The Knight’s Tour.

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Presentation transcript:

The Knight’s Tour

The Problem A gallant and brave knight must traverse the lands to rescue the princess and claim his rightful place in the kingdom A Knight on a board has to visit every square without passing through the same square more than once. Then returns to the starting square

Give students a knight and see if they can solve it

The tourists get upset if they visit the same place twice A similar Problem? You are a tour guide and must come up with a tour that gets a tourist from their London hotel to all the city sights and back to their hotel at the end of the day. The tourists get upset if they visit the same place twice How might we solve this?

Consider another way Computer Scientist create a diagram This is called a Graph It is easier to plan and find the solution

Abstraction Using abstraction to make a model Hides all the detail apart from what is needed Abstraction is one of the four cornerstones of Computer Science. It involves filtering out – essentially, ignoring the characteristics that we don't need in order to concentrate on those that we do.

1. Use Abstraction to solve the Knight’s Tour 1 , 7 1, 9 1, 6

Use Abstraction to solve the Knight’s Tour 1 Add the nodes which the Knight can go to from a particular square. 6 9 7

Use Abstraction to solve the Knight’s Tour 1 Continue until all the Boxes have numbers in them. This will create a ‘messy’ diagram of the possible paths that the Knight can go to 2 3 6 8 9 10 7

Another way to Use Abstraction to solve the Knight’s Tour Start at a square and move to the next square that you can Number it and draw a line between the points Then jump to the next free square Repeat until you cannot move any further Select a new square, repeat steps 1, 2, 3, 4 1 2 6 7 8 12

RESULT

RESULT

RESULT

RESULT

Solution Now you have the diagram of the route You need to tidy it up into a graph form so that it is easy to view Ensuring that all the correct nodes touch each other pull the route apart and make it easier to view Create a nice diagram

What is the final solution?

What have you learnt?