## Square?

Friday, March 18, 2011

A recent code golf requested a way to determine if 4 points form a square. Factor may not be the shortest answer, but I thought I would contribute it anyway.

We require four unique points to be provided. We then use the distance formula to compute the distances between all pairs of points. For a square, there should be just two lengths (the side and the diagonal) not counting zero (the distance from a point to itself).

```
USING: kernel math math.combinatorics math.vectors sequences sets ;
: square? ( seq -- ? )
members [ length 4 = ] [
2 [ first2 v- [ sq ] map-sum ] map-combinations
{ 0 } diff length 2 =
] bi and ;
```

We can write some unit tests to make sure it works.

```
USE: tools.test
[ t ] [
{
{ { 0 0 } { 0 1 } { 1 1 } { 1 0 } } ! standard square
{ { 0 0 } { 2 1 } { 3 -1 } { 1 -2 } } ! non-axis-aligned square
{ { 0 0 } { 1 1 } { 0 1 } { 1 0 } } ! different order
{ { 0 0 } { 0 4 } { 2 2 } { -2 2 } } ! rotated square
} [ square? ] all?
] unit-test
[ f ] [
{
{ { 0 0 } { 0 2 } { 3 2 } { 3 0 } } ! rectangle
{ { 0 0 } { 3 4 } { 8 4 } { 5 0 } } ! rhombus
{ { 0 0 } { 0 0 } { 1 1 } { 0 0 } } ! only 2 distinct points
{ { 0 0 } { 0 0 } { 1 0 } { 0 1 } } ! only 3 distinct points
} [ square? ] any?
] unit-test
```

Since it’s code golf (fewest characters possible), how might you make it shorter?