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])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: 𝑛−1,𝑛−1,𝑛−1,𝑛−1,𝑛−3,𝑛−3,𝑛−3,𝑛−3,...etc.
As the size of the given array is the square of 𝑛, I don't see why you would need to pass 𝑛 as argument. It is redundant information.
So:
function sumDiagonals(arr) {
let n = Math.sqrt(arr.length);
if (n % 1) throw "Array size should be perfect square";
let sum = 0;
let len = n*2 - n%2; // The number of values on diagonals
for (let i = 0, j = 0; j < len; i += n - 1 - (j++ >> 2)*2) {
sum += arr[i];
}
return sum;
}
let arr = [1, 2, 3, 8, 9, 4, 7, 6, 5];
console.log(sumDiagonals(arr));