Write an algorithm that prints the factorial for the first 20 even numbers. Then, give the big-O for your algorithm.
To print the factorial for the first 20 even numbers, you can follow these steps:
1. Create a variable named `factorial` and initialize it to 1.
2. Create a for loop to iterate from 2 to 40 (inclusive), incrementing by 2 in each iteration (since we want to consider only even numbers).
3. Inside the loop, update the `factorial` variable by multiplying it with the current number.
4. Print the value of `factorial` after the loop.
Here is an example implementation in Python:
```python
factorial = 1
for num in range(2, 41, 2):
factorial *= num
print(factorial)
```
Now, let's analyze the time complexity of this algorithm. The for loop iterates through 20 even numbers, so it has a constant number of iterations. The multiplication operation inside the loop takes constant time as well. Therefore, the time complexity of this algorithm is O(1), which means it has constant time complexity. Regardless of the input size (in this case, the number of even numbers), the time taken by the algorithm remains constant.