# GATE | GATE CS 2019 | Question 49

• Last Updated : 02 Dec, 2019

Consider the following statements:

• I. The smallest element in a max-heap is always at a leaf node.
• II. The second largest element in a max-heap is always a child of the root node.
• III. A max-heap can be constructed from a binary search tree in Θ(n) time.
• IV. A binary search tree can be constructed from a max-heap in Θ(n) time.

Which of the above statements is/are TRUE?
(A) II, III and IV
(B) I, II and III
(C) I, III and IV
(D) I, II and IV

Explanation: Statement (I) is correct. 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)

```         12
/  \
/      \
8         7
/ \        / \
/     \    /     \
2      3   4       5 ```

Statement (II) is also correct, otherwise it will not satisfy max-heap property.

Statement (III) is also correct, as build-heap always takes Θ(n) time, (Refer: Convert BST to Max Heap).

Statement (IV) is false, because construction of binary search tree from max-heap will take O(nlogn) time.

So, option (B) is correct.

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