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    <p><a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.45.5606&amp;rep=rep1&amp;type=ps" rel="nofollow noreferrer">This</a> seems to indicate that it is possible to do in O(lg^2 n) space. I cannot see how to prove that it is impossible to merge in constant space, but I cannot see how to do it either.</p> <p>Edit: Chasing references, Knuth Vol 3 - Exercise 5.5.3 says "A considerably more complicated algorithm of L. Trabb-Pardo provides the best possible answer to this problem: It is possible to do stable merging in O(n) time and stable sorting in O(n lg n) time, using only O(lg n) bits of auxiliary memory for a fixed number of index variables.</p> <p>More <a href="http://comjnl.oxfordjournals.org/cgi/reprint/35/6/643.pdf" rel="nofollow noreferrer">references</a> that I have not read. Thanks for an interesting problem.</p> <p>Further edit: This article claims that the article by Huang and Langston have an algorithm that merges two lists of size m and n in time O(m + n), so the answer to your question would seem to be yes. Unfortunately I do not have access to the article, so I must trust the second hand information. I'm not sure how to reconcile this with Knuth's pronouncement that the Trabb-Pardo algorithm is optimal. If my life depended on it, I'd go with Knuth.</p> <p>I now see that this had been asked as and earlier Stack Overflow <a href="https://stackoverflow.com/questions/2126219/how-to-merge-two-sorted-integer-array-in-place-using-on-time-and-o1-space-cos">question</a> a <a href="https://stackoverflow.com/questions/2571049/how-to-sort-in-place-using-the-merge-sort-algorithm">number</a> of times. I don't have the heart to flag it as a duplicate.</p> <p>Huang B.-C. and Langston M. A., Practical in-place merging, Comm. ACM 31 (1988) 348-352</p>
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    1. COYou are right. I am able to read the paper since I am the University. It seems like it is possible although the technique is quite sophisticated. Thanks for the pointer.
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    2. COYou can find the paper at CiteSeerX. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.8523
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    3. CO@Daniel Thanks. My googling skills need improvement.
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