Valid Square | Problems

You're given four points on a plane, listed in no particular order. Work out whether they're the corners of a genuine square — meaning all four sides are the same length and all four interior angles are right angles.

Input Format

Implement validSquare(p1, p2, p3, p4). Inputs below show JavaScript function arguments; there is no stdin parsing.

Output Format

Return the result described in the statement.

Sample Input and Output

Example 1 · Run Sample

Input

p1 = [0,0]
p2 = [1,1]
p3 = [1,0]
p4 = [0,1]

Output

true

Example 2

Input

p1 = [0,0]
p2 = [0,0]
p3 = [1,1]
p4 = [1,0]

Output

false

Constraints

Coordinates are integers in range [-10^4, 10^4]

Test Cases (2)

Case 1

Args: [[0,0],[1,1],[1,0],[0,1]] Expected: true

Case 2

Args: [[0,0],[0,0],[1,1],[1,0]] Expected: false

Topics

Matrix BFS DFS

Distance Check

A valid square has 4 equal sides and 2 equal diagonals.

javascript

function validSquare(p1, p2, p3, p4) {
  function dist(a, b) { return (a[0]-b[0])**2 + (a[1]-b[1])**2; }
  const dists = [dist(p1,p2),dist(p1,p3),dist(p1,p4),dist(p2,p3),dist(p2,p4),dist(p3,p4)].sort((a,b)=>a-b);
  return dists[0] > 0 && dists[0]===dists[1] && dists[1]===dists[2] && dists[2]===dists[3] && dists[4]===dists[5];
}

Time: O(1) | Space: O(1)

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