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question 10 is it possible to have a single tree that satisfies the following traversals: inorder: x h c k y a s m w q d r l postorder: x c h y s a w m d q l r k if so, draw the tree. if not, explain which value(s) would not allow such traversals at the same time.

User Camdub
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Final answer:

It is not possible to create a single binary tree that fits the provided inorder and postorder traversals due to a conflict when trying to place certain nodes in accordance with both traversal orders.

Step-by-step explanation:

The student is asking if it is possible to have a single binary tree that fits the given inorder and postorder traversals. To determine the answer, one must understand that in inorder traversal, nodes are visited in a left-root-right sequence, while in postorder traversal, nodes are visited in a left-right-root sequence.

In the given inorder traversal (x h c k y a s m w q d r l), 'k' is the root since it is the last node in the postorder traversal (x c h y s a w m d q l r k). However, trying to construct the tree will quickly lead to a conflict. For example, 'd' should be a right child of 'r' based on postorder but should come before 'r' in inorder; this is impossible in a binary tree structure. Hence, it is not possible to have a single tree that satisfies both given traversals.

User Pixic
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