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Assume a person has 10 distinct numbered balls. He wants to place these balls in 10 fixed slots of binary search tree (initially all slots are empty). In how many ways can the person place those balls in the slots of binary search tree? Each slot can occupy atmost 1 ball.
- a)1
- b)2
- c)3
- d)6
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Assume a person has 10 distinct numbered balls. He wants to place thes...
There is only one way. The minimum value has to go to the leftmost node and the maximum value to the rightmost node. Recursively we can define for other nodes.
Most Upvoted Answer
Assume a person has 10 distinct numbered balls. He wants to place thes...
Explanation:
To solve this problem, we need to understand the concept of binary search trees (BST) and the rules for placing the numbered balls in the slots.
Binary Search Tree (BST):
A binary search tree is a binary tree where the value of each node is greater than all values in its left subtree and less than all values in its right subtree.
Rules for Placing Balls in BST:
1. Each slot can only occupy at most 1 ball.
2. The numbered balls are distinct, meaning that no two balls have the same number.
3. The balls need to be placed in such a way that the resulting tree is a valid binary search tree.
Analysis:
Since the numbered balls are distinct, each slot in the binary search tree can have at most 1 ball. This means that we can place a ball in a slot if and only if the slot is empty.
In a binary search tree, the left subtree contains all the elements that are less than the root, and the right subtree contains all the elements that are greater than the root.
Placement Strategy:
To form a valid binary search tree, we need to place the numbered balls in such a way that each ball is placed in the correct slot based on its value.
Let's consider the placement of the balls in the slots step by step:
1. We have 10 numbered balls and 10 slots in the binary search tree.
2. We can place the first ball in any of the 10 slots since all the slots are empty.
3. Once the first ball is placed, there are 9 remaining balls and 9 empty slots.
4. For the second ball, we need to consider the value of the ball and the value of the ball in the first slot.
- If the value of the second ball is less than the value of the ball in the first slot, we can place it in the left subtree of the first slot.
- If the value of the second ball is greater than the value of the ball in the first slot, we can place it in the right subtree of the first slot.
5. Similarly, for each subsequent ball, we need to compare its value with the value of the balls already placed in the tree to determine the correct placement.
6. Finally, after placing all the balls, we will have a valid binary search tree.
Conclusion:
Since each ball can be placed in any of the 10 slots initially and the placement of subsequent balls depends on the values of the balls already placed, there is only one way to place the balls in the slots of the binary search tree. Hence, the correct answer is option 'A'.
To solve this problem, we need to understand the concept of binary search trees (BST) and the rules for placing the numbered balls in the slots.
Binary Search Tree (BST):
A binary search tree is a binary tree where the value of each node is greater than all values in its left subtree and less than all values in its right subtree.
Rules for Placing Balls in BST:
1. Each slot can only occupy at most 1 ball.
2. The numbered balls are distinct, meaning that no two balls have the same number.
3. The balls need to be placed in such a way that the resulting tree is a valid binary search tree.
Analysis:
Since the numbered balls are distinct, each slot in the binary search tree can have at most 1 ball. This means that we can place a ball in a slot if and only if the slot is empty.
In a binary search tree, the left subtree contains all the elements that are less than the root, and the right subtree contains all the elements that are greater than the root.
Placement Strategy:
To form a valid binary search tree, we need to place the numbered balls in such a way that each ball is placed in the correct slot based on its value.
Let's consider the placement of the balls in the slots step by step:
1. We have 10 numbered balls and 10 slots in the binary search tree.
2. We can place the first ball in any of the 10 slots since all the slots are empty.
3. Once the first ball is placed, there are 9 remaining balls and 9 empty slots.
4. For the second ball, we need to consider the value of the ball and the value of the ball in the first slot.
- If the value of the second ball is less than the value of the ball in the first slot, we can place it in the left subtree of the first slot.
- If the value of the second ball is greater than the value of the ball in the first slot, we can place it in the right subtree of the first slot.
5. Similarly, for each subsequent ball, we need to compare its value with the value of the balls already placed in the tree to determine the correct placement.
6. Finally, after placing all the balls, we will have a valid binary search tree.
Conclusion:
Since each ball can be placed in any of the 10 slots initially and the placement of subsequent balls depends on the values of the balls already placed, there is only one way to place the balls in the slots of the binary search tree. Hence, the correct answer is option 'A'.
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