The missionaries and cannibals problem is usually stated as follows. Three missionaries and three cannibals are on one side of a river, along with a boat that can hold one or two people. Find a way to get everyone to the other side without ever leaving a group of missionaries in one place outnumbered by the cannibals in that place. This problem is famous in AI because it was the subject of the first paper that approached problem formulation from an analytical viewpoint (Amarel, 1968). b. Implement and solve the problem optimally using an appropriate search algorithm. (Mention the name of the search algorithm, and write the complete answers, Draw the answer using the searching algorithms with complete and all paths and branches.)

The missionaries and cannibals problem is usually stated as follows. Three missionaries and three cannibals are on one side of a river, along with a boat that can hold one or two people. Find a way to get everyone to the other side without ever leaving a group of missionaries in one place outnumbered by the cannibals in that place. This problem is famous in AI because it was the subject of the first paper that approached problem formulation from an analytical viewpoint (Amarel, 1968). b. Implement and solve the problem optimally using an appropriate search algorithm. (Mention the name of the search algorithm, and write the complete answers, Draw the answer using the searching algorithms with complete and all paths and branches.)

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter9: Integer Programming

Section: Chapter Questions

Problem 33RP

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Consider the following bridge crossing problem where n people with speeds s1, ··· , sn wish to cross the bridge as quickly as possible. The rules remain: • It is nighttime and you only have one flashlight. • A maximum of two people can cross at any one time • Any party who crosses, either 1 or 2 people must have the flashlight with them. • The flashlight must be walked back and forth, it cannot be thrown, etc. • A pair must walk together at the rate of the slower person’s pace. Give an efficient algorithm to find the fastest way to get a group of people across the bridge. You must have a proof of correctness for your method.
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Problem 17.6. There were n Immortal Warriors born into our world, but in the end there can be only one. The Immortals’ original plan was to stalk the world for centuries, dueling one another with ancient swords in dramatic landscapes until only one survivor remained. However, after a thought-provoking discussion probability, they opt to give the following protocol a try: (i) The Immortals forge a coin that comes up heads with probability p. (ii) Each Immortal flips the coin once. (iii) If exactly one Immortal flips heads, then they are declared The One. Otherwise, the protocol is declared a failure, and they all go back to hacking each other up with swords. One of the Immortals (Kurgan from the Russian steppe) argues that as n grows large, the probability that this protocol succeeds must tend to zero. Another (McLeod from the Scottish highlands) argues that this need not be the case, provided p is chosen carefully. (a) A natural sample space to use to model this problem is fH; T g n…
This characteristic is met by a problem if it is feasible to develop an optimum solution for it by first creating optimal solutions for its subproblems. a) Subproblems that overlap; b) substructure that's optimum; c) memorization; d) greedy
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John is training for a marathon and he can easily alternate between running a mile and walking a mile. If he runs for 2 miles in a row, he becomes fatigued, and must then walk for 2 miles in a row in order to no longer be fatigued. When he is fatigued, he can still alternate between running a mile and walking a mile, but if he runs 2 miles in a row while already fatigued, he will collapse on the side of the road. If he runs 3 miles in a row at any point, he will also collapse. Let the letter 'a' stand for John running 1 mile, and the letter 'b' stand for John walking 1 mile. Draw a DFA which accepts all possible runs in which John does not collapse on the side of the road.
(This problem assumes knowledge of the basic rules of basketball.) One controversial topic in basketball (college or any other level) is whether to foul a player deliberately with only a few seconds left in the game. Consider the following scenario. With about 10 sec- onds left in the game, team A is ahead of team B by three points, and team B is just about to inbound the ball. Assume team A has committed enough fouls so that future fouls result in team B going to the free-throw line. If team A purposely commits a foul as soon as possible, team B will shoot two foul shots (a point apiece). The thinking is that this is better than letting team B shoot a three-point shot, which would be their best way to tie the game and send it into over- time. However, there is a downside to fouling. Team B could make the first free throw, purposely miss the second, get the rebound, and score a two-point shot to tie the game, or it even score a three-point shot to win the game. Examine this decision,…
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