Valid Square Problem in Java

It is a problem frequently asked in interviews of top IT companies like Google, Amazon, TCS, Accenture, etc. By solving the problem, one wants to check the logical ability, crit-ical thinking, and problem-solving skill of the interviewee. So, in this section, we are go-ing to solve valid square problem with different approaches and logic. Also, we will create Java programs for the same.

The valid square problem is a common coding interview question that involves determining if four given points in a 2D plane can form a square. To solve this problem, one needs to check the distances between the points to ensure that they can form a square with equal side lengths and equal diagonals.

Problem Statement

Given four points represented as (x1, y1), (x2, y2), (x3, y3), and (x4, y4), determine if these points can form a square.

Approach

To determine if the given points form a square, we can follow these steps:

Calculate the squared distances between all pairs of points.
Sort these distances.
For the points to form a square, the following conditions must be satisfied:
- There must be exactly four equal smallest distances (sides of the square).
- There must be exactly two equal largest distances (diagonals of the square).
- The diagonal length should be twice the side length in a square.

Let's implement the above steps in a Java program.

File Name: Valid Square.java

 
import java.util.Arrays;
public class ValidSquare {
    // Method to calculate squared distance between two points
    private static int squaredDistance(int[] p1, int[] p2) {
        return (p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1]);
    }
 // Method to check if four points can form a valid square
    public static boolean isValidSquare(int[] p1, int[] p2, int[] p3, int[] p4) {
        int[] distances = new int[6];
        distances[0] = squaredDistance(p1, p2);
        distances[1] = squaredDistance(p1, p3);
        distances[2] = squaredDistance(p1, p4);
        distances[3] = squaredDistance(p2, p3);
        distances[4] = squaredDistance(p2, p4);
        distances[5] = squaredDistance(p3, p4);
        Arrays.sort(distances);
        // Check the first four distances (sides) are equal and the last two distances (diagonals) are equal 
       return distances[0] > 0 && distances[0] == distances[1] && distances[1] == distances[2] && distances[2] == distances[3]                && distances[4] == distances[5] && distances[4] == 2 * distances[0];
    }
    public static void main(String[] args) {
        int[] p1 = {0, 0};
        int[] p2 = {1, 1};
        int[] p3 = {1, 0};
        int[] p4 = {0, 1};
        if (isValidSquare(p1, p2, p3, p4)) {
            System.out.println("The given points form a valid square.");
        } else {
            System.out.println("The given points do not form a valid square.");
        }
    }
}   

Output:

 
The given points form a valid square.

Explanation

By not computing the square root, the squaredDistance() function computes the squared distance between two points without causing floating-point precision problems. The squared distances between each pair of points are first determined using the isValidSquare() method, which then sorts the results.

It verifies that the final two lengths, which represent the diagonals, and the initial four smallest distances, that represent the square's sides, are equal. It also guarantees that the length of the diagonal is twice that of the sides. The main() method prints whether the sample set of points forms a valid square by utilising the isValidSquare() method.

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