Searching Algorithms Questions Long
Jump search is a searching algorithm that is used to find the position of a target value within a sorted array. It is an improvement over linear search as it reduces the number of comparisons required to find the target value.
The concept of jump search involves dividing the array into smaller blocks or subarrays of equal size. The size of these blocks is determined by the square root of the length of the array. For example, if the array has a length of n, then the size of each block would be √n.
To perform a jump search, the following steps are followed:
1. Start by initializing two variables, namely "step" and "prev". The "step" variable represents the size of the block, while the "prev" variable keeps track of the previous block's index.
2. Compare the target value with the last element of the current block. If the target value is greater, then move to the next block by updating the "prev" variable to the current block's index and incrementing the "step" variable.
3. Repeat step 2 until the target value is either found or becomes smaller than the last element of the current block.
4. Once the target value is found to be smaller than the last element of the current block, perform a linear search within that block to find the exact position of the target value.
5. If the target value is found, return its index. Otherwise, return -1 to indicate that the target value is not present in the array.
The time complexity of jump search is O(√n), where n is the length of the array. This makes it more efficient than linear search, especially for large arrays. However, it is not as efficient as binary search, which has a time complexity of O(log n).
In conclusion, jump search is a searching algorithm that combines the advantages of both linear search and binary search. It is particularly useful for sorted arrays where the elements are uniformly distributed.