How do you calculate tree height and check balance?

A naive balance check computes the height of every subtree separately, which can become O(n^2) on a skewed tree. The better approach returns both the height and a balance signal from one postorder traversal, so each node is visited once.

function checkBalance(node) {
  if (node === null) return 0;
  const left = checkBalance(node.left);
  if (left === -1) return -1;
  const right = checkBalance(node.right);
  if (right === -1) return -1;
  if (Math.abs(left - right) > 1) return -1;
  return Math.max(left, right) + 1;
}

function isBalanced(root) {
  return checkBalance(root) !== -1;
}

Definitions to keep straight

• Height of a leaf is 0 by the edge-count convention
• Height of an empty tree is often defined as -1 or 0 depending on context
• Depth is measured from the root down to a node
• A balanced tree has height O(log n)
• The check must apply to every node, not just the root

Height is also the space complexity of a recursive traversal, because the call stack follows one root-to-leaf path. That is why a skewed tree can overflow even though the node count is manageable.