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    <p>It would be reasonable to assign 'am' or 'an' position to Item B and use binary division steps for another insertions. This resembles 26-al number system, where 'a'..'z' symbols correspond to 0..25.</p> <pre><code>a b //0 1 a an b //insert after a - middle letter of alphabet a an au b //insert after an a an ar au b //insert after an again (middle of an, au) a an ap ar au b //insert after an again a an ao ap ar au b //insert after an again a an ann ao... //insert after an, there are no more place after an, have to use 3--symbol label .... a an anb... //to insert after an, we treat it as ana a an anan anb // it looks like 0 0.5 0.505 0.51 </code></pre> <p>Pseudocode for binary tree structure:</p> <pre><code>function InsertAndGetStringKey(Root, Element): string if Root = nil then return Middle('a', 'z') //'n' if Element &gt; Root then if Root.Right = nil then return Middle(Root.StringKey, 'z') else return InsertAndGetStringKey(Root.Right, Element) if Element &lt; Root then if Root.Left = nil then return Middle(Root.StringKey, 'a') else return InsertAndGetStringKey(Root.Left, Element) Middle(x, y): //equalize length of strings like (an, anf)-&gt; (ana, anf) L = Length(x) - Length(y) if L &lt; 0 then x = x + StringOf('a', -L) //x + 'aaaaa...' L times else if L &gt; 0 then y = y + StringOf('a', L) if LL = LastSymbol(x) - LastSymbol(y) = +-1 then return(Min(x, y) + 'n') // (anf, ang) - &gt; anfn else return(Min(x, y) + (LastSymbol(x) + LastSymbol(y))/2) // (nf, ni)-&gt; ng </code></pre>
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    1. COPerhaps I'm being blind, but if you keep inserting after "an" you'll end up with "a an ana anb anc ...". How do you now insert between an and ana?
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    3. COMy head's spinning :) In the first case you managed to insert between "an" and "ao" by adding "ann". In the second case to insert between "an" and "anb" we can't use "ana" but we have to move to 4 characters. I feel like the algorithm itself is slipping around the sides of my head and refuses to enter.
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