Communications of the ACM
Internal Sorting Using a Minimal Tree Merge Strategy
ACM Transactions on Mathematical Software (TOMS)
Algorithm 488: A Gaussian pseudo-random number generator
Communications of the ACM
Communications of the ACM
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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 [2]. 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.