Given the root of a binary tree, return the length of the diameter of the tree.

The diameter of a binary tree is the length of the longest path between any two nodes. This path may or may not pass through the root. To find the diameter without recursion, we can use an iterative post-order traversal. We maintain a stack storing tuples of (node, visited_children_flag). When we first encounter a node, we push it onto the stack with the flag set to false. If the flag is false, we check its children. If a child exists, we push it onto the stack with the flag set to false and break to process the child first. If both children have been processed (or don't exist), we pop the current node, calculate its height based on its children's heights (which we store in a dictionary), and update the overall diameter by comparing it with the sum of the heights of its left and right children. The height of a null child is considered -1, and the height of a leaf node is 0. The diameter at any node is the sum of the heights of its left and right subtrees.