## Pure Storage Interview Question

Backend Developers**Country:**United States

**Interview Type:**Phone Interview

```
bool isSquare(Point p1, Point p2, Point p3, Point p4)
{
int d2 = distSq(p1, p2); // from p1 to p2
int d3 = distSq(p1, p3); // from p1 to p3
int d4 = distSq(p1, p4); // from p1 to p4
// If lengths if (p1, p2) and (p1, p3) are same, then
// following conditions must met to form a square.
// 1) Square of length of (p1, p4) is same as twice
// the square of (p1, p2)
// 2) Square of length of (p2, p3) is same as twice the square of (p1, p2)
if (d2 == d3 && 2 * d2 == d4 && 2 * d2 == distSq(p2, p3)) {
int d = distSq(p2, p4);
return (d == distSq(p3, p4) && d == d2);
}
// The below two cases are similar to above case
if (d3 == d4 && 2 * d3 == d2 && 2 * d3 == distSq(p3, p4)) {
int d = distSq(p2, p3);
return (d == distSq(p2, p4) && d == d3);
}
if (d2 == d4 && 2 * d2 == d3 && 2 * d2 == distSq(p2, p4)) {
int d = distSq(p2, p3);
return (d == distSq(p3, p4) && d == d2);
}
return false;
}
```

for every set of 4 points (a, b, c, d)

'ab' and 'cd' are either opposite sides or diagonals, in a square they have to be equal

if they are sides, then either 'ac' is a side and 'ad' a diagonal or vice versa

if they are diagonals, then 'ac', 'bc', 'ad' and 'bd' are the 4 sides

Note that a,b,c,d are labelled without loss of generality i.e. for every set of 4 points (x1,y1), (x2,y2), (x3,y3), (x4,y4), label them as a,b,c,d in any order

- dmitry.labutin February 27, 2017