Final answer:
The student is asked to construct a binary tree using given inorder and preorder traversals. The first step is identifying the root from the preorder traversal, then recursing through both traversals to build the complete tree.
Step-by-step explanation:
The question asks us to construct a binary tree given an inorder traversal (C A B D E F) and a preorder traversal (D C B A F E). To construct the binary tree, we will use the preorder traversal to determine the root and the order in which the nodes are to be inserted. The first element in the preorder traversal is always the root of the tree.
The root of our binary tree is 'D' since it is the first element in the preorder list. Then by looking at the inorder traversal, we can split the remaining elements into the left and right subtrees of the root. The in-order sequence 'C A B' comes before 'D', so these are in the left subtree, and 'E F' comes after 'D', hence they are in the right subtree.
To construct the left subtree, we take the next element in the preorder list, which is 'C', and find its position in the inorder sequence, which gives us the new subtrees. This process is recursively applied to all nodes until the full binary tree is constructed.