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Algorithms Question
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Question 3 A priority queue data structure can be implemented as a heap. Consider an example illustrated by the partially ordered tree below. (a) Present an array implementation of the heap given by the above figure. For each element, specify its index. (b) In your implementation, what are the indices of the two child nodes, whose parent node has index i in the array? (c) How many levels are there in a partially ordered binary tree consisting of n nodes? (d) Consider the partially ordered tree given by the above figure. Show how insertion of a new element with key 16 is done. (e) Consider the original tree (before inserting the element with key 16). Show how the element with the maximum key is removed. (f) What is the time complexity of inserting a new element? What is the time complexity of removing the element with the maximum key? Provide an explanation. (g) Explain how a heap can be used to sort an array of n numbers. What is the time complexity of heapsort? Show transcribed image text Question 3 A priority queue data structure can be implemented as a heap. Consider an example illustrated by the partially ordered tree below. (a) Present an array implementation of the heap given by the above figure. For each element, specify its index. (b) In your implementation, what are the indices of the two child nodes, whose parent node has index i in the array? (c) How many levels are there in a partially ordered binary tree consisting of n nodes? (d) Consider the partially ordered tree given by the above figure. Show how insertion of a new element with key 16 is done. (e) Consider the original tree (before inserting the element with key 16). Show how the element with the maximum key is removed. (f) What is the time complexity of inserting a new element? What is the time complexity of removing the element with the maximum key? Provide an explanation. (g) Explain how a heap can be used to sort an array of n numbers. What is the time complexity of heapsort?
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