i need an algorithm to read elements from a 8x8 matrix and want to store in a 1-D buffer like the link below
http://www.ascc.net/nl/84/
from that 1-D buffer i again want to create the same matrix.
.... of course the elements could be anything (fraction/positive/negativ
.......its called zigzag and anti-zigzag scanning of matrix.
can anybody give some algorithm/sample code/any idea ??????
thanks
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by: KdoPosted on 2004-01-02 at 09:18:47ID: 10029701
Hi sanko50,
If you have an 8x8 matrix, the elements are already in a predictable order. C organizes a matrix over contiguous memory and converts the matrix syntax [][] into an offset from the first element. Using your 8x8 example, item [0][0] is the first item, item [0][1] is the second, item [1][0] is the eighth, item [2][1] is the 17th, etc.
You can very easily convert that to a one-dimensional array by simply recasting a variable:
int Matrix[8][8];
int *Vector;
Vector = (int *) Matrix;
You can now reference Matrix[0][0] or Vector[0] to get to the same address.
But it appears that the framers of your question have made it tougher than this by organizing the data along diagonals. So let's describe the order of the data in the sample matrix.
0 [0][0]
1 [0][1]
2 [1][0]
3 [2][0]
4 [1][1]
5 [0][2]
6 [0][3]
7 [1][2]
8 [2][1]
9 [3][0]
10 [4][0]
11 [3][1]
12 [2][2]
13 [1][3]
14 [0][4] etc...
You can build a conversion so that looking up item[a][b] returns the currect offset, or you can devise a function to return the offset based on a and b. The length of each diagonal is fixed and predictable. The first diagonal contains the value 0 and has a length of 1. The second diagonal contains the values 1 and 2 and has a length of 2. In fact, the first 8 diagonals increase in length by one item over the previous length. The last 7 diagonal decrease in length from the previous length. The 15 diagonals have lengths of 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1. The diagonals are traversed alternately from lower-left to upper-right, then from upper-right to lower-left. You now have enough information to build your conversion algorithm.
DiagonalLengths[15] = {1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1};
int ComputeDiagonalFromItem (int Item) /* Compute the diagonal where a particular item resides */
{
}
int ComputeDiagonalFromMatrix (int x, int y) /* Compute the diagonal of an item based on its x,y coordinates */
{
}
If the diagonal number is even (the first diagonal number is zero) the diagonal is traversed from the lower-left.
Since this does look like a programming assignment, I'll leave the actual coding up to you. Only a small amount of C code is required to actually implement this.
Good Luck,
Kent