Representation of Search State Space and Search Operators In Details:
We will use a single search tree representation in graph search and maze search examples in this chapter. Search trees consist of nodes that define locations in state space and links to other nodes. For some small problems, the search tree can be easily specified statically; for example, when performing the search in game mazes, we can compute and save a search tree for the entire state space of the maze. For many problems, it is impossible to completely enumerate a search tree for a state space so we must define successor node search operators that for a given node produce all nodes that can be reached from the current node in one step; for example, in the 5 2 Search game of chess we can not possibly enumerate the search tree for all possible games of chess, so we define a successor node search operator that given a board position (represented by a node in the search tree) calculates all possible moves for either the white or black pieces. The possible chess moves are calculated by a successor node search operator and are represented by newly calculated nodes that are linked to the previous node. Note that even when it is simple to fully enumerate a search tree, as in the game maze example, we still might want to generate the search tree dynamically as we will do in this chapter).
For calculating a search tree we use a graph. We will represent graphs as a node with links between some of the nodes. For solving puzzles and for game related search, we will represent positions in the search space with Java objects called nodes. Nodes contain arrays of references to both child and parent nodes. A search space using this node representation can be viewed as a directed graph or a tree. The node that has no parent nodes is the root node and all nodes that have no child nodes a called leaf nodes.
Search operators are used to move from one point in the search space to another. We deal with quantized search spaces in this chapter, but search spaces can also be continuous in some applications. Often search spaces are either very large or are infinite. In these cases, we implicitly define a search space using some algorithm for extending the space from our reference position in the space. Figure 2.1 shows representations of search space as both connected nodes in a graph and as a two-dimensional grid with arrows indicating possible movement from a reference point denoted by R. When we specify a search space as a two-dimensional array, search operators will move the point of reference in the search space from a specific grid location to an adjoining grid location. For some applications, search operators are limited to moving up/down/left/right and in other applications operators can additionally move the reference location diagonally. When we specify a search space using node representation, search operators can move the reference point down to any child node or up to the parent node. For search spaces that are represented implicitly, search operators are also responsible for determining legal child nodes, if any, from the reference point.
