Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4...
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Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers. What is the in-order traversal sequence of the resultant tree?
- a)7 5 1 0 3 2 4 6 8 9
- b)0 2 4 3 1 6 5 9 8 7
- c)0 1 2 3 4 5 6 7 8 9
- d)9 8 6 4 2 3 0 1 5 7
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that ...
Explanation:
To determine the in-order traversal sequence of the resultant binary search tree, we need to understand how the numbers are inserted into the tree and how they are arranged.
Binary Search Tree:
A binary search tree is a binary tree in which each node has a value greater than all the values in its left subtree and less than all the values in its right subtree.
Insertion Process:
To insert the numbers into the binary search tree, we start with an empty tree and insert each number in the given order.
- The first number, 7, becomes the root of the tree.
- The second number, 5, is less than 7, so it becomes the left child of 7.
- The third number, 1, is less than 7 and 5, so it becomes the left child of 5.
- The fourth number, 8, is greater than 7, so it becomes the right child of 7.
- The fifth number, 3, is greater than 1 and becomes the right child of 1.
- The sixth number, 6, is greater than 5 and becomes the right child of 5.
- The seventh number, 0, is less than 1 and becomes the left child of 1.
- The eighth number, 9, is greater than 7 and becomes the right child of 8.
- The ninth number, 4, is greater than 3 and becomes the right child of 3.
- The tenth number, 2, is greater than 1 and becomes the right child of 1.
In-Order Traversal:
In-order traversal is a depth-first traversal method where the left subtree is traversed first, then the root, and finally the right subtree.
Traversing the Resultant Tree:
- The left subtree of the root 7 contains the numbers 5, 1, 0, 3, 2, 4, and 6.
- The right subtree of the root 7 contains the numbers 8 and 9.
Traversing the left subtree:
- The left subtree of 5 contains the numbers 1, 0, 3, 2, 4, and 6.
- The left subtree of 1 contains the number 0.
- The right subtree of 1 contains the numbers 3, 2, 4, and 6.
- The left subtree of 3 contains the number 2.
- The right subtree of 3 contains the number 4.
- The right subtree of 5 contains the number 6.
Traversing the right subtree:
- The right subtree of 8 contains the number 9.
In-Order Traversal Sequence:
The in-order traversal sequence of the resultant tree is obtained by traversing the left subtree, visiting the root, and then traversing the right subtree.
The in-order traversal sequence is:
0 1 2 3 4 5 6 7 8 9
Therefore, option C, 0 1 2 3 4 5 6 7 8 9, is the correct answer.
To determine the in-order traversal sequence of the resultant binary search tree, we need to understand how the numbers are inserted into the tree and how they are arranged.
Binary Search Tree:
A binary search tree is a binary tree in which each node has a value greater than all the values in its left subtree and less than all the values in its right subtree.
Insertion Process:
To insert the numbers into the binary search tree, we start with an empty tree and insert each number in the given order.
- The first number, 7, becomes the root of the tree.
- The second number, 5, is less than 7, so it becomes the left child of 7.
- The third number, 1, is less than 7 and 5, so it becomes the left child of 5.
- The fourth number, 8, is greater than 7, so it becomes the right child of 7.
- The fifth number, 3, is greater than 1 and becomes the right child of 1.
- The sixth number, 6, is greater than 5 and becomes the right child of 5.
- The seventh number, 0, is less than 1 and becomes the left child of 1.
- The eighth number, 9, is greater than 7 and becomes the right child of 8.
- The ninth number, 4, is greater than 3 and becomes the right child of 3.
- The tenth number, 2, is greater than 1 and becomes the right child of 1.
In-Order Traversal:
In-order traversal is a depth-first traversal method where the left subtree is traversed first, then the root, and finally the right subtree.
Traversing the Resultant Tree:
- The left subtree of the root 7 contains the numbers 5, 1, 0, 3, 2, 4, and 6.
- The right subtree of the root 7 contains the numbers 8 and 9.
Traversing the left subtree:
- The left subtree of 5 contains the numbers 1, 0, 3, 2, 4, and 6.
- The left subtree of 1 contains the number 0.
- The right subtree of 1 contains the numbers 3, 2, 4, and 6.
- The left subtree of 3 contains the number 2.
- The right subtree of 3 contains the number 4.
- The right subtree of 5 contains the number 6.
Traversing the right subtree:
- The right subtree of 8 contains the number 9.
In-Order Traversal Sequence:
The in-order traversal sequence of the resultant tree is obtained by traversing the left subtree, visiting the root, and then traversing the right subtree.
The in-order traversal sequence is:
0 1 2 3 4 5 6 7 8 9
Therefore, option C, 0 1 2 3 4 5 6 7 8 9, is the correct answer.
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Community Answer
Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that ...
In-order traversal of a BST gives elements in increasing order. So answer c is correct without any doubt.
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Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers. What is the in-order traversal sequence of the resultant tree?a)7 5 1 0 3 2 4 6 8 9b)0 2 4 3 1 6 5 9 8 7c)0 1 2 3 4 5 6 7 8 9d)9 8 6 4 2 3 0 1 5 7Correct answer is option 'C'. Can you explain this answer?
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