Final answer:
The constructing a binary tree from given post order and in order traversals. The last node in post order is the root, and the in order traversal indicates the left and right sub trees. The process continues until the binary tree is fully reconstructed.
Step-by-step explanation:
The constructing a binary tree based on given postorder and inorder traversals. To draw the binary tree, we must determine the root and the structure of the tree by understanding the traversals provided. In postorder traversal, the last node visited is the root of the tree. In the given postorder (A6 A5 A3 A8 A7 A4 A2 A1), A1 is the root.
In inorder traversal, the nodes to the left of the root are part of the left subtree, and those to the right are part of the right subtree. For the given inorder (A6 A3 A5 A1 A2 A8 A4 A7), the left subtree of A1 consists of (A6 A3 A5), and the right subtree consists of (A2 A8 A4 A7).
Continuing this process, we identify the root of each subtree and its corresponding left and right children from the postorder and inorder lists until the entire tree is reconstructed. The final binary tree as per the given traversals would look like this:
A1
/ \
A5 A2
/ \
A3 A6 A8 A7
/ \
A4