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In a binary max heap containing n numbers, the smallest element can be found in time  
  • a)
    0(n)
  • b)
    O(logn)
  • c)
    0(loglogn)
  • d)
    0(1)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In a binary max heap containing n numbers, the smallest element can be...
In a max heap, the smallest element is always present at a leaf node. So we need to check for all leaf nodes for the minimum value. Worst case complexity will be O(n)
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Most Upvoted Answer
In a binary max heap containing n numbers, the smallest element can be...
Explanation:

  • A binary max heap is a complete binary tree where the value of each node is greater than or equal to the values of its children.

  • The smallest element in a binary max heap is located at one of the leaf nodes, which are the nodes without any children.

  • Since the heap is complete, the leftmost leaf node is the one with the smallest value.

  • Therefore, to find the smallest element in a binary max heap containing n numbers, we need to examine all the leaf nodes.

  • Since there are n/2 leaf nodes in a complete binary tree, we need to examine all n/2 leaf nodes to find the smallest element.

  • Therefore, the time complexity of finding the smallest element in a binary max heap containing n numbers is O(n).


Therefore, the correct option is (a) O(n).
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