Create Check Square.cpp

Author: MohammedHamzaMalik

Competitive-Programming/Geometry I/Check Square.cpp

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+/*
+Check Square
+Send Feedback
+You are given four points on a two-dimensional coordinate system.
+Can you check if those four points make a square?
+Example:
+Let the input be [1,0,2,1] and [0,1,1,2].
+So, the coordinates of the four points be [ {1, 0}, {0, 1}, {2, 1}, {1, 2} ]
+example
+
+From the above image, we can see that it is a square. Thus, the output will be ‘Yes’.
+Input format:
+The first line of input contains an integer ‘T’ denoting the number of test cases.
+
+The first line of each test case contains four space-separated integers representing x-coordinates of the four points.
+
+The second line of each test case contains four space-separated integers representing y-coordinates of the four points.
+Output format :
+For each test case, print ‘Yes’ if four points make a square otherwise print ‘No’.
+Note:
+Don’t print anything, just return True if four points make a square otherwise return False.
+Constraints:
+1 <= T <= 10^4
+-10^9 <= xi, yi <= 10^9
+
+Time limit: 1 sec
+Sample Input 1:
+2
+1 0 2 1
+0 1 1 2
+1 0 0 1
+1 0 1 2
+Sample Output 1:
+Yes
+No
+Explanation For Sample Input 1:
+Test Case 1: Refer to the example described above.
+
+Test Case 2:
+    The quadrilateral for the given four points is represented below.
+test case 2
+
+As we can clearly see this is not a square. Thus, the answer will be ‘No’.
+Sample Input 2:
+2
+1 2 4 2
+0 2 4 2
+0 1 2 3
+1 -1 2 0
+Sample Output 2:
+No
+Yes
+*/
+
+
+
+/*
+    Time Complexity: O(1)
+    Space Complexity: O(1)
+*/
+
+#include <algorithm>
+
+bool isSquare(vector<int> x, vector<int> y) {
+    vector<long long> distSq;
+    for(int i = 0; i < 4; i++) {
+        for(int j = i + 1 ; j < 4; j++) {
+            long long dist = (1LL * (x[i] - x[j]) * (x[i] - x[j])) + (1LL * (y[i] - y[j]) * (y[i] - y[j]));
+            distSq.push_back(dist);
+        }
+    }
+
+    sort(distSq.begin(), distSq.end());
+
+    
+    //Check if the distance of all the sides are equal 
+    //and the length of the diagonals are equal to the length of each side * root(2).
+    if(distSq[0] == distSq[1] &&
+       distSq[1] == distSq[2] &&
+       distSq[2] == distSq[3] &&
+       distSq[4] == distSq[5] &&
+       distSq[0] * 2LL == distSq[4] &&
+       distSq[0] > 0){
+        return true;
+    }
+    return false;
+}