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Math Help - A matrix solution ?

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    15

    A matrix solution ?

    hello all,

    I have this advanced computer and math problem that I have to solve.

    it goes something like this
    Matrix A is given of order n where n <=100
    Matrix B is given of the same order n<=100 as A
    Elements of A and B are 1's and 0's
    We have to achieve B from A. For achieving B from A we can do the following 2 operations
    1 - complement any row of matrix A
    2 - complement any column of matrix A

    The solution is minimum number of complements row-wise along with the index of the complemented rows and minimum number of complements column-wise along with index of complemented columns.
    If no solution is possible then simply write the answer as -1
    The matrix index starts from 0.

    Example :

    n = 3

    A =
    0 0 0
    1 1 0
    1 1 0

    B =
    1 1 0
    1 1 1
    1 1 1

    now to get B from A.
    Ans :
    Number of row complements = 1
    Row index that have to be complemented = 0
    Number of column complements = 1
    Column index that have to be complements = 2

    Simulation of solution

    Row : 0 index complement
    A =
    0--> 1 1 1
    1--- 1 1 0
    2--- 1 1 0

    Column : 2 index complement
    A =
    1 1 0
    1 1 1
    1 1 1

    Thus in these 2 operations we get A == B

    So can a mathematical solution exist here ?
    Theres a similar game called lights off which has a math solution , so i thought this is very similar to that game and probably might have a math solution which I am unable to figure out !!

    Thanks for reading patiently

    Tanvi
    Last edited by tanvi.azgaonkar; October 1st 2009 at 08:40 PM. Reason: Formatting problems !
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  2. #2
    Newbie
    Joined
    Sep 2009
    Posts
    15
    Have I posted the query in the wrong place ?

    To the mods : The addition is because I was wondering there was no reply from anyone in 10 days that it has to be either a real tough nut or I have posted to query in the wrong section.
    Please clarify !!
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