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GATE CSE
Divide and Conquer Method
Algorithms
Previous Years Questions
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Marks 1
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Consider a sequence of 14 elements: A = [-5, -10, 6, 3, -1, -2, 13, 4, -9, -1, 4, 12, -3, 0]. The subsequence sum $$S\le...
GATE CSE 2019
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You have an array of n elements. Suppose you implement quicksort by always choosing the central element of the array as ...
GATE CSE 2014 Set 3
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Which one of the following correctly determines the solution of the recurrence relation with T(1) = 1? T(1) = 2T (n/2) +...
GATE CSE 2014 Set 2
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Let P be a QuickSort Program to sort numbers in ascending order using the first element as pivot. Let t1 and t2 be the n...
GATE CSE 2014 Set 1
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The minimum number of arithmetic operations required to evaluate the polynomial P(X) = X5 + 4X3 + 6X + 5 for a given val...
GATE CSE 2014 Set 3
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Which of the following statement(s) is / are correct regarding Bellman-Ford shortest path algorithm? P: Always finds a n...
GATE CSE 2009
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The usual $$\Theta ({n^2})$$ implementation of Insertion Sort to sort an array uses linear search to identify the positi...
GATE CSE 2003
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The solution to the recurrence equation T(2k) = 3 T(2k-1) + 1, T (1) = 1, is:
GATE CSE 2002
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Randomized quicksort is an extension of quicksort where the pivot is chosen randomly. What is the worst case complexity ...
GATE CSE 2001
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Let s be a sorted array of n integers. Let t(n) denote the time taken for the most efficient algorithm to determined if ...
GATE CSE 2000
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If one uses straight two-way merge sort algorithm to sort the following elements in ascending order 20, 47, 15, 8, 9, 4,...
GATE CSE 1999
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A sorting technique is called stable if:
GATE CSE 1999
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Merge sort uses
GATE CSE 1995
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Which of the following statements is true? I. As the number of entries in a hash table increases, the number of collisio...
GATE CSE 1995
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For merging two sorted lists of sizes m and n into a sorted list of size m+n, we require comparisons of
GATE CSE 1995
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Marks 2
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Consider the following statements: I. The smallest element in a max-heap is always at a leaf node II. The second larg...
GATE CSE 2019
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Consider the following pseudo code. What is the total number of multiplications to be performed? D = 2 for i = 1 to n do...
GATE CSE 2014 Set 1
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The minimum number of comparisons required to find the minimum and the maximum of 100 numbers is ________
GATE CSE 2014 Set 1
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Consider the following function: int unknown(int n) { int i, j, k = 0; for (i = n/2; i <= n; i++) fo...
GATE CSE 2013
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Consider the following operation along with Enqueue and Dequeue operations on queues, where k is a global parameter. Mul...
GATE CSE 2013
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A list of n strings, each of length n, is sorted into lexicographic order using the merge-sort algorithm. The worst case...
GATE CSE 2012
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In quick sort, for sorting n elements, the (n/4)th smallest element is selected as pivot using an O(n) time algorithm. W...
GATE CSE 2009
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The running time of an algorithm is represented by the following recurrence relation: $$T(n) = \begin{cases} n &...
GATE CSE 2009
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Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into tw...
GATE CSE 2008
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An array of n numbers is given, where n is an even number. The maximum as well as the minimum of these n numbers needs t...
GATE CSE 2007
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The median of n elements can be found in O(n) time. Which one of the following is correct about the complexity of quick ...
GATE CSE 2006
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Consider the following recurrence: $$T\left( n \right){\rm{ }} = {\rm{ 2T(}}\left\lceil {\sqrt n } \right\rceil {\rm{) +...
GATE CSE 2006
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Suppose T(n) = 2T (n/2) + n, T(0) = T(1) = 1 Which one of the following is FALSE?
GATE CSE 2005
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Let T(n) be the function defined by $$T(1) =1, \: T(n) = 2T (\lfloor \frac{n}{2} \rfloor ) + \sqrt{n}$$ Which of the fol...
GATE CSE 1997
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The recurrence relation T(1) = 2 T(n) = 3T(n/4) + n has the solution, T(n) equals to
GATE CSE 1996
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Quicksort is run on two inputs shown below to sort in ascending order taking first element as pivot i) 1, 2, 3,......., ...
GATE CSE 1996
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The recurrence relation that arises in relation with the complexity of binary search is:
GATE CSE 1994
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Assume that the last element of the set is used as partition element in Quicksort. If n distinct elements from the set [...
GATE CSE 1992
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Find a solution to the following recurrence equation T(n) = T(n - 1)+ n T(1) = 1
GATE CSE 1987
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Let P be a quicksort program to sort numbers in ascending order. Let t1 and t2 be the time taken by the program for the ...
GATE CSE 1987
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