This is not a very intuitive problem for me, I have to spent quite a while drawing figures to understand it. As shown in the figure, 1 shows the original tree, you can think about it as a comb, with 1, 2, 4 form the bone, and 3, 5 as the teeth. All we need to do is flip the teeth direction as shown in figure 2. We will remove the link 1--3, 2--5, and add link 2--3, and 4--5. And node 4 will be the new root.

As the recursive solution, we will keep recurse on the left child and once we are are done, we found the newRoot, which is 4 for this case. At this point, we will need to set the new children for node 2, basically the new left node is 3, and right node is 1. Here is the recursive solution:

Recursive:

```
public TreeNode upsideDownBinaryTree(TreeNode root) {
if(root == null || root.left == null) {
return root;
}
TreeNode newRoot = upsideDownBinaryTree(root.left);
root.left.left = root.right; // node 2 left children
root.left.right = root; // node 2 right children
root.left = null;
root.right = null;
return newRoot;
}
```

For the iterative solution, it follows the same thought, the only thing we need to pay attention to is to save the node information that will be overwritten.

```
public TreeNode upsideDownBinaryTree(TreeNode root) {
TreeNode curr = root;
TreeNode next = null;
TreeNode temp = null;
TreeNode prev = null;
while(curr != null) {
next = curr.left;
// swapping nodes now, need temp to keep the previous right child
curr.left = temp;
temp = curr.right;
curr.right = prev;
prev = curr;
curr = next;
}
return prev;
}
```