Simple Algorithm - I need clarity of Expression and Formula

N

NotGoodAtAll

New member
Joined
Oct 30, 2019
Messages
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Hi,

Simple algorithm:

While n is greater than 1
Print n ! symbols
go to next line
make n equal n-1

If n - 5 the output reads:
!!!!!
!!!!
!!!
!!

There would be no single ! symbol as 1 is not greater than 1 (I assume this is correct, please correct me if not)

I need an expression that gives the number of symbols regardless of the value n, and write a formula.

I have drawn this out, bashed my head against the wall and I seem to be having an issue.

I have so far ascertained that the following works but not sure what else I can do:
1574864539919.png

Any assistance would be hugely appreciated.
 
I've also hit upon the following eqaution:

n = n-1 + n

where n-1 is the previous value of n in a recursive set. That make any better sense?
 
You have a sequence n, n-1, ...,, 2. This is an arithmetic sequence. There is a formula for the sum of such sequence. Can you look it up?
 
None of it makes much sense including the algorithm, which does not say what is to be done if n = 1. So how do you know that the last line prints an exclamation point?

In any case is the n! a symbol for n factorial?

What was the exact and complete statement of the problem?
 
The full problem was presented as is:

Consider the following simple Algorithm:

While n is greater than 1
Print n ! symbols
go to next line
make n equal n-1

Show what is printed when n = 5

Then come up with an expression that would be true for the amount of ! marks regardless of the value of n. Write down the equation you could use.

My understanding is that the value for 1 doesn't exist, as 1 is not greater than 1 and the algorithm couldn't run in this case. The operative word "While" suggests a recursive algorithm until we reach 1 and then stop.

For background I'm working through a cryptography problem paper, nothing spectacular and strictly for recreation.

Hope this provides a little clarity.
 
lev888 said:
You have a sequence n, n-1, ...,, 2. This is an arithmetic sequence. There is a formula for the sum of such sequence. Can you look it up?
Click to expand...
Hi, yes I have looked at it. the sequence I mean, and that's why i stumbled across the n=n-1 +n type of solution.

I'm trying to get my head around it, I don't much care for the Answer, more the solution, if you get my meaning? I want to understand how to come to the right expression and equation.

Cheers
 
NotGoodAtAll said:
The full problem was presented as is:

Consider the following simple Algorithm:

While n is greater than 1
Print n ! symbols
go to next line
make n equal n-1

Show what is printed when n = 5

Then come up with an expression that would be true for the amount of ! marks regardless of the value of n. Write down the equation you could use.

My understanding is that the value for 1 doesn't exist, as 1 is not greater than 1 and the algorithm couldn't run in this case. The operative word "While" suggests a recursive algorithm until we reach 1 and then stop.

For background I'm working through a cryptography problem paper, nothing spectacular and strictly for recreation.

Hope this provides a little clarity.
Click to expand...
For the formula see my post above. Regarding the algorithm, I would say "while" suggests a loop (iteration), not recursion.
 
NotGoodAtAll said:
Hi, yes I have looked at it. the sequence I mean, and that's why i stumbled across the n=n-1 +n type of solution.

I'm trying to get my head around it, I don't much care for the Answer, more the solution, if you get my meaning? I want to understand how to come to the right expression and equation.

Cheers
Click to expand...
You want to derive the formula yourself?
 
So I have come to this:

General Expression
Xn= Xn-1 + n
X5= 9 + 5
X5= 14

Equation

((n+1)*n) / 2) - 1

I have somewhat buried myself in something else, so have been distracted but his is what I noted in my last scribbles. Can anyone advise if either one of these makes sense? before I go back to my notes and see why I got to this?

Many thanks
 
NotGoodAtAll said:
So I have come to this:

General Expression
Xn= Xn-1 + n
X5= 9 + 5
X5= 14
Equation
((n+1)*n) / 2) - 1 CORRECT!
Click to expand...
The sum of the first \(\displaystyle N\) positive integers is \(\displaystyle \frac{N(N+1)}{2}\). But you do not use 1 so subtract it off.
 
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