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Topic: select x numbers from n numbers in sequence evenly (Read 668 times) |
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maaz
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select x numbers from n numbers in sequence evenly
« on: Mar 17th, 2008, 8:23pm » |
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This is my first and hopefully many more to post in future:
So, we are given a list of n numbers from 1-n and a number d. d < n. We need to select d numbers from n such that the selected numbers are evenly distributed.
So, n = [1...100] and d = 15. So, we need to select 15 values from n which are mostly evenly distributed.
Any ideas ?
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towr
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Re: select x numbers from n numbers in sequence ev
« Reply #1 on: Mar 18th, 2008, 1:45am » |
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There's numerous ways.
Simplest would be to pick one uniformly, swap it to the front, pick one from the rest of the list uniformly, swap it to second place etc. Similar to how you'd could randomize a list of number, except you stop after d.
There's also a nice solution here in case n isn't known beforehand and you're only allowed one pass .
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Grimbal
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Re: select x numbers from n numbers in sequence ev
« Reply #2 on: Mar 18th, 2008, 3:40am » |
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Another one
S={};
for ( int i=n-d ; i<n ; i++ )
{
int a = rand()%(i+1);
if !(a in S) S = S+{a};
else S = S+{i};
}
Explained here.
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| « Last Edit: Mar 18th, 2008, 3:41am by Grimbal » |
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Grimbal
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Re: select x numbers from n numbers in sequence ev
« Reply #3 on: Mar 18th, 2008, 3:42am » |
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on Mar 17th, 2008, 8:23pm, maaz wrote:| So, we need to select 15 values from n which are mostly evenly distributed. |
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Why "mostly"?
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maaz
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Posts: 7
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Re: select x numbers from n numbers in sequence ev
« Reply #4 on: Mar 18th, 2008, 8:17am » |
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Ok. So I made a mistake in my question.
The numbers in n are in sequence. Say 1...100. All 100 numbers in sequence and sorted.
If we are given pick up 10 numbers, we need to pick up 10, 20, 30..100. so that they are all evenly spaced.
They cannot be selected randomly as they need to be evenly spaced so the sequence of k numbers selected looks good. Now, if k is 15 or 7, how do we select k numbers that are evenly spaced here ?
for example, consider that k of these n numbers need to be plotted an x axis of a graph of n numbers and we need them to be as evenly spaced as possible. Picking them at random is not the solution.
Also, the random() % i+1 could be a little biased as say if k is 3 and n is 100, then we would always do random() % 98, 99, 100 and then we need to know how big the random() should be as compared to n.
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| « Last Edit: Mar 18th, 2008, 8:38am by maaz » |
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towr
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Re: select x numbers from n numbers in sequence ev
« Reply #5 on: Mar 18th, 2008, 8:54am » |
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Huh.. well, in that case, just take i* N/k for i=1..k
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| « Last Edit: Mar 18th, 2008, 8:54am by towr » |
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Hippo
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Re: select x numbers from n numbers in sequence ev
« Reply #6 on: Mar 18th, 2008, 11:23am » |
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on Mar 18th, 2008, 8:54am, towr wrote:| Huh.. well, in that case, just take i*N/k for i=1..k |
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More interesting question would be if the numbers were not sorted and the values defined by the sorted list should be taken. .... Can you find the O(n) algorithm?
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towr
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Re: select x numbers from n numbers in sequence ev
« Reply #7 on: Mar 18th, 2008, 1:33pm » |
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on Mar 18th, 2008, 11:23am, Hippo wrote:
More interesting question would be if the numbers were not sorted and the values defined by the sorted list should be taken. .... Can you find the O(n) algorithm? |
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First find the smallest and largest number
Then make a length d array, where every position has a target value you want to approach, a long the lines of theprevious solution.
For each number try to put it in the closest bin, but only if it's closer to the target than what's in there already.
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