Hi. The question I'm having problems with:
Write the body of an iterative function to compute n!, where n! = n(n-1)(n-2)...1.
Then, analyze this function where the work unit is the multiplication operation.
I think I have the first part, but I'm confused on the second part.
Please help!!
When multiplying, use shorthand notation.
Example
56*n!
where you thinking something like
f(n+1) = (n+1)f(n), n>1, f(1)=1
To analyze the function in terms of the work units, we need to determine how many multiplication operations are being performed in the iterative function.
First, let's take a look at the iterative function to compute n!:
```python
def factorial(n):
result = 1
for i in range(1, n+1):
result *= i
return result
```
In this function, we initialize the `result` variable to 1. Then, we use a `for` loop to iterate from 1 to `n` (inclusive). Within the loop, we multiply the current value of `result` by `i`. Finally, we return the `result` as the factorial of `n`.
Now, let's analyze the function in terms of the work units. In this case, the work units represent the number of multiplication operations performed.
If `n` is a large number, the number of multiplication operations required to compute `n!` can be quite significant. Each iteration of the `for` loop performs one multiplication operation.
The total number of multiplication operations can be calculated by counting the number of iterations in the `for` loop, which is `n`. So, the number of work units for computing `n!` using this iterative function is `n`.
For example, if `n = 5`, the function will perform 5 multiplication operations (`1*2*3*4*5`), which matches the value of `n`.
In general, the number of work units required to compute `n!` using this iterative function is equal to the value of `n`.