By C. Bron
Communications of the ACM,
Vol. 15 No. 5, Pages 357-358
Sorting by means of a two-way merge has a reputation of requiring a clerically complicated and cumbersome program. This ALGOL 60 procedure demonstrates that, using recursion, an elegant and efficient algorithm can be designed, the correctness of which is easily proved . Sorting n objects gives rise to a maximum recursion depth of [log2(n - 1) + 2]. This procedure is particularly suitable for sorting when it is not desirable to move the n objects physically in store and the sorting criterion is not simple. In that case it is reasonable to take the number of compare operations as a measure for the speed of the algorithm. When n is an integral power of 2, this number will be comprised between (n × log2n)/2 when the objects are sorted to begin with and (n × log2n - n + 1) as an upper limit. When n is not an integral power of 2, the above formulas are approximate.
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