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Topic: School classes (Read 1512 times) |
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bd
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School classes
« on: Oct 11th, 2012, 1:33pm » |
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I do not have an answer to this riddle, any hint is appreciated.
In a school there are n students belonging to m distinct classes, numbered from 1 to m. A sensor placed at the entrance provides two things: the class (that is, the integer that identifies it) of a student who passes through the entrance and if the student is leaving or entering the building. Now, taking into account that in this school everyone is free to come and go as they please, you must describe an algorithm that, looking at the data provided by the sensor, is able at any time to answer the question: "Do all the students currently inside the school belong to the same class? ".
The algorithm can use only a constant number of variables and must answer in O(1) time. You can assume that each variable can contain O(log m + log n) bits of information.
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towr
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Re: School classes
« Reply #1 on: Oct 11th, 2012, 10:46pm » |
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Do we know the sizes of each class?
There's a fairly simple way using m+1 variables, but the requirements seem to be a bit stricter than than.
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Wikipedia, Google, Mathworld, Integer sequence DB
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bd
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Re: School classes
« Reply #2 on: Oct 11th, 2012, 11:19pm » |
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We don't know the size of each class.
The number of variables can not depend on m or n.
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| « Last Edit: Oct 12th, 2012, 3:51am by bd » |
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