Runtime analysis done in Python3.

Algorithms:

1. Iterative factorial:

• Input: integer
• initialize factorial variable with 1
• for numbers in range 2 to input + 1 factorial += number
• return factorial

2. Recursive factorial:

• Input: integer
• if input is 0 return 1
• else return factorial function with $n - 1$ as argument n times

3. Tail recursive factorial:

• Input: integer, accumulator = 1
• if input is 0 return accumulator
• else return factorial function with $n - 1$ as argument n times

4. Linear search:

• Input: array and element to be found
• iterate through the array and check if the element exists
• if found return the index of the element

5. Binary search:

• Input: array and element to be found
• initialize lower and mid to 0 and high to the length of the array
• as long as low <= high
• mid = middle of the array
• if mid < element low becomes mid
• if mix > element high becomes mid
• if mid = element return mid