Author: Amit Patel

Someone asked me about an algorithm that, given a location of a unit, would tell you what locations can be reached in the next turn. I’m assuming you have a MovementCost function that tells you how hard it is to walk from one space to another. You can use Dijkstra’s algorithm to find this area.

Let Costs be an array (as big as your map) of integers, init. value = -1

Function Find(UnitLocation)
    Let Open be a priority queue of locations /* sorted by Costs[x] */
    Let Closed be a set of locations

    Put Location in Open

    While Open isn't empty:
        Remove a location X from Open
        Add X to Closed
        If Costs[X] is less than the Movement Limit:
            For each Y that is a neighbor of X:
                NewCost = Costs[X] + MovementCost(from X to Y)
                If Costs[Y] is -1 or NewCost is less than Costs[Y]:
                    Set Costs[Y] to NewCost
                    Add Y to Open if it's not already in Open

    Let Results be a list of locations
    For each X in Closed:
        If Costs[X] is less than the Movement Limit:
            Add X to Results
        Set Costs[X] to -1

(It’s important to keep Costs outside the Find function; otherwise the initialization time for that big array would slow down the whole algorithm. The algorithm restores Costs to -1 at the end so that you can use it the next time you want to Find.)

This algorithm should be pretty fast. In practice the number of things that go into Open should be the area (which are spaces you can reach) + the perimeter (which are spaces just out of reach), which is not too high as long as the unit’s movement is pretty limited.