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GATE CSE
Searching and Sorting
Algorithms
Previous Years Questions
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Marks 1
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An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at r...
GATE CSE 2019
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Assume that the algorithms considered here sort the input sequences in ascending order. If the input is already in ascen...
GATE CSE 2016 Set 2
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The worst case running times of Insertion sort, Merge sort and Quick sort, respectively, are:
GATE CSE 2016 Set 1
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Consider the following array of elements. $$\,\,\,\,\,\,\,\,$$$$〈89, 19, 50, 17, 12, 15, 2, 5, 7, 11, 6, 9, 100〉$$ The m...
GATE CSE 2015 Set 3
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An unordered list contains $$n$$ distinct elements. The number of comparisons to find an element in this list that is ne...
GATE CSE 2015 Set 2
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Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for ...
GATE CSE 2015 Set 1
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A priority queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is: 1...
GATE CSE 2014 Set 2
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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 ...
GATE CSE 2011
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What is the number of swaps required to sort n elements using selection sort, in the worst case?
GATE CSE 2009
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The Breadth First Search algorithm has been implemented using the queue data structure. One possible order of visiting t...
GATE CSE 2008
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The most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m e...
GATE CSE 2008
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Which of the following sorting algorithms has the lowest worst-case complexity?
GATE CSE 2007
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Consider the DAG with $$V = \{1,2,3,4,5,6\}$$, shown below. Which of the following is NOT a topological ordering?...
GATE CSE 2007
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An element in an array X is called a leader if it is greater than all elements to the right of it in X. The best algorit...
GATE CSE 2006
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Which one of the following in place sorting algorithms needs the minimum number of swaps?
GATE CSE 2006
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In a binary max heap containing n numbers, the smallest element can be found in time
GATE CSE 2006
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The tightest lower bound on the number of comparisons, in the worst case, for comparison-based sorting is of the order o...
GATE CSE 2004
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In a heap with n elements with the smallest element at the root, the 7th smallest element can be found in time...
GATE CSE 2003
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Consider any array representation of an n element binary heap where the elements are stored from index 1 to index n of t...
GATE CSE 2001
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The number of articulation points of the following graph is ...
GATE CSE 1999
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Suppose we want to arrange the n numbers stored in any array such that all negative values occur before all positive one...
GATE CSE 1999
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Give the correct matching for the following pairs: Group - 1 (A) $${\rm O}(\log n)$$ (B) $${\rm O}(n)$$ (C) $${\rm O}(n\...
GATE CSE 1998
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The correct matching for the following pairs is .tg {border-collapse:collapse;border-spacing:0;border:none;} .tg td{fo...
GATE CSE 1997
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Marks 2
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Consider the following array. 23 32 45 69 72 73 ...
GATE CSE 2021 Set 1
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The number of possible min-heaps containing each value from $$\left\{ {1,2,3,4,5,6,7} \right\}$$ exactly once is _____.
GATE CSE 2018
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A complete binary min-heap is made by including each integer in $$[1,1023]$$ exactly once. The depth of a node in the he...
GATE CSE 2016 Set 2
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An operator $$delete(i)$$ for a binary heap data structure is to be designed to delete the item in the $$i$$-th node. As...
GATE CSE 2016 Set 1
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Assume that a mergesort algorithm in the worst case takes $$30$$ seconds for an input of size $$64.$$ Which of the follo...
GATE CSE 2015 Set 3
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Suppose you are provided with the following function declaration in the C programming language. int partition(int a[], ...
GATE CSE 2015 Set 2
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Consider a max heap, represented by the array: 40, 30, 20, 10, 15, 16, 17, 8, 4. .tg {border-collapse:collapse;border-...
GATE CSE 2015 Set 1
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Consider a binary max-heap implemented using an array. Which one of the following array represents a binary max-heap?
GATE CSE 2009
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Consider a binary max-heap implemented using an array. What is the content of the array {25, 14, 16, 13, 10, 8, 12} afte...
GATE CSE 2009
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We have a binary heap on n elements and wish to insert n more elements (not necessarily one after another) into this hea...
GATE CSE 2008
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Consider the process of inserting an element into a Max Heap, where the Max Heap is represented by an array. Suppose we ...
GATE CSE 2007
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A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be repres...
GATE CSE 2006
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A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be repres...
GATE CSE 2006
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Given two arrays of numbers a1,......,an and b1,......, bn where each number is 0 or 1, the fastest algorithm to find th...
GATE CSE 2006
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Let G(V, E) an undirected graph with positive edge weights. Dijkstra's single-source shortest path algorithm can be impl...
GATE CSE 2005
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Suppose there are $$\lceil \log n \rceil$$ sorted lists of $$\left\lfloor {{n \over {\log n}}} \right\rfloor $$ elements...
GATE CSE 2005
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The elements 32, 15, 20, 30, 12, 25, 16, are inserted one by one in the given order into a max Heap. The resultant max H...
GATE CSE 2004
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If T1 = O(1), give the correct matching for the following pairs: List - I (M) Tn = Tn - 1 + n (N) Tn = Tn/2 + n (O) Tn =...
GATE CSE 1999
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The average number of key comparisons done on a successful sequential search in list of length n is
GATE CSE 1996
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The minimum number of interchanges needed to convert the array 89, 19, 40, 17, 12, 10, 2, 5, 7, 11, 6, 9, 70 into a heap...
GATE CSE 1996
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Which one of the following statements is false?
GATE CSE 1994
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Following algorithm(s) can be used to sort n integers in the range [1....... n3] in O(n) time
GATE CSE 1992
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Minimum number of comparisons required to sort 5 elements
GATE CSE 1991
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Match the pairs in the following: List - I (a) Heap construction (b) Constructing hash table witn linear probing (c) AVL...
GATE CSE 1990
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Match the pairs in the following: List - I (a) Straseen's matrix multiplication algorithm (b) Kruskal's minimum spanning...
GATE CSE 1990
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