Description

Course: Artificial Intelligence (IAIN532C)

Instruction for preparing Solutions: Before programming, first brief the solution strategy in terms of initial state and different types of permissible moves, final states and draw the derivation diagram showing execution trace for the following problems. After defining the Solution Strategy write the prolog program for the following problems.
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1) Write a prolog program to define two predicates evenlength (list) and oddlength(list) so that they are true if their argument is a list of even or odd length.
2) Write a recursive Prolog program Towers of Hanoi puzzle Description about problem:
This object of this famous puzzle is to move N disks from the left peg to the right peg using the center peg as an auxiliary holding peg. At no time can a larger disk be placed upon a smaller disk. The following diagram depicts the starting setup for N=3 disks.

3) Write a prolog program of water jug problem.
Description about problem:
Note 0 ≤ x ≤ 4, and 0 ≤ y ≤ 3. Our initial state: (0,0) Goal Predicate – state = (2,y) where 0 ≤ y ≤ 3.
4) Write a prolog program for missionaries and cannibals Description About problem:
In this problem, three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks, that the missionaries present on the bank cannot be outnumbered by cannibals. The boat cannot cross the river by itself with no people on board.

Hint:
First let us consider that both the missionaries (M) and cannibals(C) are on the same side of the river.

Left Right
Initially the positions are: 0M, 0C and 3M, 3C (B)
Now let’s send 2 Cannibals to left of bank: 0M, 2C (B) and 3M, 1C
Send one cannibal from left to right: 0M, 1C and 3M, 2C (B)
Now send the 2 remaining Cannibals to left: 0M, 3C (B) and 3M, 0C
Send 1 cannibal to the right: 0M, 2C and 3M, 1C (B)
Now send 2 missionaries to the left: 2M, 2C (B) and 1M, 1C
Send 1 missionary and 1 cannibal to right: 1M, 1C and 2M, 2C (B)
Send 2 missionaries to left: 3M, 1C (B) and 0M, 2C
Send 1 cannibal to right: 3M, 0C and 0M, 3C (B)
Send 2 cannibals to left: 3M, 2C (B) and 0M, 1C
Send 1 cannibal to right: 3M, 1C and 0M, 2C (B)
Send 2 cannibals to left: 3M, 3C (B) and 0M, 0C

• Here (B) shows the position of the boat after the action is performed. Therefore, all the missionaries and cannibals have crossed the river safely.
5) i. The following relation classifies numbers into three classes: positive, zero and negative: Class (Number, positive) :- Number > 0.
Class (0, zero).
Class (Number, negative) :- Number < 0.
Define this procedure in a more efficient way using cuts.
ii. Define the procedure
split(Numbers, Positives, Negatives)
which splits a list of numbers into two lists: positive ones (including zero) and negative ones. For example,
split([3,-1,0,5,-2], [3,0,5], [-1,-2])
Propose two versions: one with a cut and one without.