Assignment Four
Assignment Four
Objectives
• Understand how to represent graphs using adjacency lists
• Understand how to traverse graphs
• Understand how to find a shortest path
Admin
Marks 10 marks, excluding bonus marks. Marking is based on the correctness and
efficiency of your code. Your code must be well commented.
Group? This assignment is completed individually.
Due Time 23:59:59pm Sunday 3 June 2018. 23:59:59pm Wed 6 June 2018.
Late Submissions Late submissions will not be accepted!
In this assignment, you will implement a graph ADT (Abstract Data Type) with several
functions. A graph G considered in this assignment consists of a set V of vertices and a set E
of edges, where each vertex in V is a point on a Cartesian plane, and each edge is a line
segment between the two points in V. Consequently, G is an undirected graph. Each point
has a x-coordinate and a y-coordinate. We assume that the x-coordinate and the y-coordinate
of each point are integers.
The distance of between two points v1=(x1, y1) and v2=(x2, y2) is √(𝑥1 − 𝑥2)
2 + (𝑦1 − 𝑦2)
2.
The length of an edge is the distance between its two end points. Therefore, each edge has
an implicit weight which is its edge length.
Given a path in a graph, its path length is the sum of lengths of all its edges. A path between
two vertices is a shortest path if it has the minimum path length among all the paths between
the two vertices.
Given two vertices u and v in a graph, u is reachable from v if there is a path from u to v.
Basic types are provided as follows:
// A vertex is a 2D point
typedef struct Vertex {
int x; // x-coordinate
int y; // y-coordinate
} Vertex;
// each edge is a pair of vertices (end-points)
typedef struct Edge {
Vertex *p1; // first end point
Vertex *p2; // second end point
} Edge;
// A vertex node stores a vertex and other information, and you need to expand this type
typedef struct VertexNode {
Vertex *v;
} VertexNode;
typedef struct GraphRep { // graph header
VertexNode *vertices; // an array of vertices or a linked list of vertices
int nV; // #vertices
int nE; // #edges
} GraphRep;
typedef struct GraphRep *Graph;
The above types serve as a starting point only. You can revise them and add more types.
You need to implement the following functions:
• Graph CreateEmptyGraph(). This function creates an empty graph and returns it.
• int InsertEdge(Graph g, Edge *e). This function does the following task. Check if the
edge e is in the graph g. If e is not in g, insert e into g and return 1. Otherwise, return
0.
• void DeleteEdge(Graph g, Edge *e). This function deletes the edge e from the graph g.
If e is not in g, it does nothing.
• void ReachableVertices(Graph g, Vertex *v). This function finds all the vertices
reachable from the vertex v in g and prints them on the screen in non-decreasing order
of their x-coordinates. In the output, each vertex is displayed as a pair (x’, y’), where x’
and y’ are its x-coordinate and y-coordinate, and two adjacent vertices are separated
by a comma (,). If no vertex is reachable from v, nothing will be printed. If v is not a
vertex of g, this function does nothing.
• void ShortestPath(Graph g, Vertex *u, Vertex *v). This function finds the shortest path
between the vertex u and the vertex v, and print all the edges of the shortest path in
order starting with the vertex u in the form of (x1, y1), …, (x2, y2), where the first and
second element of each pair are the x-coordinate and y-coordinate of the
corresponding vertex. If either u or v is not a vertex of g, this function does nothing.
This function is optional. You will get 2 bonus marks if you apply Dijkstra’s shortest
path algorithm using a heap-based priority queue to correctly implement this
function with a time complexity of O((m+n) log n), where m and n are the number of
edges and the number of vertices of graph g.
• void FreeGraph(Graph g). This function frees the heap space occupied by the graph g.
• void ShowGraph(Graph g). This function prints each edge of g once in breadth-first
order. Your breadth-first search algorithm can pick any vertex as the first vertex to be
visited in the breadth-first search. In the output, each vertex is displayed as a pair (x’,
y’), where x’ and y’ are its x-coordinate and y-coordinate, and each edge (x1,y1)-(x2,y2)
is displayed as (x1,y1),(x2,y2), and two adjacent edges are separated by a white space.
Time complexity analysis
You need to include the time complexity analysis of each function as comments in your
program. Try your best to make each function time-efficient. Any time complexity that goes
against the best algorithm you have learned in this course will receive some penalty. For
example, the time complexity of your ShortestPath() function should not be higher than that
of the Dijkstra’s shortest path algorithm using a heap-based priority queue. There is no
specific requirement on the space complexity.
How to submit your code?
a. Go to the Assignment Four page
b. Click on Make Submission
c. Submit your MyGraph.c file that contains all the code.
Plagiarism
This is an individual assignment. Each student will have to develop their own solution without
help from other people. In particular, it is not permitted to exchange code or pseudocode.
You are not allowed to use code developed by persons other than yourself. All work
submitted for assessment must be entirely your own work. We regard unacknowledged
copying of material, in whole or part, as an extremely serious offence. For further information,
see the Course Information.