to Introduction Computer Science II Program #6: Over the river ... Due: Wednesday, March 5th, 2008 at 9PM
Write a C program to find the least cost path through a scene.
Scenes, Cells, and Paths
A scene is an N xN grid in which grid cells represent grass, highways, fences, rivers, and swamps. Each cell Ci,j is connected to its grid neighbors. Cell C1,1 is the start cell and cell CN,N is the final cell. There is a path from cell Ci,j Ck,l if Ci,j and Ck,l are neighbors, or if there exists a cell Ci ,j , such that Ci,j and Ci ,j are neighbors and there is a path from Ci ,j Ck,l . The starting path contains exactly one cell: C1,1 , the starting cell. A final path is a path from the starting cell to the final cell (C1,1 CN,N ). Each cell type (highway, etc) has a cost associated with it. The cost of a path is the sum of the cost of the cells along the path. Our goal is to compute the least cost path from the start cell C1,1 and the final cell CN,N .
A search algorithm
In CS 151, you learned about depth first search (DFS). In a recursive implementation of DFS, the recursion stack keeps track of partially constructed paths. DFS is a fine algorithm for finding a path through a scene, but not for our goal of finding the least cost path through the scene. In this assignment, you will use the A or best-first graph search algorithm to find the least cost path through the scene. Instead of using the recursion stack to keep track of partially explored path, A uses a priority queue. The algorithm has the following form: create a priority queue, insert the starting path into the queue. Then, remove the path, Ci,j Ck,l with the lowest priority from the queue. For each neighbor Ck ,l of Ck,l add the path Ci,j Ck,l Ck ,l to the priority queue. Continue this process until the priority queue is empty or a final path is encountered. A uses a distance-plus-cost heuristic for computing priorities. For our application, the priority function, f (p), computes the cost of the path p plus an estimate of the cost of extending p to CN,N . The Manhattan distance, d, between two cells, Ci,j and Ck,l measures the distance between them following a "grid-like" path. Specifically, d = |k - i| + |l - j| This distance from Ck,l , the last cell on to p, CN,N would be a reasonable estimate of the cost. A better estimate would weight the this distance with the cell cost for highways, the least cost cell type. Given an appropriate priority function, the search space can be reduced further by avoiding cycles in paths. In our application, we can detect cycles by keeping track of the cells that have been visited.
Data structures:
We have implemented a data structure for scenes, including the code necessary to read a scene from a file. This code can be found in: /home/amr/152/scene.{c,h}. You may not change this code. You must implement a path data structure, a priority queue for tracking paths, a hash table for tracking visited cells, and the search algorithm. The scene implementation provides a mechanism for tracking whether a cell has been visited, but this mechanism is provided for testing purposes only.
Input and Output:
The input format for scenes is: N Row 0 Row 1 ... Row N where N is the size of the scene and a row is a string of N characters drawn from the set {g, G, h, H, f, F, r, R, s, S}. You can find sample scenes in /home/amr/152/p6. Your program should output a list of cells that constitute a least-cost path or "No path found," if no such path exists. Extra credit: use FTG to produce a graphical representation of the solution.
Submission:
Your program will be...