The shortest path problem is one of the most practical and popular problems in computer science (think GPS
navigation, robot routing, etc.). We are interested in the instance where a robot must find a shortest path in
a maze. Maze is represented by a two-dimensional binary array (or grid) n × m, where the top-left corner
has coordinates (0,0) and the bottom-right corner has coordinates (n-1,m-1). 0 at position (x,y) in the array
indicates open space (or passage) to which our robot can move freely. 1 indicates a wall that blocks the robot,
that is, the robot cannot move to a position occupied by a wall. The array below is an example of a 4 × 5
The robot starts at the position (sx,sy) and must find a shortest path to the position (fx,fy). In a single step
the robot can move in one of four directions (up, down, left or right) but only to a position that is open. The
shortest path is a path that requires the least number of moves from the robot to reach (fx,fy) starting at (sx,sy).
For instance, if we consider our example maze, and (sx=0,sy=0) and (fx=3,fy=2), then there are two possible
shortest paths of length 5, i.e. the robot must make 5 moves to reach the finishing position (3,2) from the
starting position (0,0).
Your task is to implement a function that will find the length of a shortest path of our robot for a given maze,
starting position (sx,sy) and finishing position (fx,fy). You can assume that such path always exists. To
implement the function consider the following observation. After making a move from (sx,sy) to a new position,
the length of the best path the robot can take to (fx,fy), which potentially can be the shortest, is equal 1 + the
length of a shortest path from the new position to (fx,fy).
Read about BFS and DFS. If you plan on implementing this using DFS, read about dynamic programming.
1. Create directory A3 where you will place your code.
2. Download A3handout.tar from the piazza resources section.
3. Untar handout, and move a3.hpp,a3.cpp and Maze.hpp to your A3 directory. These files provide all
functionality to: read input maze and input parameters, invoke your distance function and generate output.
Additionally, Maze.hpp defines the interface to interact with the input maze (see below).
4. Create Makefile to automate compilation process of your code. You can directly adopt Makefile from
A0 (replace a0 with a3).
5. a3.hpp implement function distance considering the following:
(a) Arguments sx,sy,fx,fy represent the starting position (sx,sy) and finishing position (fx,fy).
(b) Argument maze of the type Maze represents the input maze.
(c) Class Maze provides the following methods, which are the only methods you can use to interact
with the maze:
• int nrow() const; — returns the number of rows in the maze.
• int ncol() const; — returns the number of columns in the maze.
• bool is_visited(int x, int y) const; — returns true if position (x,y) in the maze
has been marked as visited, false otherwise. For any position outside the maze, e.g. (-1,0),
it returns true.
• bool is_open(int x, int y) const; — returns true if position (x,y) in the maze is
open and the robot can move to it, false otherwise. For any position outside the maze, e.g.
(-1,0), it returns false.
• void mark(int x, int y); — marks position (x,y) as visited, which implies that is_visited(x,y)
will return true. If (x,y) is outside the maze, or is not open, the method does nothing.
• void unmark(int x, int y); — removes visited mark if position (x,y) was marked as
visited otherwise does nothing.
(d) The return value must be the length of a shortest path between (sx,sy) and (fx,fy) in the maze.
(e) Arguments passed to distance are always correct and (fx,fy) is always reachable from (sx,sy).
6. You can edit only a3.hpp and all your code must be contained in this file only.
7. To test your code you can use the a3.txt file provided in the handout. If passed to a3 like this:
./a3 4 5 0 0 3 2 a3.txt
it should product the following output:
Here, 4 5 are maze dimensions, 0 0 corresponds to sx sy, 3 2 corresponds to fx fy, and 5 is the
length of the resulting shortest path.
1. Remove your binary code and other unrelated files (e.g. your test files).
2. Create a tarball with your A3 folder.
3. Follow to https://autograder.cse.buffalo.edu and submit A3.tar for grading.
4. You can make five submissions, and the last submission will be graded.
5. Any submission after the deadline will have 50% points deducted.
• 5pt: Code builds via make and README is provided.
• 5pt: The example a3.txt above works.
• 90pt: There will be nine test cases. You will get 10pt for each correctly solved maze.
• If your code is extremely inefficient, autograder will terminate your code and you will receive 0pt.
• Make sure that all file and directory names are exactly as instructed. Otherwise the grading system will
miss your submission and you will get 0pt.
• Make sure that you start working on the assignment early! If you wait to the very last moment, you may
expect delays from autograder (overloaded by other students who like you waited with their submission).
• If you are having trouble, have a discussion on piazza! Before posting your question, ask yourself: Am
I giving enough information where someone who is not looking at my code can still help? Do not, of
course, share your code.