題目

Given a binary tree, check whether it is a mirror of itself (ie, symmetric around its center).

For example, this binary tree [1,2,2,3,4,4,3] is symmetric:

    1
   / \
  2   2
 / \ / \
3  4 4  3

But the following [1,2,2,null,3,null,3] is not:

    1
   / \
  2   2
   \   \
   3    3

Note:
Bonus points if you could solve it both recursively and iteratively.

題意

給定一個二叉樹，檢查它是否是對稱的。

分析及解答

• 【結構，內容】結構上要一致，同時內容上要相同。
  

方法1（遞迴）：

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);
}
 

 public boolean isSymmetric(TreeNode root) {
        Queue<TreeNode> q = new LinkedList<TreeNode>();
        if(root == null) return true;
        q.add(root.left);
        q.add(root.right);
        while(q.size() > 1){
            TreeNode left = q.poll(),
                     right = q.poll();
            if(left== null&& right == null) continue;
            if(left == null ^ right == null) return false;
            if(left.val != right.val) return false;
            q.add(left.left);
            q.add(right.right);
            q.add(left.right);
            q.add(right.left);            
        }
        return true;
    }
 

方法2.2（較為複雜）

public boolean isSymmetric(TreeNode root) {
    if(root==null)  return true;
    
    Stack<TreeNode> stack = new Stack<TreeNode>();
    TreeNode left, right;
    if(root.left!=null){
        if(root.right==null) return false;
        stack.push(root.left);
        stack.push(root.right);
    }
    else if(root.right!=null){
        return false;
    }
        
    while(!stack.empty()){
        if(stack.size()%2!=0)   return false;
        right = stack.pop();
        left = stack.pop();
        if(right.val!=left.val) return false;
        
        if(left.left!=null){
            if(right.right==null)   return false;
            stack.push(left.left);
            stack.push(right.right);
        }
        else if(right.right!=null){
            return false;
        }
            
        if(left.right!=null){
            if(right.left==null)   return false;
            stack.push(left.right);
            stack.push(right.left);
        }