Talk:Rare numbers: Difference between revisions
→30 mins not 30 years
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::::: Incidentally, I regard it as bad form to use concurrent processing (i.e. goroutines) in RC tasks unless this is specifically asked for or is otherwise unavoidable (for processing events in some GUI package for example). It is difficult for languages which don't have this stuff built in to compete and it may disguise the usage of what are basically poor algorithms. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 23:04, 24 September 2019 (UTC)
===A few more mins.===
Above I considered n-r=L and investigated the nature of L. It is difficult to estimate complexity with increasing number of digits for this algorithm because: it depends on the number of L which happen to be a perfect square, which is neither random nor easy to predict; each L which is a perfect square expands into varying number of r. At first sight n+r=H does not look promising. For the number n....g n+g may take the values 1 to 18 rather than 1 to 9 for n-g and for an odd number of digits x doesn't disappear, rather it creates 10 times the number of possibilites.
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For a rare number H-L=(n+r)-(n-r)=2r which implies that for a Rare number H and L must both be odd or even. From the lists H and R I can produce all the candidates for r. n is H-r therefore I must simply determine for each candidate is r H-r reversed (see C++ on the task page). The nice thing is that it is easy to determine the size of H and L and they predict timings for this algorithm. The time does not depend on the number of L which happen to be a perfect square. This simplicity means that I can predict optimizations which will make significant difference to the run time for increasing number of digits. The programming skill then is to compute the Cartesian Product of n/2 for L and (n+1)/2 for H integer ranges; then calculate the Inner Product of each with 10**x-10**y for L and 10**x+10**y for H. Efficiently!!! I especially like that this can be described as a problem in Linear Algebra subject to analysis and representation as a graph.--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 12:19, 20 December 2019 (UTC)
== the 1<sup>st</sup> REXX version ==
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