Sum of the diagonal elements in a Spiral Matrix in Javascript-CodePudding

So I have been given an array = [ 1 2 3 8 9 4 7 6 5 ] which is a spiral traversal of a square matrix of size n x n. What I needed to do was to compute the sum of primary and secondary diagonals and print it. I was able to convert this 1D array into a 2D array of size n*n and compute the sum of both diagonals like this:

p.s.: array is something like this [ [1, 2, 3], [6, 5, 8], [7, 4, 9] ]

function spDiag(n,arr){
    let mat = [];
    let primary = 0, secondary = 0;
    while(arr.length) mat.push(arr.splice(0, n));
    
    for(let i = 0; i < n; i  ){
        for(let j = 0; j < n; j  ){
            if(i === j) primary  = mat[i][j];
            
            if((i   j) === (n-1)) secondary  = mat[i][j];
        }
        
    }
    console.log(primary   secondary)
    console.log(JSON.stringify(mat));
    
}

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

But the task was to form a spiral matrix and then compute the sum of diagonals and not just a 2D matrix and because of this my output is coming wrong. How can I convert this 1D array to a spiral matrix?

CodePudding user response：

You don't really need to turn the 1D array into a 2D array, nor do you need to visit each value in the array. The diagonals follow an easy pattern, as the index-distance between 2 consecutive elements on a diagonal follows a pattern.

See for instance for a matrix of 7x7 which indexes of the spiral sequence are on a diagonal:

 0  .  .  .  .  .  6
 . 24  .  .  . 28  .
 .  . 40  . 42  .  .
 .  .  . 48  .  .  .
 .  . 46  . 44  .  .
 . 36  .  .  . 32  .
18  .  .  .  .  . 12

The gaps between two consecutive indices that are on the diagonal (in order of index) are: 6, 6, 6, 6, 4, 4, 4, 4, 2, 2, 2, 2. The general pattern for these gaps is: