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    <p>What a great opportunity to put my classes of "Derivation of algorithms", the Dijkstra method, back from the days of University into practice here. This is the <strong>'clean' version</strong></p> <pre><code>require 'set' def generate_perms(str) if str.length == 1 return Set.new([str.downcase, str.upcase]) else head = str[0..0] tail = str[1..-1] perms_sub = generate_perms(tail) d = Set.new(perms_sub.collect{|p| head.downcase + p}) u = Set.new(perms_sub.collect{|p| head.upcase + p}) return d | u end end </code></pre> <p><strong>EDIT</strong>: Dijkstra taught us not to optimize prematurely, so I figured the Array-version would better be added separately :-) :</p> <pre><code>def perms(str) if str.length == 1 return Array.new([str.downcase, str.upcase]) else head = str[0..0] tail = str[1..-1] perms_sub = perms(tail) d = perms_sub.collect{|p| head.downcase + p} u = perms_sub.collect{|p| head.upcase + p} return (d + u).uniq end end </code></pre> <p>And to make it blazing fast one converts into tail recursion, with the help of an extra method argument:</p> <pre><code># tail recursion version, no stack-overflows :-) def perms_tail(str, perms) if str.length == 1 return perms.collect{|p| [p + str.upcase, p+ str.downcase]}.flatten.uniq else tail = perms.collect{|p| [p + str[0..0].upcase, p+ str[0..0].downcase]}.flatten perms_tail(str[1..-1], tail) end end begin perms_tail("tst1",[""]).each{|p| puts p} end </code></pre> <p>Now this is actually very slow, but tail recursion allows for a simple re-write (see for yourself) into <strong>the optimized version</strong>:</p> <pre><code>def perms_fast_tail(str) perms = [""] tail = str.downcase while tail.length &gt; 0 do head, tail, psize = tail[0..0], tail[1..-1], perms.size hu = head.upcase for i in (0...psize) tp = perms[i] perms[i] = tp + hu if hu != head perms.push(tp + head) end end end perms end </code></pre> <p>How much does this matter? Well let's run some timed tests, for the fun of it:</p> <pre><code>begin str = "Thequickbrownfox" start = Time.now perms_tail(str,[""]) puts "tail: #{Time.now - start}" start2 = Time.now perms(str) puts "normal: #{Time.now - start2}" start3 = Time.now perms_fast_tail(str) puts "superfast: #{Time.now - start3}" end </code></pre> <p>On my machine this shows the difference:</p> <pre><code>tail: 0.982241 normal: 0.285104 superfast: 0.168895 </code></pre> <p>The speed increase and performance benefits become visible from non-trivial strings; "tst1" will run fast in the clean version. Hence, Dijkstra was right: no need to optimize. Though it was just fun to do it anyway.</p>
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    1. COBiggest bonus of the Dijkstra method is that no one break/touch your code, because it will be too dense to read. You can't play around with it, you have to 'grok' it before tampering with it :-)
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