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POGiven a dictionary, find all possible letter orderings
 

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  1. POGiven a dictionary, find all possible letter orderings
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    <p>I was recently asked the following interview question:</p> <blockquote> <p>You have a dictionary page written in an alien language. Assume that the language is similar to English and is read/written from left to right. Also, the words are arranged in lexicographic order. For example the page could be: ADG, ADH, BCD, BCF, FM, FN<br/> You have to give all lexicographic orderings possible of the character set present in the page.</p> </blockquote> <p>My approach is as follows: A has higher precedence than B and G has higher precedence than H. Therefore we have the information about ordering for some characters:</p> <pre><code>A-&gt;B, B-&gt;F, G-&gt;H, D-&gt;F, M-&gt;N </code></pre> <p>The possible orderings can be ABDFGNHMC, ACBDFGNHMC, ... My approach was to use an array as position holder and generate all permutations to identify all valid orderings. The worst case time complexity for this is N! where N is the size of character set. Can we do better than the brute force approach.</p> <p>Thanks in advance.</p>
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    1. USChristian Ammer
    1. USuser434345
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      1. USAziz Shaikh
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    1. COYou could construct a (not-necessarily-connected) DAG of the partial orders implied by the words you have, then exhaustively find all the routes from each node (letter) through all other nodes using the rule that you can go to any node except one that's "upstream" of you or any node you've already visited. Hence you can immediately prune any paths where you'd step to a node that has "upstream" of it a node you haven't used yet, beating brute force. There's probably something cleverer, though.
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      1. USSteve Jessop
    2. COI don't think you can do better then n!, but identifying if a pattern is valid or not is going to add some complexity, so I don't believe what you're suggesting is `n!`, either. It sounds like `m*n^2 * n!`, where `m` is the number of rules, although you don't really specify how you would validate each one.
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      1. POGiven a dictionary, find all possible letter orderings
      1. USjswolf19
    3. CO@jswolf19: you can't do better than `n!` for the simple reason that if the input is a single word `ABCDE` then all `5!` orderings are possible, so you have to output them all. But you can hope to do "better" than `n!` by some term that depends what constraints are imposed, accepting that the term is `O(bupkis)` for some inputs. In the best case, where the input is 5 one-letter words, `A B C D E` then we should be able to answer pretty quickly.
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      1. USSteve Jessop
 

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