Check if Two Trees are Symmetric in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of symmetric tree check function

What is the output of the following code that checks if two binary trees are symmetric?

DSA Python

class Node:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def is_symmetric(t1, t2):
    if not t1 and not t2:
        return True
    if not t1 or not t2:
        return False
    return (t1.val == t2.val) and is_symmetric(t1.left, t2.right) and is_symmetric(t1.right, t2.left)

# Construct trees
tree1 = Node(1, Node(2), Node(3))
tree2 = Node(1, Node(3), Node(2))

print(is_symmetric(tree1, tree2))

A True

B None

C TypeError

D False

💡 Hint

Check if the left subtree of one tree matches the right subtree of the other.

The function is_symmetric recursively checks if two trees are mirror images. Here, tree1 and tree2 are not symmetric because the left child of tree1 does not match the right child of tree2 and vice versa.

❓ Predict Output

intermediate

Output when one tree is None

What is the output of the code below when checking symmetry between a tree and None?

DSA Python

class Node:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def is_symmetric(t1, t2):
    if not t1 and not t2:
        return True
    if not t1 or not t2:
        return False
    return (t1.val == t2.val) and is_symmetric(t1.left, t2.right) and is_symmetric(t1.right, t2.left)

# Construct tree
tree1 = Node(1, Node(2), Node(3))
tree2 = None

print(is_symmetric(tree1, tree2))

A False

B True

C AttributeError

D None

💡 Hint

If one tree is empty and the other is not, they cannot be symmetric.

The function returns False because one tree is None and the other is not, so they cannot be symmetric.

🔧 Debug

advanced

Identify the error in symmetric tree check

What error will the following code produce when checking symmetry of two trees?

DSA Python

class Node:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def is_symmetric(t1, t2):
    if t1 is None and t2 is None:
        return True
    if t1 is None or t2 is None:
        return False
    return (t1.val == t2.val) and is_symmetric(t1.left, t2.left) and is_symmetric(t1.right, t2.right)

# Construct trees
tree1 = Node(1, Node(2), Node(3))
tree2 = Node(1, Node(3), Node(2))

print(is_symmetric(tree1, tree2))

A False

B RecursionError

C True

D None

💡 Hint

Check the recursive calls comparing left with left and right with right.

The function incorrectly compares left subtree with left subtree and right with right, so it returns False for symmetric trees that are mirror images.

🧠 Conceptual

advanced

Understanding mirror symmetry in trees

Which statement best describes the condition for two trees to be symmetric?

A Both trees must have the same structure and node values in the same positions.

B Both trees must have the same number of nodes regardless of structure.

C The left subtree of one tree must be a mirror image of the right subtree of the other tree, and vice versa.

D The root nodes must have different values but identical subtrees.

💡 Hint

Think about how mirror images reflect each other.

Symmetry means one tree is the mirror image of the other, so left subtree of one matches right subtree of the other.

❓ Predict Output

expert

Output of complex symmetric tree check

What is the output of the code below that checks if two complex trees are symmetric?

DSA Python

class Node:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def is_symmetric(t1, t2):
    if not t1 and not t2:
        return True
    if not t1 or not t2:
        return False
    return (t1.val == t2.val) and is_symmetric(t1.left, t2.right) and is_symmetric(t1.right, t2.left)

# Construct trees
tree1 = Node(1,
             Node(2, Node(4), Node(5)),
             Node(3, None, Node(6)))
tree2 = Node(1,
             Node(3, Node(6), None),
             Node(2, Node(5), Node(4)))

print(is_symmetric(tree1, tree2))

A False

B True

C AttributeError

D None

💡 Hint

Check each corresponding subtree carefully for mirror symmetry.

The trees are mirror images with matching node values in symmetric positions, so the function returns True.

Practice

1. What does it mean for two binary trees to be symmetric?

easy

A. They are mirror images of each other around their center.

B. They have the same number of nodes.

C. They have the same root value only.

D. They have identical left subtrees only.

Solution

1. Step 1: Understand symmetry in trees

   Two trees are symmetric if one is the mirror reflection of the other around the center.

2. Step 2: Compare structure and node values

   Both structure and node values must match in a mirrored way for symmetry.

