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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?
What is the average number of comparisons used to heap sort a random permutation of N distinct items?
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?
Consider the Quick sort algorithm in which the partitioning procedure splits elements into two sub-arrays and each sub-array contains at least one-fourth of the elements. Let T(n) be the number of comparisons required to sort array of n elements. Then T(n)<=?
Consider the Quick sort algorithm which sorts elements in ascending order using the first element as pivot. Then which of the following input sequence will require a maximum number of comparisons when this algorithm is applied on it?
Let Xij =I { zi is compared to zj in quick sort algorithm} is an indicator variable, and zi is the ith smallest number. Which of the following sequence of the numbers give the X2,5 = 1? Note: Assume that there is a divide and conquer quick sort algorithm and in partition algorithm the first element of the lists is taken as pivot-element.
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)?
The average of eight batsmen J, K, L, M, N, O, R, and T is compared. The number of batsman having average less than L are same as the number of batsman having average more than M. Average of T is less than M and more than K. Average of L is less than K. Average of two batsman lies between the average of M and L. Average of O is less than N and K both. Which of the following can be the correct sequence of their averages?
In a company there are 252 engineers, in which the ratio of the number of electronics engineers and computer engineers is 2 ∶ 1. The ratio of the number of electronics engineers and computer engineers becomes 1 ∶ 1 after recruitment of some more computer engineers. The average age of all the engineers is now 22 years and the average age of the computer engineers is 2 years less than the average age of electronics engineers. (A) The average age (in years) of electronics engineers is 21 (B) The average age (in years) of computer engineers is 21 (C) The average age (in years) of electronics engineers is 23 (D) The average age (in years) of electronics engineers is 25 (E) The average age (in years) of computer engineers is 23 Choose the correct answer from the options given below: