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# GATE CS 2022 : Algorithm-3

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Question 1

Which of the following represent the relation for Heapify Procedure (Min Heapify)?

Question 2

The following problems are solved using Dynamic Programming/Greedy Algorithms. Match these problems to their respective time complexity : Question 3

If the array elements are already in the increasing order, then which of the following sorting algorithms takes worst case Time Complexity.

I. Insertion sort

II. Quick sort

III. Heap sort

Question 4

The following problems are solved using Divide and Conquer. Match these problems to their respective recurrence relation : Question 5

Consider an array consisting of the following elements in unsorted order (placed randomly), but 60 as first element.
60, 80, 15, 95, 7, 12, 35, 90, 55
Quick sort partition algorithm is applied by choosing first element as pivot element. How many total number of arrangements of array integers is possible preserving the effect of first pass of partition algorithm.

Question 6

Consider a hash table which has 12 slots in which we want to store 10 keys. Then find the expected number of probes in successful search of an open addressing technique __________. (upto two decimal places)
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