Final answer:
Yes, with the postorder and inorder traversal sequences of a binary tree where all nodes have unique values, you can reconstruct the original tree by using the last element of the postorder sequence as the root and partitioning the inorder sequence to find the subtrees recursively.
Step-by-step explanation:
If you are given the order of the nodes as visited by a postorder traversal and the order of the nodes as visited by an inorder traversal, you do have enough information to reconstruct the original binary tree, provided that all nodes have unique values. The postorder traversal gives you the order in which the nodes are visited for the last time, which importantly includes the root node of the tree as the last element. The inorder traversal gives you the sequence of nodes such that for any given node, all nodes in its left subtree are visited before it and all nodes in its right subtree are visited after it.
To reconstruct the binary tree, you would start with the last node in the postorder sequence, which is the root of the tree. You would then find this root node's position in the inorder sequence. The nodes to the left of the root in the inorder sequence constitute the left subtree, and the nodes to the right constitute the right subtree. You continue this process recursively, each time considering the rightmost node in the postorder sequence as the new subtree root, and partitioning the inorder sequence accordingly, to find the subtrees for every node. This step-by-step approach allows you to reconstruct the original tree accurately.