3. Final Answer:

   They are mirror images of each other around their center. -> Option A

4. Quick Check:

   Symmetry means mirror image = A [OK]

Hint: Symmetric trees mirror each other exactly [OK]

Common Mistakes:

• Thinking same number of nodes means symmetric
• Ignoring node values in comparison
• Checking only left or right subtree

2. Which of the following Python function signatures is correct to check if two trees are symmetric?

easy

A. def is_symmetric(tree1, tree2)

B. def is_symmetric(tree1 tree2):

C. def is_symmetric(tree1, tree2) -> bool:

D. def is_symmetric(tree1, tree2): return True

Solution

1. Step 1: Check syntax for function definition

   Python functions require parentheses around parameters and a colon at the end.

2. Step 2: Identify correct type hint usage

   def is_symmetric(tree1, tree2) -> bool: uses correct syntax with type hint and colon, making it valid and clear.

3. Final Answer:

   def is_symmetric(tree1, tree2) -> bool: -> Option C

4. Quick Check:

   Correct Python function syntax with type hint = D [OK]

Hint: Use parentheses and colon; type hints are optional but clear [OK]

Common Mistakes:

• Missing comma between parameters
• Omitting colon at function end
• Incorrect parameter syntax without parentheses

3. What will be the output of the following code snippet?

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

def is_mirror(t1, t2):
    if not t1 and not t2:
        return True
    if not t1 or not t2:
        return False
    return (t1.val == t2.val) and is_mirror(t1.left, t2.right) and is_mirror(t1.right, t2.left)

root1 = Node(1)
root1.left = Node(2)
root1.right = Node(3)

root2 = Node(1)
root2.left = Node(3)
root2.right = Node(2)

print(is_mirror(root1, root2))

medium

A. True

B. False

C. None

D. Error

Solution

1. Step 1: Check base cases for empty nodes

   Both trees have root 1, and their left and right children are swapped but equal in value.

2. Step 2: Recursively verify mirror condition

   Left of root1 (2) matches right of root2 (2), and right of root1 (3) matches left of root2 (3), so all conditions return True.

3. Final Answer:

   True -> Option A

4. Quick Check:

   Mirror check returns True for swapped children = A [OK]

Hint: Mirror means left of one equals right of other [OK]

Common Mistakes:

• Confusing left and right children in recursion
• Ignoring base cases for None nodes
• Assuming same structure means symmetric

4. Identify the error in this code snippet that checks if two trees are symmetric:

def is_symmetric(t1, t2):
    if t1 is None and t2 is None:
        return True
    if t1 is None or t2 is None:
        return False
    if t1.val != t2.val:
        return False
    return is_symmetric(t1.left, t2.left) and is_symmetric(t1.right, t2.right)

medium

A. It does not check for None nodes.

B. It compares left with left and right with right instead of mirror sides.

C. It returns True too early without checking values.

D. It uses 'is' instead of '==' for value comparison.

Solution

1. Step 1: Analyze recursive calls for symmetry

   The function compares left subtree of t1 with left subtree of t2 and right with right, which is incorrect for mirror symmetry.

2. Step 2: Correct mirror comparison

   It should compare left of t1 with right of t2 and right of t1 with left of t2 to check mirror symmetry properly.

3. Final Answer:

   It compares left with left and right with right instead of mirror sides. -> Option B

4. Quick Check:

   Mirror check requires cross comparison = B [OK]

Hint: Mirror means cross compare left with right [OK]

Common Mistakes:

• Comparing same sides instead of mirror sides
• Confusing 'is' and '==' for values
• Missing base cases for None nodes

5. Given two binary trees, write a function to check if they are symmetric considering that one tree might be None. Which approach correctly handles this edge case?

hard

A. Return False immediately if either tree is None.

B. Ignore None checks and compare node values only.

C. Only compare root values and ignore subtrees.

D. Return True if both trees are None, else check mirror recursively.

Solution

1. Step 1: Handle None edge cases carefully

   If both trees are None, they are symmetric by definition, so return True.

2. Step 2: Recursively check mirror symmetry

   If only one is None, return False. Otherwise, compare root values and recursively check left of one with right of other and vice versa.

3. Final Answer:

   Return True if both trees are None, else check mirror recursively. -> Option D

4. Quick Check:

   Both None means symmetric, else recurse mirror check = C [OK]

Hint: Both None means symmetric; one None means not symmetric [OK]

Common Mistakes:

• Returning False if either tree is None without checking both
• Skipping recursive mirror checks
• Comparing only root values