# 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)

An array of 50 numbers | |

An array of 100 numbers | |

An array of 500 numbers | |

A dynamically allocated array of 550 numbers |

**Array**

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Question 1 Explanation:

See question 1 of http://www.geeksforgeeks.org/data-structures-and-algorithms-set-22/

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.

Find the ith largest element | |

Delete an element | |

Find the ith smallest element | |

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

Θ(n) | |

Θ(logn) | |

Θ(log*n) | |

Θ(1) |

**GATE CS 2008**

**Array**

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Question 3 Explanation:

If you answered Theta(1), then think of examples {1, 2, 2, 2, 4, 4}, {1, 1, 2, 2, 2, 2, 3, 3}
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.

- 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.
- 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.
- Now number of occuerence of that element(count) is (j-i+1). Overall time complexity = log n +log n +1 = O(logn)

**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]);

The matrix A itself | |

Transpose of matrix A | |

Adding 100 to the upper diagonal elements and subtracting 100 from diagonal elements of A | |

None of the above |

**GATE-CS-2014-(Set-3)**

**Array**

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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}delete 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?Unsorted array | |

Min-heap | |

Sorted array | |

Sorted doubly linked list |

**GATE-CS-2015 (Set 1)**

**Array**

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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.

- For unsorted array, we can always insert an element at end and do insert in O(1) time
- For Min Heap, insertion takes O(Log n) time. Refer Binary Heap operations for details.
- For sorted array, insert takes O(n) time as we may have to move all elements worst case.
- For sorted doubly linked list, insert takes O(n) time to find position of element to be inserted.

Question 6 |

Consider an array consisting of –ve and +ve numbers. What would be the worst case time complexity of an algorithm to segregate the numbers having same sign altogether i.e all +ve on one side and then all -ve on the other ?

O(N) | |

O(N Log N) | |

O(N * N) | |

O(N Log Log N) |

**GATE 2017 Mock**

**Array**

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Question 6 Explanation:

Here we can use the partition algorithm of quick sort for segregation and answer will be O(N).
Choose the first element as pivot whatever may be its sign we don’t care and keep an extra index at pivot position .

Question 7 |

Let A[1...n] be an array of n distinct numbers. If i < j and A[i] > A[j], then the pair (i, j) is called an inversion of A. What is the expected number of inversions in any permutation on n elements ?

n(n-1)/2 | |

n(n-1)/4 | |

n(n+1)/4 | |

2n[logn] |

**UGC NET CS 2016 July – III**

**Array**

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Question 7 Explanation:

There are n(n-1)/2 pairs such that i < j. For a pair (a

_{i}, a_{j}), probability of being inversion is 1/2. Therefore expected value of inversions = 1/2 * (n(n-1)/2) = n(n-1)/4.Question 8 |

A three dimensional array in ‘C’ is declared as int A[x][y][z]. Consider that array elements are stored in row major order and indexing begins from 0. Here, the address of an item at the location A[p][q][r] can be computed as follows (where w is the word length of an integer):

&A[0][0][0] + w(y * z * q + z * p + r) | |

&A[0][0][0] + w(y * z * p + z*q + r) | |

&A[0][0][0] + w(x * y * p + z * q+ r) | |

&A[0][0][0] + w(x * y * q + z * p + r) |

**UGC NET CS 2015 Dec - II**

**Array**

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Question 8 Explanation:

According to above question we have to find the address of A[p][q][r]
To reach pth row we must have to cross 0 to p-1 row i.e. p rows and each rows contains y∗z elements
Hence ,
= y∗z∗p
Now to reach qth element in pth row we have to cross q rows and each row contains z(total columns) elements
=z∗q
to reach rth elements we have to cross r elements in (p+1)th row
Total elements to cross =(y∗z∗p+z∗q+r)
Now each element occupies m amount of space in memory
Therefore total space occupied by these elements = m(y∗z∗p+z∗q+r)
Hence , address of A[p][q][r]=base address+ Space Occupied by the Elements Before it.
=&A[0][0][0]+m(y*z*p+z*q+r)
Hence Option (B) is correct.

Question 9 |

Which of the following correctly declares an array?

int geeks[20]; | |

int geeks; | |

geeks{20}; | |

array geeks[20]; |

**ISRO CS 2008**

**Array**

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Question 9 Explanation:

Option A is correct. Int is the data type used,geeks is the name of the array and [20] is the size of the array.

Question 10 |

Consider a two dimensional array A[20][10]. Assume 4 words per memory cell, the base address of array A is 100, elements are stored in row-major order and first element is A[0][0]. What is the address of A[11][5] ?

560 | |

460 | |

570 | |

575 |

**UGC NET CS 2014 Dec - II**

**Array**

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Question 10 Explanation:

Element A[11][0] is stored at "Base Address + 11 * 10 * 4" which is "Base Address + 440" = 540. So A[11][5] is stored at 540 + 5*4 = 560.

There are 11 questions to complete.