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Math Help - LEXICOGRAPHIC ORDER OF PERMUTATIONS

  1. #1
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    LEXICOGRAPHIC ORDER OF PERMUTATIONS

    Find the next larger permutation in lexicographic order after each of these
    permutations.
    a) 1342
    b) 13245
    c) 1623547
    d) 31528764
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    Hello, dh214!

    Could you explain the problem, please?


    Find the next larger permutation in lexicographic order ??
    after each of these permutations.

    a) 1342
    b) 13245
    c) 1623547
    d) 31528764

    "Lexicographic" means "like a dictionary."

    It sounds like we write out all the possible permutations in words,
    . . then list them in alphabetical order.

    This is perhaps the silliest "math" problem ever!

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    Quote Originally Posted by Soroban View Post
    Hello, dh214!

    Could you explain the problem, please?



    "Lexicographic" means "like a dictionary."

    It sounds like we write out all the possible permutations in words,
    . . then list them in alphabetical order.

    This is perhaps the silliest "math" problem ever!

    That's because you don't know how it is applied to mathematics
    Lexicographical order - Wikipedia, the free encyclopedia

    Quote Originally Posted by dh214 View Post
    Find the next larger permutation in lexicographic order after each of these
    permutations.
    a) 1342
    b) 13245
    c) 1623547
    d) 31528764
    Okay, here is what to do, for the first one.

    There are 4 digits : {1,2,3,4}
    You're asked for the one following 1342.
    Since these are permutations, you have to change at least 2 digits.
    So let's start with the last 2 digits. If you permutate them, you get 1324. But following the lexicographical order, this is not larger than 1342.

    So you'll have to change the 2nd digit. What comes right after 3 in the list ? 4.
    So it'll start with 14..
    there are 2 and 3 remained to be sitted :P Since 2<3, it'll be 1423.




    For c) :
    1623547
    what if you permutate the last 2 digits ?
    It'll give 1623574, and obviously, it is larger. You're done.


    etc, etc...
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