COS3751
EXAM PACK
Revision PACK
Questions. Answers
,COS3751 Examination Preparation
Question 1 State Spaces [7]
(a) Define the concept of a Fully observable environment. (1)
An environment is said to be Fully observable if an agent’s sensors give it access to
the complete state of the environment at each point in time.
(b) Consider a game of chess. Is this a deterministic or stochastic environment?
Clearly explain why. (2)
Deterministic: because, in chess, the next state of the game (environment) is
completely determined by the current state of the game and the move (action)
executed by a player (agent).
(c) Differentiate between discrete and continuous environments. Provide an example of
each (4)
An environment is said to be discrete if its state-space is finite and, for each state,
there are only finitely many percepts to be perceived and only finitely many
actions to choose from. The game of chess is an example of such an environment.
On the other hand, a continuous environment has infinitely many distinct states,
infinitely many percepts, and infinitely many actions to choose from at any state.
Taxi driving is an example of a continuous environment.
Question 2 Searching [16]
̂
Consider the provided diagram and answer the questions that follow (the ℎ value of each
node is provided in brackets after the node name, and the 𝑔̂ value is provided next to the
edges between nodes)
m(1)
2
e(4) 5 k(2)
1
2 4 n(0)
3
a(10) 3 d(5)
7 6
b(12) l(1)
8 7
3
10
i(4)
c(4)
f(7) 5 4
8
3
5 h(5)
g(4)
©ornelis Dubbelman-48269328 Page 1 of 12
,COS3751 Examination Preparation
(a) Explain what an admissible heuristic is. (2)
An admissible heuristic is one that never overestimates the true cost of reaching
the nearest goal.
(b) List the nodes and their 𝑓̂ values that are added to the frontier when node d is
expanded. Assume that node a is already on the explored (closed) list. (3)
l(10), i(14)
Not enough information is provided to answer this question…
Which search strategy should we use, Greedy-Best-First or A*?
If A*, which node is the initial (root) node? You cannot calculate PATH-cost if you
don’t know where the root is!
Let’s ASSUME that A* should be used, and that node a is the start node.
Expanding a gives
e(4) f(e) = 6
2
a(10) 3 d(5) f(d) = 8
b(12) 7
8
f(b) = 19
c(4) f(c) = 12
Next; e has the lowest f-cost, so it will be expanded next:
5 k(2) f(k) = 9
e(4)
2
a(10) 3 d(5) f(d) = 8
b(12) 7
8
f(b) = 19
c(4) f(c) = 12
Finally, expanding node d:
5 k(2) f(k) = 9
e(4)
2
a(10) 3 d(5) 6
b(12) 7 l(1) f(l) = 10
8 7
f(b) = 19
c(4) f(c) = 12 i(4) f(i) = 14
Notice that k is already on the frontier.
This is how I got to my answer…
©ornelis Dubbelman-48269328 Page 2 of 12
, COS3751 Examination Preparation
(c) Suppose we have the following frontier list (i(14), c(12), g(20)). Which one of these
nodes will be selected for expansion next? State why. (2)
Node c: because it has the lowest f-cost among all current frontier nodes. (I assume
that the values in brackets indicate f-costs)
(d) Explain what is meant by consistence with respect to heuristic searches (1)
If the heuristic function of a graph-search strategy is consistent, then the algorithm
is guaranteed to be optimal (and complete when the branching factor is finite).
For every node in the search tree, the following inequality must hold
𝒉(𝒏) ≤ 𝒄(𝒏, 𝒂, 𝒏′ ) + 𝒉(𝒏’).
(e) Assume that a graph-search is used. Is the heuristic used in this diagram consistent?
Explain why/why not. (2)
No, this heuristic is not consistent!
𝟏𝟎 = 𝒉̂ (𝐚) ≰ 𝒈 ̂ (𝐞) = 𝟔
̂ (𝐚, 𝐞) + 𝒉
or
𝟏𝟎 = 𝒉 ̂ (𝐚) ≰ 𝒈 ̂ (𝐝) = 𝟖
̂ (𝐚, 𝐝) + 𝒉
(f) Consider the following diagram
J K L M
H I
E F G
A B C D
Assume that loops are detected and that you consider moves in the order Up, Right,
Down, Left. Also assume that the start node is node E, and the goal node is node G.
List the order in which nodes are visited for a depth-first search. (6)
E, A, B, C, D, G
NB: Depth-first search uses a LIFO queue. A LIFO queue means that the most
recently generated node is chosen for expansion.
I used depth-first-GRAPH-search to obtain my solution (see diagram below)
The labels on the left of each node has the form GENERATE| EXPAND, where
GENERATE depicts the order in which nodes are generated and EXPAND depicts the
order in which nodes are expanded (visited).
