Question And Answer.

Transcription

1 Q.1 What is the number of swaps required to sort n elements using selection sort, in the worst case? A. &#920(n) B. &#920(n log n) C. &#920(n2) D. &#920(n2 log n) ANSWER : Option A &#920(n) Note that we are concerned about the swaps, not the comparisons. In the best case, there is no need for any swap. The best case scenario is when the given list of elements is already in sorted order. In the worst case, we need (n-1) swaps. For example, consider the list 10, 5, 6, 7, 8, 9. We need 5 swaps. To conclude, 0 <= (the number of required swaps) < n Q.2 A machine took 200 sec to sort 200 names, using bubble sort. In 800 sec, it can approximately sort? A. 400 names B. 800 names C. 750 names D. 800 names ANSWER : Option A 400 names For sorting 200 names bubble sort makes 200 x 199/2 = comparisons. The time needed for 1 comparison is 200 sec. In 800 sec it can make 80,000 comparisons. We have to fine n, such that n(n - 1)/2 = 80,000. From this n is approximately 400. Q.3 A machine needs a minimum of 100 sec to sort 1000 names by quick sort.the minimum time needed to sort 100 names will be approximately? A sec B. 6.7 sec C sec D sec ANSWER : Option B 6.7 sec In the best case quick sort algorithm makes n log(n) comparisons. so 1000 x log (1000) = 9000 comparisons, which takes 100 sec. To sort 100 names a minimum of 100 log(100) = 600 comparisons are needed. This takes 100 x 600/9000 = 6.7 sec. Q.4 Which of following algorithm scans the list by swapping the entries whenever pair of adjacent keys are out of desired order? A. Insertion sort B. Quick sort C. Shell sort Page 1

2 D. Bubble sort ANSWER : Option D Bubble sort Bubble sort only is the algorithm from the given options which compares the adjacent keys. Q.5 For the quick sort algorithm, what is the time complexity of the best/worst case? A. best case: O(n) worst case: O(n*n) B. best case: O(n) worst case: O(n*log(n)) C. best case: O(n*log(n)) worst case: O(n*log(n)) D. best case: O(n*log(n)) worst case: O(n*n) ANSWER : Option D best case: O(n*log(n)) worst case: O(n*n) The worst case here is, if the list is already sorted in descending order and we want to sort it in ascending order. In this case it takes O(n2) time. Otherwise it takes O( n * log(n) ) time. Q.6 To sort many large object or structures, it would be most efficient to A. Place reference to them in and array an sort the array B. Place them in a linked list and sort the linked list C. Place pointers to them in an array and sort the array D. Place them in an array and sort the array ANSWER : Option B Place them in a linked list and sort the linked list Dynamic structure (Memory Allocated at run-time). We can have more than one datatype. Re-arrange of linked list is easy (Insertion-Deletion). It doesn^aeurtmt waste memory. Q.7 The complexity of multiplying two matrices of order m*n and n*p is A. mnp B. mp C. mn D. np ANSWER : Option A mnp The complexity of multiplying two matrices of order m*n and n*p is mnp Q.8 Which of the following is not a limitation of binary search algorithm? A. must use a sorted array B. requirement of sorted array is expensive when a lot of insertion and deletions are needed C. there must be a mechanism to access middle element directly Page 2

3 D. binary search algorithm is not efficient when the data elements are more than ANSWER : Option D binary search algorithm is not efficient when the data elements are more than binary search algorithm is not efficient when the data elements are more than 1000.We can search more than 1000 element in binary search there is no limitation. Q.9 The way a card game player arranges his cards as he picks them up one by one, is an example of? A. bubble sort B. selection sort C. insertion sort D. merge sort ANSWER : Option C insertion sort He scans throught the rest of the cards and pick the one with least value and places it next to the point till which he has already sorted the cards Q.10 Binary search algorithm cannot be applied to A. sorted linked list B. sorted binary trees C. sorted linear array D. pointer array ANSWER : Option A sorted linked list The binary search algorithm depends on equal (or direct) access time for any selected element of a list. A linked list, however, does not provide that, so a binary search is inappropriate for a linked list. Q.11 The average search time of hashing, with linear probing will be less if the load factor A. Is far less than one B. equals one C. is far greater than one D. none of these ANSWER : Option A Is far less than one Load factor is the ratio of number of records that are currently present and the total number of records that can be present. If the load factor is less, free space will be more. This means probability of collision is less. So, search time will be less. Q.12 If a node having two children is deleted from a binary tree, it is replaced by its Page 3

4 A. Inorder predecessor B. Inorder successor C. Preorder predecessor D. None of the above ANSWER : Option B Inorder successor In Binary Tree, Inorder successor of a node is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inoorder traversal. In Binary Search Tree, Inorder Successor of an input node can also be defined as the node with the smallest key greater than the key of input node. So, it is sometimes important to find next node in sorted order. Q.13 The searching technique that takes O (1) time to find a data is A. Linear Search B. Binary Search C. Hashing D. Tree Search ANSWER : Option C Hashing Hash tables are often used to implement associative arrays, sets and caches. Like arrays, hash tables provide constant-time O(1) lookup on average, regardless of the number of items in the table. However, the rare worst-case lookup time can be as bad as O(n). Compared to other associative array data structures, hash tables are most useful when large numbers of records of data are to be stored. Q.14 For the bubble sort algorithm, what is the time complexity of the best/worst case? (assume that the computation stops as soon as no more swaps in one pass) A. best case: O(n) worst case: O(n*n) B. best case: O(n) worst case: O(n*log(n)) C. best case: O(n*log(n)) worst case: O(n*log(n)) D. best case: O(n*log(n)) worst case: O(n*n) ANSWER : Option A best case: O(n) worst case: O(n*n) Best Case is the one in which it is already sorted, and hence it takes O(n) time, otherwise it takes O(n2) time. Q.15 Which of the following is not the required condition for binary search algorithm? A. The list must be sorted B. The list must be sorted C. There must be mechanism to delete and/or insert elements in list D. none of above Page 4

5 ANSWER : Option C There must be mechanism to delete and/or insert elements in list There is no such require condition in binary search algorithm. It^aEURTMs not necessary that you^aeurtmve to add or delete any element in list. Q.16 The time taken by nondeterministic sorting algorithm is A. O(1) B. O(log n) C. O(n log n) D. O(n). ANSWER : Option D O(n). As there it sorts the entries in one loop. Because in nondeterministic sorting algorithms the abstractions are used which can^aeurtmt be programmed. Q.17 In worst case Quick Sort has order A. O (n log n) B. O (n2/2) C. O (log n) D. O (n2/4) ANSWER : Option B O (n2/2) Each partition gives unbalanced split. We get T(n) = T(n  1) + (n) = &#920(n2). In worst case, Quick Sort as bad as BubbleSort. The worst-case occurs when the list is already sorted, and the last element chosen as pivot. Page 5