Monday, November 8, 2010

Find the min difference among two numbers in an Array

Given an array of n integers A, find the minimum difference between two numbers in A. It's easy to make it in O(n log n). Can you make it in O(n)?

7 comments:

  1. 1. Use partiting step from quick sort
    2. compare [L/2 + 1] - [L/2] or [L/2] - [L/2 - 1]

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  2. This does seem hard and I can't figure a way to attack it without that extra logN. It can be solved in order N EXPECTED time but not true O(N) limits. (Interesting: the tougher 2D generalization of the problem, finding 2 points that are closest in a 2D plane, is O(n Log n) but also has an expected order N randomized algorithm. See for example the Kleinburg/Tardos textbook.)

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  3. vstepanov, that requires you to descend recursively into both halves of the partition, making it O(n log n).

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  4. Got it!

    These are integers so it's possible to use a O(n) radix sort! So sort the numbers, then scan down the list and look at the pairwise differences, return the largest.

    If the numbers are reals, I think O(n log n) is the true limit. But computer integers or 32/64 bit floats are sortable in O(n) so this will work.

    Good puzzle, I had given up. But that "integer" clue in the problem description was key.

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  5. Can we make any assumptions about the numbers in the array? like possible range of values?

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  6. Can you make any assumptions about the integer range?

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