Question

is there a good algorithm for checking whether there are 5 same elements in a row or a column or diagonally given a square matrix, say 6×6?

there is ofcourse the naive algorithm of iterating through every spot and then for each point in the matrix, iterate through that row, col and then the diagonal. I am wondering if there is a better way of doing it.

Answer 1

You can check whether there are k same elements in a matrix of integers in a single pass.

Suppose that n is the size of the matrix and m is the largest element. We have n column, n row and 1 diagonal.
Foreach column, row or diagonal we have at most n distinct element.

Now we can create a histogram containing (n + n + 1) * (2 * m + 1) element. Representing
the rows, columns and the diagonal each of them containing at most n distinct element.

size = (n + n + 1) * (2 * m + 1)
histogram = zeros(size, Int)

Now the tricky part is how to update this histogram ?

Consider this function in pseudo-code:

updateHistogram(i, j, element)

    if (element < 0)
        element = m - element;

    rowIndex        = i * m + element
    columnIndex     = n * m + j * m + element
    diagonalIndex   = 2 * n * m + element

    histogram[rowIndex] = histogram[rowIndex] + 1
    histogram[columnIndex] = histogram[columnIndex] + 1

    if (i = j)
        histogram[diagonalIndex] = histogram[diagonalIndex] + 1

Now all you have to do is to iterate throw the histogram and check whether there is an element > k