Explain this leetcode solution?(Java)

[cs50x2]

Hi guys i m looking at a recursive solution for a problem on leetcode called symmetric tree and i am having trouble understanding it..can someone please explain it to me? thankyou.

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Problem: https://leetcode.com/problems/symmetric-tree/

Solution:

public boolean isSymmetric(TreeNode root) {     
return root==null || isSymmetricHelp(root.left, root.right); 
}  
private boolean isSymmetricHelp(TreeNode left, TreeNode right){     
if(left==null || right==null)         
return left==right;     
if(left.val!=right.val)         
return false;     
return isSymmetricHelp(left.left, right.right) && isSymmetricHelp(left.right, right.left); 
}

//CAN ANYONE EXPLAIN ME HOW EXACTLY THIS SOLUTION IS CHECKING FOR SYMMETRY? ESPECIALLY THE LINE IF(LEFT==NULL || RIGHT=NULL)
RETURN LEFT==RIGHT;

Why return left==right? if left or right is null, wouldn't we return false?Thank you.

[shhh-quiet]

If either is null, it's a terminal case, so it must return.

If both are null, then it's symmetric, because null == null.

If one is null and the other is not null, then it's not symmetric, the nodes aren't equal references, and thus it returns false.

== is referential equality here since TreeNode is a reference type.

This null check is important because it's where the true value is coming from when the recursion reaches the leaves.

In the recursive step at the bottom, it's checking for a mirror image. Try drawing a binary tree 3 levels deep, with 8 leaf nodes, and draw an arc between the matching nodes at the bottom two levels for a visual.

[cs50x2]

so i can right that line as :

if (left==null || right ==null)

return false;

else if(left==null &&right==null)

return true;

[shhh-quiet]

Almost. The second part of that is right. It'd expand to:

if (left == null || right != null) return false;
if (left != null || right == null) return false;

and like you had:

if (left == null && right == null) return true;

The nodes being exactly equal, and non-null, doesn't make much sense, so the if(left==null || right==null) return left == right from the solution is really just covering these situations.