Searching algorithms are used to find an element in a collection (like an array or a list). Two common searching algorithms are:

1. Linear Search

Description: Linear search is the simplest searching algorithm. It works by checking each element in the list one by one until it finds the target element or reaches the end of the list.

Time Complexity:

Best case: O(1) (when the target element is at the beginning). Worst case: O(n) (when the target element is at the end or not present at all). Example: Given a list [3, 8, 4, 1, 7], to find the number 4, the algorithm will check each element in the list until it reaches 4.

2. Binary Search

Description: Binary search is more efficient but requires the list to be sorted. It works by repeatedly dividing the search interval in half. If the middle element is equal to the target value, the search is complete. Otherwise, it continues to search in either the left or right half.

Time Complexity:

Best case: O(1) (when the target element is at the middle). Worst case: O(log n) (since it halves the search space with each step). Example: Given a sorted list [1, 3, 4, 7, 8], to find the number 4, the algorithm will start by checking the middle element. If the middle is not 4, it will then search in the left half or right half based on the comparison.

Sorting algorithms are used to arrange the elements of a list in a specific order (ascending or descending). Here are a couple of commonly used sorting algorithms:

1.Bubble Sort

Description: Bubble sort repeatedly compares adjacent elements in the list and swaps them if they are in the wrong order. This process continues until no more swaps are needed.

Time Complexity:

Best case: O(n) (if the list is already sorted). Worst case: O(n²) (when the list is sorted in reverse order). Example: Given a list [5, 2, 4, 6, 1], bubble sort will go through multiple iterations to compare and swap elements until the list becomes [1, 2, 4, 5, 6].

2.Merge Sort

Description: Merge sort is a divide-and-conquer algorithm that divides the list into two halves, recursively sorts each half, and then merges the two sorted halves back together.

Time Complexity:

Best case: O(n log n). Worst case: O(n log n) (since it consistently divides and merges the list in logarithmic time). Example: Given a list [38, 27, 43, 3, 9], merge sort will divide it into smaller parts until it has individual elements, then merge them back in the correct order, resulting in [3, 9, 27, 38, 43].