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A complete binary min-heap is made by including each integer in [1, 1023] exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _____________
- a)6
- b)7
- c)8
- d)9
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A complete binary min-heap is made by including each integer in [1, 10...
here node with integer 1 has to be at root only. Now for maximum depth of the tree the following arrangement can be taken. Take root as level 1. make node 2 at level 2 as a child node of node 1. make node 3 at level 3 as the child node of node 2. .. .. and so on for nodes 4,5,6,7 .. make node 8 at level 8 as the child node of node 7. make node 9 at level 9 as the child node of node 8. Putting other nodes properly, this arrangement of the the complete binary tree will follow the property of min heap. So total levels are 9. node 9 is at level 9 and depth of node 9 is 8 from the root.
Most Upvoted Answer
A complete binary min-heap is made by including each integer in [1, 10...
To determine the maximum depth at which integer 9 can appear in a complete binary min-heap, we need to understand the structure and properties of a complete binary min-heap.
Complete Binary Min-Heap:
A complete binary min-heap is a binary tree that satisfies two properties:
1. Completeness: All levels of the tree are fully filled except possibly for the lowest level, which is filled from left to right.
2. Heap property: The value of each node is less than or equal to the values of its children (min-heap property).
Understanding the Structure:
To analyze the maximum depth at which integer 9 can appear, we need to visualize the complete binary min-heap and its structure.
- The root of the heap is at depth 0.
- Each level deeper from the root doubles the number of nodes compared to the previous level.
- The total number of nodes in a complete binary min-heap with depth d is given by 2^(d+1) - 1.
Determining the Maximum Depth:
To find the maximum depth at which integer 9 can appear, we need to determine the depth at which the number of nodes is less than or equal to 9. We can do this by checking the number of nodes at each depth and comparing it to 9.
- At depth 0, there is only one node (the root).
- At depth 1, there are 2 nodes.
- At depth 2, there are 4 nodes.
- At depth 3, there are 8 nodes.
- At depth 4, there are 16 nodes.
We can observe that at depth 3, the number of nodes (8) is less than 9. However, at depth 4, the number of nodes (16) is greater than 9. Therefore, the maximum depth at which integer 9 can appear is 3.
Answer:
The maximum depth at which integer 9 can appear in the complete binary min-heap is 3.
Explanation:
At depth 3, there are a total of 8 nodes. Since the complete binary min-heap includes each integer from 1 to 1023 exactly once, if 9 appears at depth 3, it would be one of the 8 nodes at that depth. No other depth has fewer nodes than 9. Thus, the maximum depth at which integer 9 can appear is 3.
Therefore, the correct answer is option C) 8.
Complete Binary Min-Heap:
A complete binary min-heap is a binary tree that satisfies two properties:
1. Completeness: All levels of the tree are fully filled except possibly for the lowest level, which is filled from left to right.
2. Heap property: The value of each node is less than or equal to the values of its children (min-heap property).
Understanding the Structure:
To analyze the maximum depth at which integer 9 can appear, we need to visualize the complete binary min-heap and its structure.
- The root of the heap is at depth 0.
- Each level deeper from the root doubles the number of nodes compared to the previous level.
- The total number of nodes in a complete binary min-heap with depth d is given by 2^(d+1) - 1.
Determining the Maximum Depth:
To find the maximum depth at which integer 9 can appear, we need to determine the depth at which the number of nodes is less than or equal to 9. We can do this by checking the number of nodes at each depth and comparing it to 9.
- At depth 0, there is only one node (the root).
- At depth 1, there are 2 nodes.
- At depth 2, there are 4 nodes.
- At depth 3, there are 8 nodes.
- At depth 4, there are 16 nodes.
We can observe that at depth 3, the number of nodes (8) is less than 9. However, at depth 4, the number of nodes (16) is greater than 9. Therefore, the maximum depth at which integer 9 can appear is 3.
Answer:
The maximum depth at which integer 9 can appear in the complete binary min-heap is 3.
Explanation:
At depth 3, there are a total of 8 nodes. Since the complete binary min-heap includes each integer from 1 to 1023 exactly once, if 9 appears at depth 3, it would be one of the 8 nodes at that depth. No other depth has fewer nodes than 9. Thus, the maximum depth at which integer 9 can appear is 3.
Therefore, the correct answer is option C) 8.
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A complete binary min-heap is made by including each integer in [1, 1023] exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _____________a)6b)7c)8d)9Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A complete binary min-heap is made by including each integer in [1, 1023] exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _____________a)6b)7c)8d)9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A complete binary min-heap is made by including each integer in [1, 1023] exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _____________a)6b)7c)8d)9Correct answer is option 'C'. Can you explain this answer?.
Solutions for A complete binary min-heap is made by including each integer in [1, 1023] exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _____________a)6b)7c)8d)9Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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