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package g0501_0600.s0593_valid_square;

// #Medium #Math #Geometry #2022_08_25_Time_1_ms_(97.24%)_Space_42.7_MB_(17.00%)

import java.util.Arrays;

/**
 * 593 - Valid Square\.
 *
 * Medium
 *
 * Given the coordinates of four points in 2D space `p1`, `p2`, `p3` and `p4`, return `true` _if the four points construct a square_.
 *
 * The coordinate of a point pi is represented as [xi, yi]. The input is **not** given in any order.
 *
 * A **valid square** has four equal sides with positive length and four equal angles (90-degree angles).
 *
 * **Example 1:**
 *
 * **Input:** p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
 *
 * **Output:** true 
 *
 * **Example 2:**
 *
 * **Input:** p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,12]
 *
 * **Output:** false 
 *
 * **Example 3:**
 *
 * **Input:** p1 = [1,0], p2 = [-1,0], p3 = [0,1], p4 = [0,-1]
 *
 * **Output:** true 
 *
 * **Constraints:**
 *
 * *   `p1.length == p2.length == p3.length == p4.length == 2`
 * *   -104 <= xi, yi <= 104
**/
public class Solution {
    public boolean validSquare(int[] p1, int[] p2, int[] p3, int[] p4) {
        int[] distancesSquared = new int[6];
        distancesSquared[0] = getDistanceSquared(p1, p2);
        distancesSquared[1] = getDistanceSquared(p1, p3);
        distancesSquared[2] = getDistanceSquared(p1, p4);
        distancesSquared[3] = getDistanceSquared(p2, p3);
        distancesSquared[4] = getDistanceSquared(p2, p4);
        distancesSquared[5] = getDistanceSquared(p3, p4);
        Arrays.sort(distancesSquared);
        if (distancesSquared[0] == 0) {
            return false;
        }
        if (distancesSquared[0] != distancesSquared[3]) {
            return false;
        }
        if (distancesSquared[4] != distancesSquared[5]) {
            return false;
        }
        return distancesSquared[5] == 2 * distancesSquared[0];
    }

    private int getDistanceSquared(int[] p1, int[] p2) {
        int deltaX = p2[0] - p1[0];
        int deltaY = p2[1] - p1[1];
        return deltaX * deltaX + deltaY * deltaY;
    }
}




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