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 $ \mathrm\Theta(n) $ time
IV. A binary search tree can be constructed from a max-heap in $ \mathrm\Theta(n) $ time
Which of the above statements are TRUE?
An operator delete (i) for a binary heap data structure is to be designed to delete the item in the $i$-th node. Assume that the heap is implemented in an array and i refers to the i-th index of the array. If the heap tree has depth d (number of edges on the path from the root to the farthest leaf), tthen what is the time complexity to re-fix the heap efficiently after the removal of the element?
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 _________.
Consider a max heap, represented by the array: 40, 30, 20, 10, 15, 16, 17, 8, 4.
Now consider that a value 35 is inserted into this heap. After insertion, the new heap is
Consider a complete binary tree where the left and the right subtrees of the root are max-heaps. The lower bound for the number operations to convert the tree to a heap is
Consider the following array of elements $>">89,19,50,17,12,15,2,5,7,11,6,9,100$ The minimum number of interchanges needed to convert it into a max-heap is
A priority queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is: 10, 8, 5, 3, 2. Two new elements 1 and 7 are inserted into the heap in that order. The level-order traversal of the heap after the insertion of the elements is:
A max-heap is a heap where the value of each parent is greater than or equal to the value of its children. Which of the following is a max-heap?
Consider a binary max-heap implemented using an array.
Which one of the following array represents a binary max-heap?
What is the content of the array after two delete operations on the correct answer to the previous question?
Consider the process of inserting an element into a Max Heap, where the Max Heap is represented by an array. Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element, the number of comparisons performed is: