Data Structure And Algorithm : Practice Questions and Answers

As binary search requires comparison, it is required that the list be ordered. Whereas this doesn't matter for linear search.

The best case occurs when the given element to be found is at the first position. Therefore O(1) is the correct answer.

The function calls itself till the element is found. But at the 7th call it terminates as goes outside the array.

Provided that the search starts from the first element, the function calls itself till the element is found. In this case, the element is found in 4th call.

It is used when the size of the dataset is low as its runtime is O(n) which is more when compared to the binary search O(logn).

In the worst case scenario, there might be a need of calling the stack n times. Therfore O(n).

The recursive algorithm consumes more space as it involves the usage the stack space(calls the function numerous times).

The Iterative algorithm is faster than the latter as recursive algorithm has overheads like calling function and registering stacks repeatedly.

The time complexity of jump search is O(n^{1/2}) in worst and average case. It is due to the fact that size of optimal jump is n^{1/2}.

Linear search has a time complexity of O(n) and the time complexity of jump search is O(n^{1/2}). So jump search is better than linear search in terms of time complexity.

Best case of jump search will be when the first element of the array is the element that is being searched. In this case only one comparison will be required. Thus it will have a time complexity of O(1).

Jump search only needs to jump backwards once, while a binary can jump backwards up to log n times. Thus jump search will be preferred over binary search if jumping backwards is expensive.

Binary search has the least time complexity (equal to log n) out of the given searching algorithms. This makes binary search preferable in most cases.

Jump search does not require any additional space for searching the required element. Thus its auxiliary space requirement will be O(1).

Total number of comparisons required will be n/k + k-1 in worst case. This function will be minimum for k=n^{1/2}. So this value of jump will be the best for implementing jump search.

Worst case occurs when the element being searched is present just after the element that has been compared while making the last jump. So, in this case k-1 comparisons will have to be made.

Worst case occurs when the value to be searched is in the last section of the array. So, in this case the number of jumps will be n/k.

First an element having value greater than the element being searched is found. After this linear search is performed in a backward direction.

In jump search algorithm jumps are made until element having value greater than the value of element being searched is found. After this linear search is performed in backwards direction.

Jump sort requires the input array to be sorted. The algorithm would fail to give the correct result if array is not sorted.