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By Mark B. Wells

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Extra info for Elements of Combinatorial Computing

Sample text

We examine here certain aspects of the implementation of more combinatorially oriented functions. Successive calls to the no-argument function random produce a sequence of real numbers arbitrarily selected from the interval 0 to 1. Many methods for the rapid generation of such “pseudo-random’’ sequences have been proposed [61]. The “multiplicative congruential” method of Lehmer [63] is simple and (for our purposes) reliable and is recommended. g. if the mantissa of the floating point format has 35 bits, then p = 235-31 is reasonable-see Hutchinson [60]).

26 ELEMENTS OF COMBINATORIAL COMPUTING quantified condition or part of a compound condition. Also, a quantified condition, treat­ ed as a simple condition, may be part of a compound condition. Thus extremely complex conditions may be written with little pencil; their resolution to "simpler", but more long-winded, forms may always be derived inductively from the basic resolutions illus­ trated in Fig. 10. 15) However, since the human mind generally balks at about three levels, extremely complex conditions usually appear in our algorithms partly resolved.

No standard scientific language exists for expressing such recursive operations, al­ though some programming languages (notably Algol) permit "recursive procedures'', procedures which may call themselves as part of their evaluation. g. how should the information contained in the clause "where Ai0J) is . . 17) be denoted). The development of concise and readable "recursive terminology" and associ­ ated computing techniques will surely receive much attention in the future. In our language, recursive operations are expressed in terms of the nest notation.

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