Describe the difference between the sequential search and the binary search.

Sequential search, also known as a linear search, is a simple searching algorithm that starts at the beginning of a list and iterates through each element in the list until the desired target element is found or the entire list has been searched. In the worst-case scenario, the algorithm needs to search through every element in the list, making the complexity of the sequential search O(n), where 'n' is the number of elements in the list. This approach works for both sorted and unsorted lists.

Binary search is an efficient searching algorithm that works on sorted lists. It starts by dividing the list into two equal parts and comparing the target element with the middle element of the list. If the target element is equal to the middle element, the search is successful. If the target element is less than the middle element, the search continues on the lower half of the list. If the target element is greater than the middle element, the search continues on the upper half of the list. This procedure is repeated until the target element is found or the search space becomes empty. The complexity of the binary search algorithm is O(log n), where 'n' is the number of elements in the list.

The main differences between the sequential search and the binary search are as follows: 1. Sequential search works on both sorted and unsorted lists, while binary search only works on sorted lists. 2. Sequential search goes through each element in the list one by one, while binary search divides the list in half at each step. 3. Sequential search has a time complexity of O(n), making it less efficient for large lists compared to binary search, which has a time complexity of O(log n).

- Use sequential search when: 1. The list is unsorted or small. 2. You don't have any information about the distribution of the data. 3. The cost of sorting a list before performing a search is not worth the improved performance of binary search. - Use binary search when: 1. The list is sorted or can be sorted efficiently. 2. The list is large. 3. The list's data allows for efficient comparisons (e.g., numbers or strings), and the target element can be easily compared to the middle element of the search space. In conclusion, the main difference between the sequential search and the binary search is the efficiency, as well as the fact that binary search can only work on sorted lists. Sequential search is useful for small or unsorted lists, while binary search is more suitable for large, sorted lists with easily comparable data types.