How to get diagonal numbers between two number in a matrix?

Question

How to check if two indexes of a square matrix are diagonal to each other. Consider the array.

[
 0 , 1 , 2 , 3 ,
 4 , 5 , 6 , 7 ,
 8 , 9 , 10, 11,
 12, 13, 14, 15
]

Create a function which takes three parameters array and two indexes. It should return a true if two indexes are diagonal to each other otherwise return false For above array.

0,15 => true
3,12 => true
11,6 => true
9,6  => true

4,15 => false
8,12 => false
1,10 => false //my code fails for this.

I have tried to create a function but it doesnot work at all.

function check(arr,a,b){
  let len = Math.sqrt(arr.length);
  let dif = Math.abs(a-b);
  return dif % (len+1) === 0 ||  dif % (len - 1) === 0
}

Can some give a simple solution to it.

Answer 1

只需获取col和row，并检查delta是否相同。

（实际上并不需要采用数组，所以我只是采用维度）

function check(dim,a,b){
  let [x1,y1]=[Math.floor(a/dim),a%dim]
  let [x2,y2]=[Math.floor(b/dim),b%dim]
  return Math.abs(x1-x2)==Math.abs(y1-y2)
}

console.log(check(4,0,15))
console.log(check(4,3,12))
console.log(check(4,11,6))
console.log(check(4,9,6))
console.log(check(4,4,15))
console.log(check(4,8,12))
console.log(check(4,6,12))

Answer 2

You could take the absolute delta and check with the remainder operator if the delta is multiple of the length minus one or plus one.

function check(array, i, j) {
   var length = Math.sqrt(array.length),
       delta = Math.abs(i - j),
       lines = Math.abs(Math.floor(i / length) - Math.floor(j / length));
   
   return delta === lines * (length - 1) || delta === lines * (length + 1);
}

var array = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15];

console.log(check(array, 0, 15)); // true
console.log(check(array, 3, 12)); // true
console.log(check(array, 11, 6)); // true
console.log(check(array, 9, 6)); // true

console.log(check(array, 4, 15)); // false
console.log(check(array, 8, 12)); // false
console.log(check(array, 8, 3)); // false

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