This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “Jump Search”.

**1. What is the value of jump taken for maximum efficiency while implementing jump search?**

A) n/2

B) n^{2}**C) n ^{1/2}**

D) log n

**Explanation:**In the worst-case scenario, the total number of comparisons needed will be n/k + k-1. For k=n1/2, this function will be the smallest. As a result, this jump value would be the most suitable for implementing jump search.

**2. What is the auxiliary space requirement of the jump search?**

A) O(n)

B) O(log n)

C) O(n^{1/2})**D) O(1)****Explanation: **For searching the necessary element, jump search does not require any additional space. As a result, its auxiliary storage space allowance will be O(1).

**3. Which of the following searching algorithm is fastest?**

A) jump search**B) binary search**

C) linear search

D) all are equally fast**Explanation: **Among the available searching algorithms, binary search has the shortest time complexity (log n). In most instances, binary search is preferable.

**4. In which of the following case jump search will be preferred over binary search?****A) jumping backwards takes significantly more time than jumping forward**

B) jumping forward takes significantly more time than jumping backwards

C) when the given array is very large in size

D) when the given array is very small in size**Explanation:** A binary can jump backwards up to log n times, while a jump search can only go backwards once. If jumping backwards is costly, jump search would be preferred over binary search.

**5. Best case of jump search will have time complexity of _________****A) O(1)**

B) O(n)

C) O(log n)

D) O(n log n)**Explanation:** The best case for jump search is when the element being searched is the first element of the array. Only one comparison will be needed in this case. As a result, it will have an O time complexity (1).

**6. Which of the following code correctly represent jump search?**

A)

int jumpSearch(int arr[], int x, int n) { int step = n*n; int prev = 0; while (arr[min(step, n)-1] < x) { prev = step; step += sqrt(n); if (prev >= n) return -1; } while (arr[prev] < x) { prev++; if (prev == min(step, n)) return -1; } if (arr[prev] == x) return prev; return -1; }

B)

int jumpSearch(int arr[], int x, int n) { int step = sqrt(n); int prev = 0; while (arr[min(step, n)-1] < x) { prev = step; step += sqrt(n); if (prev >= n) return -1; } while (arr[prev] < x) { prev++; if (prev == min(step, n)) return -1; } if (arr[prev] == x) return prev; return -1; }

C)

int jumpSearch(int arr[], int x, int n) { int step = sqrt(n); int prev = 0; while (arr[min(step, n)-1] < x) { prev = step; step += sqrt(n); if (prev == n) return -1; } while (arr[prev] < x) { prev++; if (prev == min(step, n)) return -1; } if (arr[prev] == x) return prev; return -1; }

D)

int jumpSearch(int arr[], int x, int n) { int step = sqrt(n); int prev = 0; while (arr[min(step, n)-1] < x) { prev = step; step += sqrt(n); if (prev >= n) return -1; } while (arr[prev] > x) { prev++; if (prev == min(step, n)) return -1; } if (arr[prev] == x) return prev; return -1; }

**Explanation:** The correct code makes hops until it finds an element that is greater than the necessary element. After that, a backwards linear search is done. We return -1 if the element is not found.

**7. Jump search is worse than linear search in terms of time complexity.**

A) True**B) False**

Explanation: The time complexity of linear search is O(n), while the time complexity of jump search is O(n1/2). In terms of time complexity, jump search is superior to linear search.

**8. Jump search has a worst case time complexity of O(n).**

A) True**B) False****Explanation:** In the worst and average cases, the time complexity of jump search is O(n1/2). The reason for this is that the optimum jump size is n1/2.

**9. Jump search algorithm requires which of the following condition to be true?****A) array should be sorted**

B) array should have not be sorted

C) array should have a less than 64 elements

D) array should be partially sorted**Explanation: **The input array must be sorted for jump sort to work. If the array is not sorted, the algorithm will fail to produce the desired result.

**10. Jumps are made in the jump search algorithm until ___________**

A) element having value less than that of the required element is found

B) element having value equal to the median of values of the array is found**C) element having value greater than that of the required element is found**

D) middle element is found equal to the element being searched**Explanation: **Jumps are rendered in the jump search algorithm before an element with a value greater than the value of the element being checked is found. After that, a backwards linear search is carried out.

**11. Which of the following step is taken after finding an element having value greater than the element being searched?**

A) linear search takes place in the forward direction**B) linear search takes place in the backward direction**

C) binary search takes place in the forward direction

D) binary search takes place in a backward direction**Explanation: **First, an element with a higher value than the one being searched is discovered. Following that, a backward linear search is done.

**12. How many jumps will be made in the worst case of jump search(let block jumped =k)?**

A) n*k**B) n/k**

C) k/n

D) n+k**Explanation:** When the value to be checked is in the last portion of the list, the worst case scenario occurs. As a result, the number of jumps will be n/k in this situation.

**13. What will be the maximum number of comparisons that can be made in jump search algorithm (assuming k to be blocks jumped)?**

A) k

B) n/k**C) k-1**

D) k-1**Explanation: **The worst-case scenario happens when the element being searched appears right after the element that was compared during the previous hop. In this case, k-1 comparisons will be needed.

A jump search or block search is a search algorithm for ordered lists in computer science. A linear search on the sublist L[(k-1)m, km] is used to find the exact location of the search key in the list. The best value for m is n, where n represents the length of the list L. Since both steps of the algorithm look at a maximum of n products, it takes O(n) time to complete. This is preferable to a linear search but inferior to a binary search. A jump search has an advantage over a binary in that it only has to jump backwards once, while a binary will jump backwards up to log n times. If jumping backwards takes much longer than jumping forward, this can be critical.