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  • Appropriate Partitioning

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    Answer it

    Given an array A of integers, choose 2 non-empty disjoint subsets X and Y such that ratio of sum of elements of X and Y is as close to 1 as possible.

    Given,

    Α : {a1, a2, .... aN}

    Find,

    X : {x1, x2....xK}

    Y : {y1, y2.....yM}

    where, X ⊂ A, Y ⊂ A, K > 0 and M > 0 and there does not exist an i, such that ai ∈ X and ai ∈ Y, and Q = abs (1.0 - Σxi / Σyi) is minimum possible. Note that there can exist i and j such that ai ∈ X and aj ∈ Y, i ≠ j but ai = aj.

    Output this minimum possible value of Q with precision up to exactly 6 decimal places.

    CONSTRAINTS

    2 ≤ N ≤ 16
    1 ≤ ai ≤ 106, ∀ i ∈ [1, N] 

    INPUT

    The first line of test file contains a single integer N. Next line contains N space separated integers representing the array A.

    OUTPUT

    Print in a single line, the value of Q with exactly 6 decimal places.

 0 Answer(s)

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