COSC1285 - Algorithms and Analysis - Path Finding - Handling Different Terrain - Engineering Assignment Help

Assignment Task:

COSC1285: Algorithms and Analysis  Engineering Assignment Help

Tasks

The assignment is broken up into a number of tasks. Apart from Task A that should be completed initially, all other tasks can be completed in an order you are more comfortable with, although completion. of task C is likely to help with task D and we consider task D as a distinction level one.

Task A: Implement Dijkstra’s Algorithm for Pathfinding 

To develop an initial approach to pathfinding, you should implement Dijkstra’s algorithm. For this task initially, if not specified, assume all locations and coordinates have unit cost to travel to the adjacent one, e.g., (2,1) to (2,2) has a unit cost/cost of 1 to travel between.

Given input, your implementation should return a (shortest) path between origin and destination. Note there may be more than one shortest path, hence we ask for a shortest path. A path should include the origin cooridinate, all coordinates between, and the destination coordinate.

Hint: For a graph representation, we can use Dijkstra’s algorithm as is. For a grid representation, you’ll need to consider how to implement Dijkstra’s on it. For both, we suggest to first figure it out conceptually, then translate into code.

Task B: Handling different Terrain 
In maps, we frequently have locations that are of different surfaces, e.g., sand, gravel, mud etc. This can affect travelling speeds. Up to this task, traversal between adjacent locations/coordinates are assumed to have a cost of 1. But in this task, now the costs can be greater than 1, and will be specified in a terrain parameter file (see Details of Files section for more details).

In this task, you’ll need to modify your data structures and algorithms to handle terrain cost greater than 1. This might mean a path that was shortest for uniform unit cost map will now be very costly, e.g., it has to go through many coordinates of high terrain cost such as mud. As an example, see Figure 4, where the original orange path of Figure 2b is no longer the shortest as it has to go through coordinates with high costs, e.g., coordinate (5,2) with cost 12. Instead the purple coloured
path is the shortest.

Hint: you’ll need to consider how to translate this into the graph representation if you using that. There are at least two ways you can model this. One is to carefully consider what is the meaning of an edge weight in the graph representation, then whether you need a directed graph representation.

Task C: Handling multiple origins and destinations 
Sometimes we can have multiple origin and destination points, e.g., we have a number of ambulances waiting at a number of hospitals (these are our origin locations) and we have a number of emergencies

Figure 4: Map with terrain cost greater than 1 (coordinates/cells with numbers). Corresponding shortest path is rediverted in the other direction because of the terrain costs. to attend to (these are the destination locations). We want to send an ambulance to one of the cases asap, hence it doesn’t matter which hospital (origin) or to which emergency (destination), as long as the path is shortest.

In this task, you’ll modify your implementation to cater for multiple origin and/or destinations. Note that we just need to find a shortest path between any of the origins to any of the destinations. As an example, see Figure 5. There are two origins and two destinations, hence four possible paths between the origins and destinations. Path labelled (1) and coloured orange is the shortest one among the four.

Figure 5: Map with multi-origin (blue) and multi-destinations (red). There are 4 possible paths, but the shortest one is the orange one, labelled (1).
Hint: Consider how Dijsktra’s searches for its shortest path.

Task D: Waypoints 
Note this task is probably the hardest of the four and we consider it as an distinction level task, but you are welcome to tackle these in the order you find easiest or desire. In path finding, it is typical that we must visit a number of waypoints when traversing from origin to destination, e.g., in a game, the player sets some waypoints so their units can avoid certain enemies etc.

Task A (4/15):
For this task, we will evaluate your implementation and algorithm on whether:

1. Implementation and Approach: It implements Dijkstra’s algorithm and adapted to solve path finding.

2. Correctness: Whether if finds a shortest path for given input maps.(4/15):

For this task, we will evaluate your implementation and algorithm on whether:

1. Implementation and Approach: It implements Dijkstra’s algorithm and adapted to solve path finding.

2. Correctness: Whether if finds a shortest path for given input maps.

Task B (3/15):
For this task, we will evaluate your implementation and algorithm on whether:

1. Implementation and Approach: It takes a reasonable approach and can incorporate terrain information when computing shortest paths.

2. Correctness: Whether if finds a shortest path for given input maps (which can include terrain information).

Task C (3/15):
For this task, we will evaluate your implementation and algorithm on whether:

1. Implementation and Approach: It takes a reasonable approach and can incorporate multiple origins and destinations when computing shortest paths.

2. Correctness: Whether if finds a shortest path for given input maps (which can include multiple origins and destinations).

Task D (3/15):
For this task, we will evaluate your implementation and algorithm on whether:
1. Implementation and Approach: It takes a reasonable approach and can incorporate waypoints when computing shortest paths.

2. Correctness: Whether if finds a shortest path for given input maps (which can include waypoints).

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