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ThePriest
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Max-Min in a matrix
« on: Feb 24th, 2008, 6:06am » |
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This question was given recently(2 months back in an MS interview) to one of my friends.
We have an M * N matrix, filled with random numbers, and we have to select a number (from this matrix) that's maximum among all M rows and it's also minimum among all N columns. (to be honest i too am a bit confused on whether such a number could exist or not), the interviewer did say that it does.
Any solutions?
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towr
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Re: Max-Min in a matrix
« Reply #1 on: Feb 24th, 2008, 10:24am » |
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It doesn't quite seem to make sense as it is. If it's the maximum among M rows, than it's simply the maximum in the matrix; so it can't also be the minimum among N columns (which also spans the entire matrix).
Perhaps what's meant is to find an element that's the maximum of the row it's in and the minimum of the column it's in. (Or vice versa; not like that matters qualitatively.)
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Icarus
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Re: Max-Min in a matrix
« Reply #2 on: Feb 24th, 2008, 11:30am » |
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Maybe they want the intersection of the max row (by sum) and the min column?
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Random Lack of Squiggily Lines
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Re: Max-Min in a matrix
« Reply #3 on: Feb 24th, 2008, 6:20pm » |
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i would pull out the average, think about it.
but 1+I deosnt allways make II
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ThePriest
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Re: Max-Min in a matrix
« Reply #4 on: Feb 25th, 2008, 12:35am » |
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I think, for this particular situation, what towr is saying is closest to the problem. Going by his line of reasoning, can we say for sure that there would be only one such number in the entire matrix, as proposed by the interviewer? Can any one site an example
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towr
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Re: Max-Min in a matrix
« Reply #5 on: Feb 25th, 2008, 2:14am » |
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on Feb 25th, 2008, 12:35am, ThePriest wrote:| I think, for this particular situation, what towr is saying is closest to the problem. Going by his line of reasoning, can we say for sure that there would be only one such number in the entire matrix, as proposed by the interviewer? Can any one site an example |
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If you have for example
1 3
4 2
then the minimum of the column is the minimum (rather than maximum) of the row as well. So we have no number fitting the criteria. So perhaps something else was meant after all.
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| « Last Edit: Feb 25th, 2008, 2:15am by towr » |
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ThePriest
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Re: Max-Min in a matrix
« Reply #6 on: Feb 25th, 2008, 11:58am » |
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@towr
Your example clearly shows that the criteria of maximum in a row and being minimum for that column fails
what about this matrix?
1 2 3 4
13 14 15 16
5 6 7 8
9 10 11 12
In the above matrix, 4 is a number that follows this definition, is it possible that we could have a 3 * 3 or a 4 * 4 (or higher) matrix where the condition fails? Or if it does pass, is it the unique number in that matrix (given there are no repetitions of the numbers)?
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towr
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Re: Max-Min in a matrix
« Reply #7 on: Feb 25th, 2008, 12:24pm » |
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If you put the minimum elements along the diagonal, every square matrix fails. (And in quite a few other cases as well)
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ThePriest
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Re: Max-Min in a matrix
« Reply #8 on: Feb 25th, 2008, 1:03pm » |
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thanks towr, that clears all doubts.
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