593. Valid Square
Given the coordinates of four points in 2D space, return whether the four points could construct a square.
The coordinate (x,y) of a point is represented by an integer array with two integers.
Example:
Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1] Output: True
Note:
- All the input integers are in the range [-10000, 10000].
- A valid square has four equal sides with positive length and four equal angles (90-degree angles).
- Input points have no order.
Approach #1: Math. [Java]
class Solution { public boolean validSquare(int[] p1, int[] p2, int[] p3, int[] p4) { long[] lengths = {length(p1, p2), length(p1, p3), length(p1, p4), length(p2, p3), length(p2, p4), length(p3, p4)}; long maxLen = 0, count = 0, noMaxLen = 0; for (long len : lengths) if (len > maxLen) maxLen = len; for (long len : lengths) { if (len == maxLen) count++; else noMaxLen = len; } if (count != 2) return false; for (long len : lengths) if (len != maxLen && len != noMaxLen) return false; return true; } public long length(int[] p1, int[] p2) { return (long)Math.pow(p1[0] - p2[0], 2) + (long)Math.pow(p1[1] - p2[1], 2); } }
Analysis:
Just find the square of lengths, and validate that:
There are only two equal longest lengths.
The non longest lengths are all equal.
Reference:
https://leetcode.com/problems/valid-square/discuss/103435/Simple-Java-Solution-Square-distances
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