Description:

Task

A rectangle with sides equal to even integers a and b is drawn on the Cartesian plane. Its center (the intersection point of its diagonals) coincides with the point (0, 0), but the sides of the rectangle are not parallel to the axes; instead, they are forming 45 degree angles with the axes.

How many points with integer coordinates are located inside the given rectangle (including on its sides)?

Example

For a = 6 and b = 4, the output should be 23

The following picture illustrates the example, and the 23 points are marked green.

https://files.gitter.im/myjinxin2015/raYf/blob

Input/Output

• [input] integer a A positive even integer. Constraints: 2 ≤ a ≤ 10000.
  
• [input] integer b A positive even integer. Constraints: 2 ≤ b ≤ 10000.
  
• [output] an integer The number of inner points with integer coordinates.
  

My solution:

function rectangleRotation(a, b) {
  const c= Math.ceil(Math.sqrt(Math.pow(a/2,2)+Math.pow(b/2,2)));
  let counter = 0;
  for(i=-c;i<c;i++) {
    for(j=-c;j<c;j++) {
      if(check(i,j,a,-1) && check(i,j,b,+1)) {
        counter++;
        console.log(counter);
      }
    }
  }
  function check(x,y,z,sign) {
    const one = sign*x-(z/2)*Math.sqrt(2) < y ;
    const two = sign*x+(z/2)*Math.sqrt(2) > y ;
    return one && two;
  }
  
  return counter;
}

Best solutions:

봤는데 이해가 안된다. 코드가 이해가 안되는것이 아니라 왜 저런식으로 계산하면 답이 나오는지를 모르겟다.