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The standard path finding involves finding the (shortest) path from an origin to a destination, typically on a map. This is an

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Path finding involves finding a path from A to B. Typically we want the path to have certain properties,
such as being the shortest or to avoid going through certain obstacles. As the main aim is to think
about path finding, we focus on the common task of finding shortest paths from A to B - shortest here
means the path that has less total costs (more on this later, but given if we can travel at a constant
speed over all parts of the map, then this equates to a path that is of least distance). The path is
typically on a map (e.g., game) or a surface (e.g., robot).
Consider the map below (see Figure 1a), where we want to find a shortest path from origin point
A to destination point B. There are obstacles and impassable locations (e.g., consider them walls in a
maze, or a building one cannot enter in a game etc) that we cannot traverse (these are the block areas
in the figure). If we use Euclidean distance as the cost (so the further one travels, the more costly),
then the orange path, labelled (2), in Figure 1b is the shortest one1
. The other two are possible paths but not the shortest.
To find (shortest) paths, we need to represent this map on a computer. There are several approaches
to do so, which we will describe in the following subsection.

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