Dijkstra(Graph, source, target)
distance[source] = 0;
create min-heap Q
for each vertex v in Graph:
if v is not source
distance[v] = infinity
previous[v] = -1 // *
Q.add_with_priority(v, distance[v])
end for
while Q is not empty:
u = Q.extract_min()
if u is target
previous[u] = the previous value of u // *
break out of while
for each neighbor v of u: // only consider v that are still in Q
alt = distance[u] + length(u, v)
if alt < distance[v]
distance[v] = alt
previous[v] = u
Q.decrease_priority(v, alt)
end for
end while
// Determine the shortest path from source to target using previous array
create stack S
u = target
while previous[u] is defined:
push u onto S
u = previous[u]
push u onto S
// Output path ordering with distance between each node
// Output total distance of smallest path from source to target
end function
CMPSC 122.2
April 12, 2018 Homework 5
Due: Refer to last
page for due dates
Program (100 points) Dijkastra’s Shortest Path Algorithm between two vertices on a graph
Write a program (dij.cpp) that does the following:
- Leverages the provided includes to accomplish the following:
o min-heap.h: determine the most desirable vertex to process next
o graph.h: read in a graph from a text file and store its adjacency matrix for readonly
access
o set.h: keep track of vertices that have already been visited
o stack.h: output the vertices in the shortest path
o list.h: used to implement Set and Stack
- You should accept a file name of the graph you want to test (assume the file is in the
same directory as the cpp program)
- Load the graph into memory with the Graph class
- Accept two index values representing the source vertex and target vertex
- Run Dijkstra’s Shortest Path Algorithm on the loaded graph using the source and target
vertex
- Output the entirety of the determined shortest path, with the distance of each edge in the
path and the total path between the two vertices
Input/Output Format:
Please enter location of graph file to load: graph_1_win.txt
Please enter the index of the starting vertex: 0
Please enter the index of the target vertex: 7
The shortest path from vertex 0 to vertex 7 is:
0 to 2: 2
2 to 3: 2
3 to 4: 1
4 to 6: 1
6 to 5: 2
5 to 7: 3
Total path length is 11
Template Program Files
There are eight (8) files in total that will be provided for download on Canvas.
? A starter file dij.cpp that shows how to load a graph from a text file into a graph class
? Five (5) header files with the complete implementations of all the ADTs you need to complete the
assignment
? Two (2) graph text files. The file ending in nix contains Unix style line endings and the file
ending with win contains Windows style line endings. The Graph class should be able to read in
either file regardless of the operating system you are; however, it is recommended you use the
CMPSC 122.2
April 12, 2018 Homework 5
Due: Refer to last
page for due dates
text file that is appropriate for the system you are currently on. If you are using a Mac, use the
text file with Unix style line endings.
Compiling the Program with g++
Use the following command to compile your classes. This is the command I personally use on the Sunlab
machines to compile and grade your programs:
g++ -Wall -o <output_name> <program_name.cpp>
Example:
g++ -Wall -o dij dij.cpp
Remember: Your programs must successfully compile without any errors, or a zero will be given for that
program.
Following Instructions
You are expected to follow the directives laid out in this assignment and the course syllabus. Points will
be deducted for incorrectly named files, missing/incorrectly filed out banner comments, not supplying
hardcopy submissions in a pocket folder with the appropriate information, and failing to implement
features/functionality specified in the assignment. It is expected that you will utilize the provided template
files for this assignment, and that you do not modify the names of class members/functions that are
provided in the template.
If you have questions about any portions of the assignment or what is expected, contact me for
clarification.
Submission
? Electronic Submission (Due: 5:00 PM, Thursday, April 26, 2018)
- All nine (9) files initially provided (your completed dij.cpp, all the header files, and
the two graph files)
- Submitted using the mail122 command on the Sunlab machines
? Hardcopy Submission (Due: Beginning of class, Thursday, April 26, 2018)
- Printed hardcopy of your completed dij.cpp source code
- The page of the program should be stapled together
- Submitted in a pocket folder with your name, the course, and the section number on
the front
http://www.6daixie.com/contents/13/1318.htm
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