Add solution for checking valid perfect squares

Implemented a binary search-based function to check if a number is a perfect square. Added unit tests to cover perfect squares, non-perfect squares, edge cases, and numbers near perfect squares.

Author: nicholasadamou

Diff for: Binary Search/Math/__init__.py

@@ -0,0 +1,64 @@
+# https://leetcode.com/problems/valid-perfect-square
+
+import unittest
+
+
+def is_perfect_square(num: int) -> bool:
+    left = 0
+    right = num
+
+    while left <= right:
+        mid = (left + right) // 2
+
+        squared = mid * mid
+
+        if squared == num:
+            return True
+
+        if squared < num:
+            left = mid + 1
+        else:
+            right = mid - 1
+
+    return False
+
+
+class TestIsPerfectSquare(unittest.TestCase):
+    def test_perfect_squares(self):
+        # Testing basic perfect squares
+        self.assertTrue(is_perfect_square(1))
+        self.assertTrue(is_perfect_square(4))
+        self.assertTrue(is_perfect_square(9))
+        self.assertTrue(is_perfect_square(16))
+        self.assertTrue(is_perfect_square(25))
+        self.assertTrue(is_perfect_square(36))
+        self.assertTrue(is_perfect_square(49))
+        self.assertTrue(is_perfect_square(64))
+        self.assertTrue(is_perfect_square(81))
+        self.assertTrue(is_perfect_square(100))
+
+    def test_non_perfect_squares(self):
+        # Testing numbers that are not perfect squares
+        self.assertFalse(is_perfect_square(2))
+        self.assertFalse(is_perfect_square(3))
+        self.assertFalse(is_perfect_square(5))
+        self.assertFalse(is_perfect_square(6))
+        self.assertFalse(is_perfect_square(7))
+        self.assertFalse(is_perfect_square(8))
+        self.assertFalse(is_perfect_square(10))
+        self.assertFalse(is_perfect_square(11))
+
+    def test_edge_cases(self):
+        # Test edge cases like 0, 1 and a very large number
+        self.assertTrue(is_perfect_square(0))  # 0 is a perfect square
+        self.assertTrue(is_perfect_square(1))  # Edge case where the number itself is 1
+        self.assertFalse(
+            is_perfect_square(2147483647)
+        )  # Large number that's not a perfect square
+
+    def test_numbers_around_perfect_squares(self):
+        # Testing numbers that are close to perfect squares
+        self.assertFalse(is_perfect_square(15))  # Close to 16
+        self.assertFalse(is_perfect_square(17))  # Close to 16
+        self.assertFalse(is_perfect_square(24))  # Close to 25
+        self.assertFalse(is_perfect_square(26))  # Close to 25