Question

I want to add together the cross-diagonal elements in a matrix. For example, I have a 3*3 Matrix which is two dimensional, I want to convert it to one dimensional:

      -------------------
      |  1  |  2  |  3  |
      -------------------
 A=   |  4  |  5  |  6  |
      -------------------
      |  7  |  8  |  9  |
      -------------------

final output will be,

     ____ ____ ____ ____ ____
 B= |1   | 6  | 15 | 14 |  9 |
    |____|____|____|____|____|

First cross-diagonal A[0][0] will be copied to B[0].

Then the next cross-diagonal elements A[1][0] and A[0][1] will be added and copied to B[1], i.e. 4 and 2 will be added.

Then the next cross-diagonal elements A[2][0] and A[1][1] and A[0][2] will be added and copied to B[2], i.e. 7, 5 and 3 will be added.

And so on…

Answer 1

Notice that for each diagonal, the sum of row-index and column-index is equal to the index of B array. Based on this fact, you can make a algorithm like this:

// assuming the width and length of the Matrix is N
// it's good you have some ideas of the range of idea, try figure it out by yourself? 
// definitely it should be a function of N
for (int i=0;i<F(N);i++) { 
  for (int j=0;j<=i;j++) { // consider why j should be in range (0,i) ?
    // some cumulatively add here
  }
}