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The following three are known to be the preorder, inorder and postorder sequences of a binary tree. But it is not known which is which.
MBCAFHPYK
KAMCBYPFH
MABCKYFPH
Pick the true statement from the following.
MBCAFHPYK
KAMCBYPFH
MABCKYFPH
Pick the true statement from the following.
- a)I and II are preorder and inorder sequences, respectively
- b)I and III are preorder and postorder sequences, respectively
- c)II is the inorder sequence, but nothing more can be said about the other two sequences
- d)II and III are the preorder and inorder sequences, respectively
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The following three are known to be the preorder, inorder and postorde...
The approach to solve this question is to first find 2 sequences whose first and last element is same. The reason being first element in the Pre-order of any binary tree is the root and last element in the Post-order of any binary tree is the root. Looking at the sequences given,
Pre-order = KAMCBYPFH Post-order = MBCAFHPYK Left-over sequence MABCKYFPH will be in order. Since we have all the traversals identified, let's try to draw the binary tree if possible.
Pre-order = KAMCBYPFH Post-order = MBCAFHPYK Left-over sequence MABCKYFPH will be in order. Since we have all the traversals identified, let's try to draw the binary tree if possible.
I. Post order
II. Pre order
III. Inorder
II. Pre order
III. Inorder
Most Upvoted Answer
The following three are known to be the preorder, inorder and postorde...
Explanation:
To determine the correct statement, we need to analyze the given sequences and identify the characteristics of preorder, inorder, and postorder traversals in binary trees.
Preorder Traversal:
In a preorder traversal, the root node is visited first, followed by the traversal of the left subtree, and then the traversal of the right subtree. The order of nodes visited is Root-Left-Right.
Inorder Traversal:
In an inorder traversal, the left subtree is visited first, followed by the root node, and then the right subtree. The order of nodes visited is Left-Root-Right.
Postorder Traversal:
In a postorder traversal, the left subtree is visited first, followed by the right subtree, and then the root node. The order of nodes visited is Left-Right-Root.
Analysis:
Let's analyze the given sequences: MBCAFHPYKKAMCBYPFHMABCKYFHPH
Step 1: Find the root node
In preorder traversal, the first element is always the root node. In the given sequence, the first element is "M". Therefore, "M" is the root node.
Step 2: Divide the sequences based on the root node
Using the root node "M" as a reference, we can divide the sequences into two parts: the left subtree and the right subtree.
Left subtree: BCAPHYKKACB (preorder), CBAPHYKKACB (inorder), CBAHYKKAACB (postorder)
Right subtree: YPFHMABCKYFHPH (preorder), YPFCBHMKFYHPH (inorder), YPFCBHMKFYHP (postorder)
Step 3: Analyze the left subtree
By comparing the left subtree sequences, we can determine the traversal orders.
Left subtree:
Preorder: BCAPHYKKACB
Inorder: CBAPHYKKACB
Postorder: CBAHYKKAACB
From the comparison, we can conclude that the left subtree sequences are the inorder, preorder, and postorder sequences, respectively.
Step 4: Analyze the right subtree
By comparing the right subtree sequences, we can determine the traversal orders.
Right subtree:
Preorder: YPFHMABCKYFHPH
Inorder: YPFCBHMKFYHPH
Postorder: YPFCBHMKFYHP
From the comparison, we can conclude that the right subtree sequences are the preorder and inorder sequences, respectively.
Conclusion:
Based on the analysis, we can determine that the correct statement is option D: II and III are the preorder and inorder sequences, respectively.
To determine the correct statement, we need to analyze the given sequences and identify the characteristics of preorder, inorder, and postorder traversals in binary trees.
Preorder Traversal:
In a preorder traversal, the root node is visited first, followed by the traversal of the left subtree, and then the traversal of the right subtree. The order of nodes visited is Root-Left-Right.
Inorder Traversal:
In an inorder traversal, the left subtree is visited first, followed by the root node, and then the right subtree. The order of nodes visited is Left-Root-Right.
Postorder Traversal:
In a postorder traversal, the left subtree is visited first, followed by the right subtree, and then the root node. The order of nodes visited is Left-Right-Root.
Analysis:
Let's analyze the given sequences: MBCAFHPYKKAMCBYPFHMABCKYFHPH
Step 1: Find the root node
In preorder traversal, the first element is always the root node. In the given sequence, the first element is "M". Therefore, "M" is the root node.
Step 2: Divide the sequences based on the root node
Using the root node "M" as a reference, we can divide the sequences into two parts: the left subtree and the right subtree.
Left subtree: BCAPHYKKACB (preorder), CBAPHYKKACB (inorder), CBAHYKKAACB (postorder)
Right subtree: YPFHMABCKYFHPH (preorder), YPFCBHMKFYHPH (inorder), YPFCBHMKFYHP (postorder)
Step 3: Analyze the left subtree
By comparing the left subtree sequences, we can determine the traversal orders.
Left subtree:
Preorder: BCAPHYKKACB
Inorder: CBAPHYKKACB
Postorder: CBAHYKKAACB
From the comparison, we can conclude that the left subtree sequences are the inorder, preorder, and postorder sequences, respectively.
Step 4: Analyze the right subtree
By comparing the right subtree sequences, we can determine the traversal orders.
Right subtree:
Preorder: YPFHMABCKYFHPH
Inorder: YPFCBHMKFYHPH
Postorder: YPFCBHMKFYHP
From the comparison, we can conclude that the right subtree sequences are the preorder and inorder sequences, respectively.
Conclusion:
Based on the analysis, we can determine that the correct statement is option D: II and III are the preorder and inorder sequences, respectively.
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The following three are known to be the preorder, inorder and postorder sequences of a binary tree. But it is not known which is which.MBCAFHPYKKAMCBYPFHMABCKYFPHPick the true statement from the following.a)I and II are preorder and inorder sequences, respectivelyb)I and III are preorder and postorder sequences, respectivelyc)II is the inorder sequence, but nothing more can be said about the other two sequencesd)II and III are the preorder and inorder sequences, respectivelyCorrect answer is option 'D'. Can you explain this answer?
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