Traverse Matrix in Diagonal strips

Question

I thought this problem had a trivial solution, couple of for loops and some fancy counters, but apparently it is rather more complicated.

So my question is, how would you write (in C) a function traversal of a square matrix in diagonal strips.

Example:

1  2  3
4  5  6
7  8  9

Would have to be traversed in the following order:

[1],[2,4],[3,5,7],[6,8],[9]

Each strip above is enclosed by square brackets. One of the requirements is being able to distinguish between strips. Meaning that you know when you're starting a new strip. This because there is another function that I must call for each item in a strip and then before the beginning of a new strip. Thus a solution without code duplication is ideal.

Answer 1

Here's something you can use. Just replace the printfs with what you actually want to do.

#include <stdio.h>

int main()
{
    int x[3][3] = {1, 2, 3,
                   4, 5, 6,
                   7, 8, 9};
    int n = 3;
    for (int slice = 0; slice < 2 * n - 1; ++slice) {
        printf("Slice %d: ", slice);
        int z = (slice < n) ? 0 : slice - n + 1;
        for (int j = z; j <= slice - z; ++j) {
            printf("%d ", x[j][slice - j]);
        }
        printf("\n");
    }
    return 0;
}

Output:

Slice 0: 1
Slice 1: 2 4
Slice 2: 3 5 7
Slice 3: 6 8
Slice 4: 9

Answer 2

I would shift the rows like so:

1  2  3  x  x
x  4  5  6  x
x  x  7  8  9

And just iterate the columns. This can actually be done without physical shifting.