0593. Valid Square (M)

Valid Square (M)

題目

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:

1. All the input integers are in the range [-10000, 10000].
2. A valid square has four equal sides with positive length and four equal angles (90-degree angles).
3. Input points have no order.

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題意

給定四個點的座標，判斷這四個點可否組成正方形。

思路

按照x座標從小到大、y座標從小到大的優先級進行排序，記此時四個點爲a、b、c、d，若是能造成正方形，那麼四條邊分別是ab、ac、bd、cd。只要判斷四條邊是否相等，以及對角線是否相等便可(須要先排除全部點在一個位置這一特殊狀況)。

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代碼實現

Java

class Solution {
    public boolean validSquare(int[] p1, int[] p2, int[] p3, int[] p4) {
        int[][] points = { p1, p2, p3, p4 };
        Arrays.sort(points, (p, q) -> p[0] == q[0] ? p[1] - q[1] : p[0] - q[0]);
        return calc(points[0], points[1]) != 0
                && calc(points[0], points[1]) == calc(points[0], points[2])
                && calc(points[3], points[1]) == calc(points[3], points[2])
                && calc(points[0], points[1]) == calc(points[3], points[1])
                && calc(points[0], points[3]) == calc(points[1], points[2]);
    }

    private int calc(int[] p, int[] q) {
        int a = p[0] - q[0], b = p[1] - q[1];
        return a * a + b * b;
    }
}