CS361 Introduction to Artificial Intelligence
Sheet 21-11-2016
Faculty of Information technology
Misr University For Science and Technology
Answer the following questions:
1. A Farmer with his wolf, goat and cabbage come to the edge of a river they wish to
cross. There is a boat at the river’s edge, but of course only the farmer can drive it.
The boat also can carry only two things. If the wolf is ever left alone with the goat,
the wolf will eat the goat. If the goat is ever left alone with the cabbage, the goat
will eat the cabbage. Devise a sequence of crossings of the river so that all four
characters arrive safely on the other side of the river. Formulate the problem as
search. Formulate the problem in terms of state-space search. You should:
a) Suggest a suitable representation for the problem state.
b) State what the initial and goal states are in this representation.
c) State the available operators/rules for getting from one state to the next,
giving any conditions on when they may be applied.
d) Draw the first two levels of the search tree for the given problem.
2. Compare between Depth-first search, Depth-limited search, and Iterative deepening
search in terms of completeness, optimality, time complexity, and space
complexity.
3. Given the 8-Puzzle problem. You want to reach the goal state starting from the
following initial state. Use Depth-first search and Breadth-First search to search for
a solution. Draw the tree and number the nodes in the order of visiting.
The rules are:
Precondition:
Move Blank Left
Not at extreme left
Move Blank Right
Not at extreme right
Move Blank Up
Not at top row
Move Blank Down
Not at bottom row
4. Suppose that you are solving the 8-puzzle where it has solution. Which of the
methods (DFS, BFS, and IDS) is guaranteed to find a solution, assuming no
computational limits are reached? List all that are correct.
5. Given the following maze, you are required to go from A to M using the left-hand
rule.
Faculty of Information technology
Misr University For Science and Technology
CS361 Introduction to Artificial Intelligence
Sheet 21-11-2016
Use Depth-first search and Breadth-First search to search for a solution. Draw the tree
and number the nodes in the order of visiting.
6. The water jug problem is described as follows:
If you have 2 jugs (4 gallon - 3 gallon), how can you get exactly 2 gallons into the
4 gallon jug?
The state space for this problem can be described as the set of ordered pairs of
integers (x,y) such that x = 0, 1,2, 3 or 4 and y = 0,1,2 or 3; x represents the
number of gallons of water in the 4-gallon jug and y represents the quantity of
water in 3-gallon jug
The start state is (0,0) and the goal state is (2,n).Use the following rules:
No Current state
Next State
Description
1
(x,y) if x < 4
(4,y)
Fill the 4 gallon jug
2
(x,y) if y <3
(x,3)
Fill the 3 gallon jug
3
(x,y) if x > 0
(x-d, y)
Pour some water out of the 4 gallon jug
4
(x,y) if y > 0
(x, y-d)
Pour some water out of the 3-gallon jug
5
(x,y) if x>0
(0, y)
Empty the 4 gallon jug
6
(x,y) if y >0
(x,0)
Empty the 3 gallon jug on the ground
7
(x,y) if x+y>= 4
and y >0
(x, y) if x+y>= 3
and x>0
(x, y) if x+y<=4
and y>0
(x, y) if x+y<= 3
and x>0
(4, y-(4-x))
Pour water from the 3 –gallon jug into the 4 –gallon jug
until the 4-gallon jug is full
Pour water from the 4-gallon jug into the 3-gallon jug until
the 3-gallon jug is full
Pour all the water from the 3-gallon jug into the 4-gallon
jug
Pour all the water from the 4-gallon jug into the 3-gallon
jug
8
9
10
(x-(3-y), 3)
(x+y, 0)
(0, x+y)
Sample solution:
Gallons in the 4-gallon jug
Gallons in the 3-gallon jug
Rule applied
0
0
2
0
3
9
3
0
2
3
3
7
4
2
5
0
2
9
2
0
Use Depth-first search and Breadth-First search to search for a solution. Draw the tree
and number the nodes in the order of visiting.
7. Given the following map of Romania. You are in city of Arad and want to travel to
Bucharest. Use Depth-first search and Breadth-First search, with repeated state
checks, to search for a solution. Draw the tree and number the nodes in the order of
visiting. Order children of a node in alphabetical order.
CS361 Introduction to Artificial Intelligence
Sheet 21-11-2016
Faculty of Information technology
Misr University For Science and Technology