©ornelis Dubbelman-48269328 Page 3 of 12
EXAM PACK
Revision PACK
Questions. Answers
,COS3751 Examination Preparation
Question 1 State Spaces [7]
(a) Define the concept of a Fully observable environment. (1)
An environment is said to be Fully observable if an agent’s sensors give it access to
the complete state of the environment at each point in time.
(b) Consider a game of chess. Is this a deterministic or stochastic environment?
Clearly explain why. (2)
Deterministic: because, in chess, the next state of the game (environment) is
completely determined by the current state of the game and the move (action)
executed by a player (agent).
(c) Differentiate between discrete and continuous environments. Provide an example of
each (4)
An environment is said to be discrete if its state-space is finite and, for each state,
there are only finitely many percepts to be perceived and only finitely many
actions to choose from. The game of chess is an example of such an environment.
On the other hand, a continuous environment has infinitely many distinct states,
infinitely many percepts, and infinitely many actions to choose from at any state.
Taxi driving is an example of a continuous environment.
Question 2 Searching [16]
̂
Consider the provided diagram and answer the questions that follow (the ℎ value of each
node is provided in brackets after the node name, and the 𝑔̂ value is provided next to the
edges between nodes)
m(1)
2
e(4) 5 k(2)
1
2 4 n(0)
3
a(10) 3 d(5)
7 6
b(12) l(1)
8 7
3
10
i(4)
c(4)
f(7) 5 4
8
3
5 h(5)
g(4)
©ornelis Dubbelman-48269328 Page 1 of 12
,COS3751 Examination Preparation
(a) Explain what an admissible heuristic is. (2)
An admissible heuristic is one that never overestimates the true cost of reaching
the nearest goal.
(b) List the nodes and their 𝑓̂ values that are added to the frontier when node d is
expanded. Assume that node a is already on the explored (closed) list. (3)
l(10), i(14)
Not enough information is provided to answer this question…
Which search strategy should we use, Greedy-Best-First or A*?
If A*, which node is the initial (root) node? You cannot calculate PATH-cost if you
don’t know where the root is!
Let’s ASSUME that A* should be used, and that node a is the start node.
Expanding a gives
e(4) f(e) = 6
2
a(10) 3 d(5) f(d) = 8
b(12) 7
8
f(b) = 19
c(4) f(c) = 12
Next; e has the lowest f-cost, so it will be expanded next:
5 k(2) f(k) = 9
e(4)
2
a(10) 3 d(5) f(d) = 8
b(12) 7
8
f(b) = 19
c(4) f(c) = 12
Finally, expanding node d:
5 k(2) f(k) = 9
e(4)
2
a(10) 3 d(5) 6
b(12) 7 l(1) f(l) = 10
8 7
f(b) = 19
c(4) f(c) = 12 i(4) f(i) = 14
Notice that k is already on the frontier.
This is how I got to my answer…
©ornelis Dubbelman-48269328 Page 2 of 12
, COS3751 Examination Preparation
(c) Suppose we have the following frontier list (i(14), c(12), g(20)). Which one of these
nodes will be selected for expansion next? State why. (2)
Node c: because it has the lowest f-cost among all current frontier nodes. (I assume
that the values in brackets indicate f-costs)
(d) Explain what is meant by consistence with respect to heuristic searches (1)
If the heuristic function of a graph-search strategy is consistent, then the algorithm
is guaranteed to be optimal (and complete when the branching factor is finite).
For every node in the search tree, the following inequality must hold
𝒉(𝒏) ≤ 𝒄(𝒏, 𝒂, 𝒏′ ) + 𝒉(𝒏’).
(e) Assume that a graph-search is used. Is the heuristic used in this diagram consistent?
Explain why/why not. (2)
No, this heuristic is not consistent!
𝟏𝟎 = 𝒉̂ (𝐚) ≰ 𝒈 ̂ (𝐞) = 𝟔
̂ (𝐚, 𝐞) + 𝒉
or
𝟏𝟎 = 𝒉 ̂ (𝐚) ≰ 𝒈 ̂ (𝐝) = 𝟖
̂ (𝐚, 𝐝) + 𝒉
(f) Consider the following diagram
J K L M
H I
E F G
A B C D
Assume that loops are detected and that you consider moves in the order Up, Right,
Down, Left. Also assume that the start node is node E, and the goal node is node G.
List the order in which nodes are visited for a depth-first search. (6)
E, A, B, C, D, G
NB: Depth-first search uses a LIFO queue. A LIFO queue means that the most
recently generated node is chosen for expansion.
I used depth-first-GRAPH-search to obtain my solution (see diagram below)
The labels on the left of each node has the form GENERATE| EXPAND, where
GENERATE depicts the order in which nodes are generated and EXPAND depicts the
order in which nodes are expanded (visited).
©ornelis Dubbelman-48269328 Page 3 of 12
