DEPTH FIRST SEARCH

Depth-first search is a way for computers to organize searches of a
tree without having to store the entire tree in its memory at once.

                        A
                    /       \
                /               \                   Computer's move
            /                       \
        B                               C
      / | \                           / | \
    /   |   \                       /   |   \       Human's move
  /     |     \                   /     |     \
D       E       F               G       H       I

A depth-first search of this tree would look at these positions
in the order A, B, D, B, E, B, F, B, A, C, G, C, H, C, I, C, A.
At each stage, the computer sees if it has more options to consider; 
if it does not (either because it has reached the maximum look-ahead
depth, which in this case is 2, or because it has already examined 
all the options of the current position), then it computes the 
minimax value of the position and moves back up the tree.

Using this procedure, it is possible to do a complete search
of the tree without actually storing the whole thing in memory
at any one time.  Only the positions that are relevant to
the current path through the tree and a small number of
side-branches need to be stored at any single instant.