Check if Two Trees are Symmetric in DSA Javascript - Execution Trace

Concept Flow - Check if Two Trees are Symmetric

Start with root nodes of both trees

↓

Compare values of current nodes

↓

Return false - trees not symmetric

↓

Recursively check left of Tree1 with right of Tree2

↓

Recursively check right of Tree1 with left of Tree2

↓

Both recursive calls true?

Yes↓

Return true - trees are symmetric

Start by comparing root nodes, then recursively check if left subtree of one tree matches right subtree of the other, and vice versa, returning true only if all pairs match.

Execution Sample

DSA Javascript

function isSymmetric(t1, t2) {
  if (!t1 && !t2) return true;
  if (!t1 || !t2) return false;
  if (t1.val !== t2.val) return false;
  return isSymmetric(t1.left, t2.right) && isSymmetric(t1.right, t2.left);
}

This function checks if two trees are mirror images by comparing nodes recursively.

Execution Table

Step	t1 Node Value	t2 Node Value	Condition Checked	Result	Next Action
1	1	1	Both nodes exist and values equal?	true	Check left of t1 with right of t2 and right of t1 with left of t2
2	2	2	Both nodes exist and values equal?	true	Check left of t1.left with right of t2.right and right of t1.left with left of t2.right
3	3	3	Both nodes exist and values equal?	true	Check left and right children (both null)
4	null	null	Both nodes null?	true	Return true
5	null	null	Both nodes null?	true	Return true
6	null	null	Both nodes null?	true	Return true
7	null	null	Both nodes null?	true	Return true
8	2	2	Both nodes exist and values equal?	true	Check left of t1.right with right of t2.left and right of t1.right with left of t2.left
9	3	3	Both nodes exist and values equal?	true	Check left and right children (both null)
10	null	null	Both nodes null?	true	Return true
11	null	null	Both nodes null?	true	Return true
12	null	null	Both nodes null?	true	Return true
13	null	null	Both nodes null?	true	Return true
14	All recursive calls returned true			true	Return true - trees are symmetric

💡 All corresponding nodes matched or were both null, confirming symmetry.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 8	Final
t1 Node	Root(1)	Left(2)	Left.Left(3)	Right(2)	null
t2 Node	Root(1)	Right(2)	Right.Right(3)	Left(2)	null
Result	undefined	true	true	true	true

Key Moments - 3 Insights

Why do we compare t1.left with t2.right and t1.right with t2.left instead of matching left with left and right with right?

Because symmetry means one tree is a mirror image of the other, so left subtree of one matches right subtree of the other. See execution_table steps 1 and 2 where this cross comparison happens.

What happens when both nodes are null during recursion?

If both nodes are null, it means the branches ended symmetrically, so we return true. This is shown in execution_table steps 4, 5, 6, 7, 10, 11, 12, and 13.

Why do we return false immediately if one node is null and the other is not?

Because that means the structure is not symmetric at that point. The function returns false early to stop unnecessary checks, as seen in the condition checks in the code and implied in the execution_table.

Visual Quiz - 3 Questions

Look at the execution_table at step 2, what nodes are being compared?

A t1.left with t2.right

B t1.left with t2.left

C t1.right with t2.right

D t1.right with t2.left

💡 Hint

Check the 'Next Action' column in step 1 and the 't1 Node Value' and 't2 Node Value' columns in step 2.

At which step does the function confirm that both nodes are null and returns true?

A Step 3

B Step 4

C Step 8

D Step 14

💡 Hint

Look for rows where 'Condition Checked' is 'Both nodes null?' and 'Result' is true.

If at step 1 the root node values were different, what would be the result?

A Return true

B Return false

C Continue recursion

D Ignore and check children

💡 Hint

Refer to the 'Condition Checked' and 'Result' columns in step 1 of the execution_table.

Concept Snapshot

Check if Two Trees are Symmetric:
- Compare root nodes values.
- Recursively check t1.left with t2.right and t1.right with t2.left.
- If both nodes null, return true.
- If one null or values differ, return false.
- Return true only if all pairs match.

Full Transcript

This concept checks if two trees are mirror images. It starts by comparing the root nodes. If both are null, they are symmetric at that point. If one is null or values differ, they are not symmetric. Otherwise, it recursively compares the left subtree of the first tree with the right subtree of the second tree, and the right subtree of the first tree with the left subtree of the second tree. The process continues until all nodes are checked. If all pairs match, the trees are symmetric.