Toy Problem:
Missionaries and Cannibals
On one bank of a river are three
missionaries (black triangles) and
three cannibals (red circles). There is
one boat available that can hold up
to two people and that they would
like to use to cross the river. If the cannibals ever
outnumber the missionaries on either of the river’s banks,
the missionaries will get eaten.
How can the boat be used to safely carry all the
missionaries and cannibals across the river?
Solving Problems by Searching
1
Search Problems
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initial state
set of possible actions/applicability conditions
•
•
•
successor function: state  set of <action, state>
successor function + initial state = state space
path (solution)
goal
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goal test function or goal state
path cost function
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•
assumption: path cost = sum of step costs
for optimality
Solving Problems by Searching
2
Missionaries and Cannibals:
Initial State and Actions
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initial state:
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all missionaries, all
cannibals, and the
boat are on the left
bank
5 possible actions:
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•
•
•
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one missionary crossing
one cannibal crossing
two missionaries
crossing
two cannibals crossing
one missionary and one
cannibal crossing
Solving Problems by Searching
3
Missionaries and Cannibals:
State Space
1c
1c
2c
1m
1c
2c
1m
1m
2c
2c
1m
1c
1c
1c
1c
1c
2m
2m
1m
1c
Solving Problems by Searching
4
Breadth-First Search

strategy:
• expand root node
• expand successors of root node
• expand successors of successors of root
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
node
etc.
implementation:
• use FIFO queue to store fringe nodes in
general tree search algorithm
Solving Problems by Searching
5
depth = 3
depth = 2
depth = 1
depth = 0
Breadth-First Search:
Missionaries and Cannibals
Solving Problems by Searching
6
Depth-First Search

strategy:
•
•

always expand the deepest node in the current fringe
first
when a sub-tree has been completely explored, delete
it from memory and “back up”
implementation:
•
•
use LIFO queue (stack) to store fringe nodes in
general tree search algorithm
alternative: recursive function that calls itself on each
of its children in turn
Solving Problems by Searching
7
depth = 3
depth = 2
depth = 1
depth = 0
Depth-First Search:
Missionaries and Cannibals
Solving Problems by Searching
8
Depth-First Search:
Finding the Optimal Path


first solution discovered may not be
optimal  must keep searching
continued search:
• assumption: non-decreasing path costs
• remember path cost of cheapest path found
•
so far
do not expand nodes for which path cost
exceeds cheapest found so far
Solving Problems by Searching
9