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Array

Question 1
A program P reads in 500 integers in the range [0..100] exepresenting the scores of 500 students. It then prints the frequency of each score above 50. What would be the best way for P to store the frequencies? (GATE CS 2005)
A
An array of 50 numbers
B
An array of 100 numbers
C
An array of 500 numbers
D
A dynamically allocated array of 550 numbers
Array    
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Question 2
Which of the following operations is not O(1) for an array of sorted data. You may assume that array elements are distinct.
A
Find the ith largest element
B
Delete an element
C
Find the ith smallest element
D
All of the above
Array    
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Question 2 Explanation: 
The worst case time complexity for deleting an element from array can become O(n).
Question 3
The minimum number of comparisons required to determine if an integer appears more than n/2 times in a sorted array of n integers is
(A) \theta(n)
(B) \theta(logn)
(C) \theta(log*n)
(D) \theta(n)
A
A
B
B
C
C
D
D
Array    GATE CS 2008    
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Question 3 Explanation: 
The Best way to find out whether an integer appears more than n/2 times in a sorted array(Ascending Order) of n integers, would be binary search approach. 1. The First occurence of an element can be found out in O(log(n)) time using divide and conquer technique,lets say it is i. 2. The Last occurrence of an element can be found out in O(log(n)) time using divide and conquer technique,lets say it is j. 3. Now number of occuerence of that element(count) is (j-i+1). Overall time complexity = log n +log n +1 = O(logn) See Check for Majority Element in a sorted array This solution is contributed by Nirmal Bharadwaj
Question 4
Let A be a square matrix of size n x n. Consider the following program. What is the expected output?

C = 100
for i = 1 to n do
    for j = 1 to n do
    {
        Temp = A[i][j] + C
        A[i][j] = A[j][i]
        A[j][i] = Temp - C
    } 
for i = 1 to n do
    for j = 1 to n do
        Output(A[i][j]);
A
The matrix A itself
B
Transpose of matrix A
C
Adding 100 to the upper diagonal elements and subtracting 100 from diagonal elements of A
D
None of the above
Array    GATE-CS-2014-(Set-3)    
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Question 4 Explanation: 
If we take look at the inner statements of first loops, we can notice that the statements swap A[i][j] and A[j][i] for all i and j. Since the loop runs for all elements, every element A[l][m] would be swapped twice, once for i = l and j = m and then for i = m and j = l. Swapping twice means the matrix doesn’t change. Source: http://www.geeksforgeeks.org/data-structures-algorithms-set-34/
Question 5
An algorithm performs (logN)1/2 find operations, N insert operations, (logN)1/2 operations, and (logN)1/2 decrease-key operations on a set of data items with keys drawn from a linearly ordered set. For a delete operation, a pointer is provided to the record that must be deleted. For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?
A
Unsorted array
B
Min-heap
C
Sorted array
D
Sorted doubly linked list
Array    GATE-CS-2015 (Set 1)    
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Question 5 Explanation: 
The time complexity of insert in unsorted array is O(1), O(Logn) in Min-Heap, O(n) in sorted array and sorted DLL.
  1. For unsorted array, we can always insert an element at end and do insert in O(1) time
  2. For Min Heap, insertion takes O(Log n) time. Refer Binary Heap operations for details.
  3. For sorted array, insert takes O(n) time as we may have to move all elements worst case.
  4. For sorted doubly linked list, insert takes O(n) time to find position of element to be inserted.
Since number of insertion operations is asymptotically higher, unsorted array is preferred.
Question 6
Consider an array consisting of –ve and +ve numbers. What would be the worst time comparisons an algorithm can take in order to segregate the numbers having same sign altogether i.e all +ve on one side and then all -ve on the other ?
A
N-1
B
N
C
N+1
D
(N*(N-1))/2
Array    GATE 2017 Mock    
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Question 6 Explanation: 
Here we can use the partition algorithm of quick sort for segregation and answer will be N-1.
Choose the first element as pivot whatever may be its sign we don’t care and keep an extra index at pivot position .
There are 6 questions to complete.
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