add time and space

Author: akgmage

Trees/Binary Trees/is_symmetric.c++

@@ -3,7 +3,7 @@
   if the left and right subtrees are mirror images of each other.
 
     Explanation:
-    
+
     1. The code defines a class `BinaryTree` representing a binary tree node. It has an `int` value and pointers 
        to its left and right children.
     2. The `SymmetricalTree` function is the main entry point. It calls the helper function `treesAreMirrored` 
@@ -19,7 +19,19 @@
     8. The result is printed to the console.
     9. Memory cleanup is performed by deleting the dynamically allocated nodes.
 
-Note: This code snippet assumes the use of a C++ compiler and standard library.
+    The time and space complexity of the given code snippet can be analyzed as follows:
+
+    1. Time Complexity:
+    - The `SymmetricalTree` function calls the `treesAreMirrored` function, which performs a recursive traversal of the binary tree.
+    - In the worst case, the recursion visits each node once, so the time complexity is O(N), where N is the number of nodes in the tree.
+
+    2. Space Complexity:
+   - The space complexity is determined by the maximum depth of the recursion stack.
+   - In the worst case, the binary tree is linear, resulting in a recursion depth of N, where N is the number of nodes in the tree.
+   - Therefore, the space complexity is O(N) due to the recursion stack usage.
+
+    It's important to note that the space complexity can be optimized by using an iterative approach instead of recursion. By using an iterative algorithm that leverages a stack or queue to perform a level-order traversal, we can achieve a space complexity of O(W), where W is the maximum width (number of nodes at the same level) of the binary tree.
+    
 */
 #include <iostream>