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Symmetric Tree

Certification: Basic Level Accuracy: 0% Submissions: 0 Points: 5

Write a C program to check if a binary tree is symmetric around its center, meaning it is a mirror of itself. A binary tree is symmetric if the left subtree of the root is a mirror reflection of the right subtree of the root.

Example 1
    
  
  • Input:


    Symmetric Tree - Symmetricity


    • 
  
  • Output: true
    • 
  
  • Explanation: 
    • The left subtree of the root (1) consists of nodes 2, 3, and 4. 
    • The right subtree of the root (1) consists of nodes 2, 4, and 3. 
    • The left subtree is a mirror reflection of the right subtree. 
    • The values match in mirror positions (2-2, 3-3, 4-4). 
    • Therefore, the tree is symmetric.
    •
Example 2
    
  
  • Input:


    Symmetric Tree - Not Symmetric

    • 
  
  • Output: false
    • 
  
  • Explanation: 
    • The left subtree of the root (1) consists of nodes 2 and 3.
    • The right subtree of the root (1) consists of nodes 2 and 3. 
    • In the left subtree, node 3 is the right child of node 2. 
    • In the right subtree, node 3 is also the right child of node 2. 
    • In a mirror reflection, node 3 in the right subtree should be the left child of node 2. 
    • Since this is not the case, the tree is not symmetric.
    •
Constraints
    
  
  • The number of nodes in the tree is in the range [1, 1000].
    • 
  
  • The values of nodes are integers in the range [-100, 100].
    • 
  
  • Time Complexity: O(n), where n is the number of nodes in the tree.
    • 
  
  • Space Complexity: O(h), where h is the height of the tree (due to recursion stack).
    •
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Hint
Solution

Solution Hints

    
  
  • Use a recursive approach to check if two subtrees are mirror images of each other.
    • 
  
  • Start by comparing the left and right subtrees of the root.
    • 
  
  • Two subtrees are mirror images if:
   a. Their root values are the same
   b. The left subtree of one is a mirror of the right subtree of the other
   c. The right subtree of one is a mirror of the left subtree of the other
    • 
  
  • Handle the base cases properly (e.g., when both nodes are NULL).
    • 
  
  • You can also use an iterative approach with a queue or stack if preferred.
    • 
  
  • Be careful about the comparison conditions to ensure proper mirroring.
    • 
  
  • Consider edge cases like empty trees or trees with only one node.
    •

Steps to solve by this approach:

 Step 1: Create a helper function isMirror() that checks if two subtrees are mirror images of each other.

 Step 2: In the isMirror() function, handle the base cases:
   - If both trees are NULL, return true (empty trees are mirrors of each other).
   - If only one tree is NULL, return false (they cannot be mirrors).

 Step 3: Check if the values of the current nodes are equal.

 Step 4: Recursively check if the left subtree of the first tree is a mirror of the right subtree of the second tree.

 Step 5: Recursively check if the right subtree of the first tree is a mirror of the left subtree of the second tree.

 Step 6: In the isSymmetric() function, handle the case of an empty tree (return true).

 Step 7: For non-empty trees, call the isMirror() function with the left and right subtrees of the root.

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