Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Three prisoners have been sentenced to long terms in prison, but due to over crowed conditions, one prisoner must be released.
The warden devises a scheme to determine which prisoner is to be released. He tells the prisoners that he will blindfold them and then paint a red dot or blue dot on each forehead. After he paints the dots, he will remove the blindfolds, and a prisoner should raise his hand if he sees at least one red dot on the other two prisoners. The first prisoner to identify the color of the dot on his own forehead will be release. Of course, the prisoners agree to this. (What do they have to lose?)
The warden blindfolds the prisoners, as promised, and then paints a red dot on the foreheads of all three prisoners. He removes the blindfolds and, since each prisoner sees a red dot (in fact two red dots), each prisoner raises his hand. Some time passes when one of the prisoners exclaims, "I know what color my dot is! It's red!" This prisoner is then released.
Your problem…
A spinner with three equal sections is being used in a game. One section is labeled “0 points,” and two sections are labeled “2 points.” A player can decide not to spin the spinner and score 1 point. Each player gets one turn, and the player with the higher score wins; in case of a tie, the winner is decided by one flip of a fair coin. Alex takes his turn first. Eddie, knowing Alex’s score, takes his turn next. If both players use strategies that maximize their winning probabilities, what is the probability that Alex wins?
a
1/3
b
1/2
c
2/3
d
4/9
The Josephus problem is the following game: N people, numbered 1 to N, are sitting in a circle. Starting at person 1, a hot potato is passed. After M passes, the person holding the hot potato is eliminated, the circle closes ranks, and the game continues with the person who was sitting after the eliminated person picking up the hot potato. The last remaining person wins. Thus, if M = 0 and N = 5, players are eliminated in order, and player 5 wins. If M = 1 and N = 5, the order of elimination is 2, 4, 1, 5.
Write a C program to solve the Josephus problem for general values of M and N. Try to make your program as efficient as possible. Make sure you dispose of cells.
What is the running time of your program?
If M = 1, what is the running time of your program? How is the actual speed affected by the delete routine for large values of N (N > 100,000)?
ps. provide a screenshot of output, thankss
Chapter 19 Solutions
Operations Research : Applications and Algorithms
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Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
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