Chapter 2 Depth-first search and breadth-first search
As the basic search methods for puzzles and games, we formalize depth-firt search and
breadth-first search. Both traverse tangible graphs or hypothetical graphs. In many
cases those graphs are trees. Each node of the graph (tree) corresponds to a particular
configuration of puzzle or game.
Example. 8 – game. There are 8 tiles placed on a 3 by 3 grid.
Initial configuration
goal configuration
|--------------------|
|--------------------|
| 2
8
3 |
| 1
| 1
6
4 |
| 8
5 |
| 7
| 7
|-------------------|
2
3
|
4 |
6
5 |
|-------------------|
We define a move by the movement of the vacant position. In the initial configuration,
the movement of tile 7 to the right is equivalent to move space to the left. So there are
three moves in this configuration. After several moves, we have the target as follows:
2
8
3
2
1
6
4
1
5
7
7
8
6
3
2
3
4
1
8
4
5
7
6
5
2
3
1
8
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6
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1
7
2
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4
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6
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7
2
3
4
6
5
Set up the initial configuration called “node”. We maintain the closed sets of nodes,
CLOSED, which is the set of nodes that are already finished, so to speak
procedure dfs(node, depth)
begin
if d <= depth then begin
### depth is a pre-defined depth
push node to stack; Put node into CLOSED
for all move on node do begin
if ok_dfs(move) then begin
node1=apply(move, node)
dfs(node1)
end
pop up stack to node
end
main initialize node and goal, then call dfs(node, 1)
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ok is defined as follows:
function ok_dfs( move, node)
begin
if move is legitimate then begin
node1=apply(move, node)
if node1 is not in stack and not in CLOSED then return true
end
end
Breadth-first search is described next.
procedure bfs(node)
begin
while queue is not empty do begin
take a node from queue
Put node into CLOSED
for all move on node do begin
node1=apply(move, node)
if ok_bfs(move) then add node1 to queue
end
end
end
main initialize node and goal; add node to queue; call bfs(node)
function ok_dfs( move, node)
begin
if move is legitimate then begin
node1=apply(move, node)
if node1 is not in queue and not in CLOSED then return true
end
The breadth-first search above guarantees the shortest path to the target. It stores
many nodes in queue, and not space efficient. The depth-first search may end up with
the path to the target that is not optimal. Also it may generate many unnecessary
nodes.
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