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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), then what is the time complexity to re-fix the heap efficiently after the removal of the element? 
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?
The essential part of Heap sort is construction of max-heap. Consider the tree shown below, the node 24 violates the max-heap property. Once heapify procedure is applied to it, which position will it be in?
Randomized quick sort is an extension of quicksort where the pivot is chosen randomly. what is the worst case complexity of sorting a numbers using randomized quick sort?
Questions below followed by three quantities. Find the relationship between them. Quantity I: In a class with a certain number of students if a teacher weighing 78 kg is added, then average weight of class is increased by 2 kg. If one more teacher weighing 66 kg is added, then the average weight of the class increases by 3.5 kg over the original average. What is the original average weight (in kg) of the class? Quantity II: The average age of 16 students and their teacher's age is 16 years. If the teacher's age is excluded, the average reduces by 2. What is the teacher's age? Quantity III: Average weight of three friends A, B and C is 46 kg. Another person D joins the group and now the average is 45 kg. If another person E whose weight is 6 kg more than D, joins the group replacing A, then average weight of B, C, D and E becomes 47 kg. What is the weight of A (in kg)?
Ramesh is 70% more efficient than Rakesh, but 20% less efficient than Vijay. If Rakesh is 40% more efficient than Suresh, and Vijay is 15% less efficient than Dinesh, then Dinesh is what percent more efficient than Suresh?
What is the cut-off for switching from quick sort to heap sort in the implementation of introsort?
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?
If we implement heap as min-heap, deleting root node (value 1)from the heap. What would be the value of root node after second iteration if leaf node (value 100) is chosen to replace the root at start.
If we implement heap as maximum heap , adding a new node of value 15 to the left most node of right subtree. What value will be at leaf nodes of the right subtree of the heap.