Inorder: FLTPWVDQJNYHGSBXKCRMZPreorder: SQPLFTVWDHNJYGCXBKMRZThe goal of this problem is to figure out the postorder traversal of Robert's tree, given the other two traversals above.
Question
Inorder: FLTPWVDQJNYHGSBXKCRMZPreorder: SQPLFTVWDHNJYGCXBKMRZThe goal of this problem is to figure out the postorder traversal of Robert's tree, given the other two traversals above.
Solution
First, let's understand what these traversals mean.
In an inorder traversal, we first visit the left subtree, then the root, and finally the right subtree. In the given inorder traversal "FLTPWVDQJNYHGSBXKCRMZ", the first letter "F" is the leftmost node, and the last letter "Z" is the rightmost node.
In a preorder traversal, we first visit the root, then the left subtree, and finally the right subtree. In the given preorder traversal "SQPLFTVWDHNJYGCXBKMRZ", the first letter "S" is the root of the tree.
Now, let's find the postorder traversal. In a postorder traversal, we first visit the left subtree, then the right subtree, and finally the root.
Step 1: Identify the root in the preorder traversal. The root is "S".
Step 2: Split the inorder traversal into left and right subtrees. Everything before "S" in the inorder traversal is the left subtree and everything after is the right subtree. So, the left subtree is "FLTPWVDQJNYHG" and the right subtree is "BXKCRMZ".
Step 3: For each subtree, repeat the process. Find the root in the preorder traversal (the first letter not included in the previous steps), split the inorder traversal at the root, and so on.
Step 4: Continue this process until you have visited all nodes. The order in which you visit the nodes gives you the postorder traversal.
By following these steps, you can figure out the postorder traversal of Robert's tree.
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