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What is the running time for:

-Linear Search
-Binary search
-bubble sort

For each algorithm above, why do they take the time that they do?

If you have Knuth's book Searching and Sorting, these are well explained.

Otherwise, you can find good discussions online.

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Linear Search is an algorithm used to find a specific value in a list by examining each element one by one. Its running time is directly proportional to the size of the list, referred to as O(n), where n is the number of elements. This is because in the worst-case scenario, the desired value might be at the end of the list, requiring the algorithm to traverse through all elements before finding the value. Binary Search is an efficient algorithm used to find a specific value in a sorted list by repeatedly dividing the search space in half. Its running time is logarithmic, denoted as O(log n), where n is the number of elements. This is because with each division, the search space is effectively halved, drastically reducing the number of elements to search through. As a result, binary search is significantly faster than linear search for larger lists. Bubble Sort is a simple sorting algorithm that repeatedly swaps adjacent elements if they are in the wrong order. Its running time is quadratic, denoted as O(n^2), where n is the number of elements. This is because the algorithm compares and swaps each pair of adjacent elements multiple times until the entire list is sorted. Consequently, bubble sort can become inefficient and time-consuming for larger lists.