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3.13. Simulation: Hot Potato¶
One of the typical applications for showing a queue in action is to simulate a real situation that requires data to be managed in a FIFO manner. To begin, let’s consider the children’s game Hot Potato. In this game (see Figure 2) children line up in a circle and pass an item from neighbor to neighbor as fast as they can. At a certain point in the game, the action is stopped and the child who has the item (the potato) is removed from the circle. Play continues until only one child is left.
This game is a modern-day equivalent of the famous Josephus problem. Based on a legend about the famous first-century historian Flavius Josephus, the story is told that in the Jewish revolt against Rome, Josephus and 39 of his comrades held out against the Romans in a cave. With defeat imminent, they decided that they would rather die than be slaves to the Romans. They arranged themselves in a circle. One man was designated as number one, and proceeding clockwise they killed every seventh man. Josephus, according to the legend, was among other things an accomplished mathematician. He instantly figured out where he ought to sit in order to be the last to go. When the time came, instead of killing himself, he joined the Roman side. You can find many different versions of this story. Some count every third man and some allow the last man to escape on a horse. In any case, the idea is the same.
We will implement a general simulation of Hot Potato. Our program
will input an array of names and a constant, call it “num,” to be used for
counting. It will return the name of the last person remaining after
repetitive counting by
num. What happens at that point is up to you.
To simulate the circle, we will use a queue (see
Figure 3). Assume that the child holding the potato will
be at the front of the queue. Upon passing the potato, the simulation
will simply dequeue and then immediately enqueue that child, putting her
at the end of the line. She will then wait until all the others have
been at the front before it will be her turn again. After
dequeue/enqueue operations, the child at the front will be removed
permanently and another cycle will begin. This process will continue
until only one name remains (the size of the queue is 1).
The program is shown in ActiveCode 1. A call to the
hotPotato function using 7 as the counting constant returns
Note that in this example the value of the counting constant is greater
than the number of names in the array. This is not a problem since the
queue acts like a circle and counting continues back at the beginning
until the value is reached. Also, notice that the array is loaded into
the queue such that the first name on the array will be at the front of
Bill in this case is the first item in the array and
therefore moves to the front of the queue. A variation of this
implementation, described in the exercises, allows for a random counter.