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POGenerating sorted random ints without the sort? O(n)
 

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  1. POGenerating sorted random ints without the sort? O(n)
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    <p>Just been looking at a code golf question about <a href="https://stackoverflow.com/questions/350885/create-sort-and-print-a-list-of-100-random-ints-in-the-fewest-chars-of-code">generating a sorted list of 100 random integers</a>. What popped into my head, however, was the idea that you could generate instead a list of positive deltas, and just keep adding them to a running total, thus:</p> <pre><code>deltas: 1 3 2 7 2 ints: 1 4 6 13 15 </code></pre> <p>In fact, you would use floats, then normalise to fit some upper limit, and round, but the effect is the same.</p> <p>Although it wouldn't make for shorter code, it would certainly be faster without the sort step. But the thing I have no real handle on is this: <b>Would the resulting distribution of integers be the same as generating 100 random integers from a uniformly distributed probability density function?</b></p> <p>Edit: A sample script:</p> <pre><code>import random,sys running = 0 max = 1000 deltas = [random.random() for i in range(0,11)] floats = [] for d in deltas: running += d floats.append(running) upper = floats.pop() ints = [int(round(f/upper*max)) for f in floats] print(ints) </code></pre> <p>Whose output (fair dice roll) was:</p> <pre><code>[24, 71, 133, 261, 308, 347, 499, 543, 722, 852] </code></pre> <p><b>UPDATE:</b> <a href="https://stackoverflow.com/questions/1866031/generating-sorted-random-ints-without-the-sort/1866177#1866177">Alok's answer</a> and <a href="https://stackoverflow.com/questions/1866031/generating-sorted-random-ints-without-the-sort/1866055#1866055">Dan Dyer's comment</a> point out that using an <a href="http://en.wikipedia.org/wiki/Exponential_distribution" rel="nofollow noreferrer">exponential distribution</a> for the deltas would give a uniform distribution of integers.</p>
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    1. USPhil H
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    1. COThis won't be uniform. See my answer or Rupert Nash's.
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