Explain the time complexity of jump search.

Jump search is a searching algorithm that is used to find an element in a sorted array. It works by jumping ahead a fixed number of steps in each iteration, rather than searching through each element one by one. The time complexity of jump search can be analyzed as follows:

1. Jumping Step Calculation:
- The first step in jump search is to determine the optimal jump size. This can be done by taking the square root of the array size, which gives us the step size to jump ahead in each iteration.
- Let's assume the array size is 'n'. Therefore, the jump size would be √n.

2. Jumping and Comparisons:
- In each iteration, the algorithm jumps ahead by the calculated step size and compares the element at that position with the target element.
- If the target element is smaller, it means the target element is not present in the current block, so the algorithm jumps back to the previous block and performs a linear search within that block.
- If the target element is larger, the algorithm continues to jump ahead until it either finds the target element or exceeds the array size.

3. Time Complexity Analysis:
- The time complexity of jump search can be calculated by considering the number of jumps and comparisons performed.
- The number of jumps can be calculated as the total array size divided by the jump size (√n).
- Therefore, the number of jumps would be √n.
- The number of comparisons within each block is at most the jump size (√n).
- Hence, the total number of comparisons would be √n.

- Combining the number of jumps and comparisons, the time complexity of jump search can be expressed as O(√n).

4. Comparison with Other Searching Algorithms:
- Jump search has a better time complexity compared to linear search, which has a time complexity of O(n) as it searches through each element one by one.
- However, jump search is not as efficient as binary search, which has a time complexity of O(log n).
- Binary search divides the array into two halves in each iteration, resulting in a faster search process.

In conclusion, the time complexity of jump search is O(√n), making it more efficient than linear search but less efficient than binary search.