### Some Basic Questions on Sorting

1 .In a selectionsort of n elements, how many times is the swap function called in the complete execution of the algorithm?

A. 1
B. n - 1
C. n log n
D. n^2

2 .Selectionsort and quicksort both fall into the same category of sorting algorithms. What is this category?

* A. O(n log n) sorts
* B. Divide-and-conquer sorts
* C. Interchange sorts
* D. Average time is quadratic.

3 . Suppose that a selectionsort of 100 items has completed 42 iterations of the main loop. How many items are now guaranteed to be in their final spot (never to be moved again)?

* A. 21
* B. 41
* C. 42
* D. 43

4 .Suppose we are sorting an array of ten integers using a some quadratic sorting algorithm. After four iterations of the algorithm's main loop, the array elements are ordered as shown here:

1 2 3 4 5 0 6 7 8 9

Which statement is correct? (Note: Our selectionsort picks largest items first.)

* A. The algorithm might be either selectionsort or insertionsort.
* B. The algorithm might be selectionsort, but could not be insertionsort.
* C. The algorithm might be insertionsort, but could not be selectionsort.
* D. The algorithm is neither selectionsort nor insertionsort.

5 .Suppose we are sorting an array of eight integers using a some quadratic sorting algorithm. After four iterations of the algorithm's main loop, the array elements are ordered as shown here:

2 4 5 7 8 1 3 6

Which statement is correct? (Note: Our selectionsort picks largest items first.)

* A. The algorithm might be either selectionsort or insertionsort.
* B. The algorithm might be selectionsort, but it is not insertionsort.
* C. The algorithm is not selectionsort, but it might be insertionsort.
* D. The algorithm is neither selectionsort nor insertionsort.

6 .When is insertionsort a good choice for sorting an array?

* A. Each component of the array requires a large amount of memory.
* B. Each component of the array requires a small amount of memory.
* C. The array has only a few items out of place.
* D. The processor speed is fast.

7 What is the worst-case time for mergesort to sort an array of n elements?

* A. O(log n)
* B. O(n)
* C. O(n log n)
* D. O(n^2)

8 What is the worst-case time for quicksort to sort an array of n elements?

* A. O(log n)
* B. O(n)
* C. O(n log n)
* D. O(n^2)

9 .Mergesort makes two recursive calls. Which statement is true after these recursive calls finish, but before the merge step?

* A. The array elements form a heap.
* B. Elements in each half of the array are sorted amongst themselves.
* C. Elements in the first half of the array are less than or equal to elements in the second half of the array.
* D. None of the above.

10 .Suppose we are sorting an array of eight integers using quicksort, and we have just finished the first partitioning with the array looking like this:

2 5 1 7 9 12 11 10

Which statement is correct?

* A. The pivot could be either the 7 or the 9.
* B. The pivot could be the 7, but it is not the 9.
* C. The pivot is not the 7, but it could be the 9.
* D. Neither the 7 nor the 9 is the pivot.

11 .What is the worst-case time for heapsort to sort an array of n elements?

* A. O(log n)
* B. O(n)
* C. O(n log n)
* D. O(n^2)

12.Suppose you are given a sorted list of N elements followed by f(N) randomly ordered elements.How would you sort the entire list if
* A. f(N)=O(1)
* B. f(N)=O(logN)
* C. f(N)=O(N^1/2)
* D. How large can f(N) be for the entire list still to be sortable in O(N) time?

13.Prove that any algorithm that find an element X in a sorted list of N elements requires Omega(log N) comparisons.

14.Prove that sorting N elements with integer keys in the range 1 < Key < M
takes O(M + N) time using bucket sort.

15.Suppose you have an array of N elements,containing only 2 distinct keys, true and false.Give an O(N) algorithm to sort the array.

16.Prove that any comparison based algorithm to sort 4 elements requires atleast 5 comparisons

17. In how many ways can 2 sorted arrays of combined size N be merged?

18.Show that binary insertion may reasonably be expected to be an O(n log n) sort.

19.You are given two sets of numbers Xi and Yj , where i and j run from 1 to N.
Devise an algorithm to find the M largest values of Xi −Yj . This algorithm should
not be quadratic in N, though it is permitted to be quadratic in M.
You should regard N as being of the order of 20,000 and M as being of the order
of 1,000.

20.If 1024 numbers are drawn randomly in the range 0–127 and sorted by binary
insertion, about how many compares would you expect?

1. hi
it would be nice if the solutions would be given to all sorting and searching questions for freshers

2. thanq vry much

3. please can you give me the comparison of these sorting algorithms;
bubble sort
insertion sort
selection sort
shell sort
merge sort
heap sort
quick sort

1)B
2)D
3)C
4)C
5)
6)
7)C
8)D
9)B
10)
11)D

5. 1)B
2)D
3)C
4)b
5)b
6)c
7)C
8)D
9)B
10)a
11)c

6. The answer for question 2 can't be D, it's C as the quicksort algorithm average time is
O(nlogn) and not O(n^2).

1. In this question worst case scenario has been asked, in which partition occurs such that on one side of pivot only one element is left and on the other side we have n-2 elements.We have to make pivots O(n) time and each takes O(n) comparison so ans O(n^2).