Question

The problem is as follows: A wanderer begins on the grid coordinates (x,y) and wants to reach the coordinates (0,0). From every gridpoint, the wanderer can go 8 steps north OR 3 steps south OR 5 steps east OR 6 steps west (8N/3S/5E/6W).

How can I find the shortest route from (X,Y) to (0,0) using breadth-first search?

Clarifications:

• Unlimited grid
• Negative coordinates are allowed
• A queue (linked list or array) must be used
• No obstacles present

Answer 1

I’m going to go ahead and answer my own question for future reference.

Psuedocode:

while (true) {
    if (destination reached)
        break;
    addToQueue(go north);
    addToQueue(go south);
    addToQueue(go east);
    addToQueue(go west);
    getNextFromQueue;
}

It should also be noted that the execution time for this application grows very, very fast, so test it out with small coordinate values. For example, the coordinates (1,1) gives 7 levels of breadth and requires 16384 iterations.