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Figure 9-16. What s the shortest path between point A and point B It s obvious to us humans, but how do you explain it to a computer But what is a good path In the case of finding the shortest path, it s the one that gets you to your destination sooner. The problem is that computers can t see the big picture. They can see only one small step at a time. So the strategy for telling a computer how to find the shortest path goes something like this: Break the entire path into many small steps. For each step, figure out which step to take next. Take that step, and repeat the process until you get where you re supposed to be. But the computer must still be able to tell the difference between a good path and a bad path. Let s see how to help it figure that out.
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Solve this riddle: A newspaper is delivered to your front door every morning. What s the least expensive way of picking up it up A. B. Opening the front door. Walking out the back door, jumping over your garden fence, running down the alley, hailing a taxicab, and riding around the block to your front door
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Option A was free, but option B cost you about $3.75 in cab fare. This means that option B is more expensive.
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Expensive is the term that the A* algorithm uses to describe how much work it takes to travel between two points. A* figures out the least expensive routes to a destination. It does this by assigning a cost to every possible step you can take on the path. The step with the lowest cost is the better step to take. A* works by finding the lowest cost moves and the least expensive paths.
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A* has its own set of terms and vocabulary. Cost and expense are two of those terms and, as you ll see, they re a convenient way to describe some of its core concepts. I ll be introducing a few other specific A* terms ahead. Keep a special lookout for node and heuristic, coming up soon!
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Figure 9-17 explains what I mean by cost. Imagine that you re a bacterium in a Petri dish, freefloating and minding your own business at point A. Suddenly, the shadow of a huge, hungry single-celled amoeba looms over you with the lone goal of subsuming your cellular matter. You know you re in trouble if you don t hide right away. There are only two places you can hide: point B or point C. You have a split second to decide which is the closest.
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Figure 9-17. Which is closer, B or C In the example in Figure 9-17, traveling to point B takes about one-third longer than traveling to point C. In fact, it takes exactly 1.41 times longer to travel to point B from point A. That means that point C is where you need to swim to escape that amoeba. The value 1.41 is the cost of traveling diagonally. In a rectangular grid-based game world, there are only two choices of movement, and each has a cost: Diagonally: The cost is 14. Directly across: Going horizontally or vertically, the cost is 10. It doesn t really matter what those costs are, as long as they proportionately represent the amount of time it takes to move in those directions. So, 14 versus 10 is the same proportion as 1.4 versus 1, and we conveniently don t need to worry about decimal numbers. You can certainly use 1.4 and 1 in your own code if you prefer. Figure 9-18 shows the cost of movement between cells.
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