computer science(Algorithm)

An m X n YOUNG TABLEAU is an m X n matrix such that the entries of each row are in sorted order from left to right and the entries of each column are in sorted order from top to bottom. Some of the entries of YOUNG TABLEAU maybe ¡Þ, which we treat as nonexistent elements, Thus, a YOUNG TABLEAU can be used to hold r¡Ü m n finite numbers.

(-) show how to insert a new elements into non-full m X n YOUNG TABLEAU in
O(mXn)time.

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  1. To make sure we are on the same wavelength, to me it is implicit that
    1. the matrix entries are numeric
    2. the insertion will preserve the given order horizontally and vertically,
    3. location of non existent elements are unpredictable, and
    4. The insertion of an element in a row involves shifting of elements, which in turn will disrupt the order of the elements in the columns. This has to be addressed (in mxn time!)

    Do you have any suggestions?

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  2. INSERT(Y; k)
    DECREASE-KEY(Y; m; n; k)
    DECREASE-KEY(Y; i; j; k)
    if Y [i; j] · k
    then return error
    Y [i; j]Ãk
    thresholdÃ1
    largestiÃi
    largestjÃj
    while(i > 1 or j > 1) and Y [i; j] < threshold
    do exchangeY [i; j] $ Y [largesti; largestj ]
    iÃlargesti
    jÃlargestj
    if i ¡ 1 ¸ 1 and Y [i; j] < Y [i ¡ 1; j]
    then largestiÃi ¡ 1
    largestjÃj
    if j ¡ 1 ¸ 1 and Y [largesti; largestj ] < Y [i; j ¡ 1]
    then largestiÃi
    largestjÃj ¡ 1
    thresholdÃY [largesti; largestj ]

    Is this method help?

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  3. Obviously in your algorithm, some of the > and ≥ signs have not been coded properly for HTML.

    This is a one-pass algorithm that does the work in O(m+n) BUT it does not guarantee the integrity of the tableau, namely after any exchange, there is no guarantee that both elements satisfy the criteria in both directions (see #4 above).

    If that's what your teacher accepts, that's OK.

    Example:

    1 3 4 X
    4 5 9 X
    X X X 2

    1 3 4 X
    4 5 9 2
    X X X X

    1 3 4 X
    4 5 2 9
    X X X X

    1 3 2 X
    4 5 4 9
    X X X X

    1 2 3 X
    4 5 4 9
    X X X X

    Note that row two violates the Young Tableau criteria.

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