###### Teaching Aptitude

October 4, 2023###### Teaching Aptitude

October 4, 2023# Data-Structures

Question 1 |

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 are TRUE?

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 are TRUE?

I, II and III | |

II, III and IV | |

I, III and IV | |

I, II and IV |

Question 1 Explanation:

i) TRUE: The smallest element in heap is always a leaf node but depends upon the graph, it may be left or right side of the graph.

(ii) TRUE: The second smallest element in a heap is always a child of root node.

(iii) TRUE: Converting from binary search tree to max heap will take O(n) time as well as O(n) space complexity.

(iv) FALSE: We can’t convert max heap to binary search tree in O(n) time.

(ii) TRUE: The second smallest element in a heap is always a child of root node.

(iii) TRUE: Converting from binary search tree to max heap will take O(n) time as well as O(n) space complexity.

(iv) FALSE: We can’t convert max heap to binary search tree in O(n) time.

Correct Answer: A

Question 1 Explanation:

i) TRUE: The smallest element in heap is always a leaf node but depends upon the graph, it may be left or right side of the graph.

(ii) TRUE: The second smallest element in a heap is always a child of root node.

(iii) TRUE: Converting from binary search tree to max heap will take O(n) time as well as O(n) space complexity.

(iv) FALSE: We can’t convert max heap to binary search tree in O(n) time.

(ii) TRUE: The second smallest element in a heap is always a child of root node.

(iii) TRUE: Converting from binary search tree to max heap will take O(n) time as well as O(n) space complexity.

(iv) FALSE: We can’t convert max heap to binary search tree in O(n) time.

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