can you help me about big o? - algorithm

I need help about big O.
I'm not sure.
while (i<n){
while(j=n){
j++;
}//this is I think n*(n+1)
i++;//(n+1)
}//n
I need to tell me someone how calculate this if I'm wrong.

Have you put the question correctly?
It looks like the program will newer enter the inner loop or just enter it once. If the code is correct I would say it is just O(n).

Related

In a lua for loop what is a # used for?

I know how for loops work and I use them quite often but also seem to often come across a # in others' code and I want to know what it is for and how to use it. An example of this would be:
for i = 1, #npc do local v = npc[i]
I cant seem to find anything online regarding this, maybe my searches just aren't good but it would be nice if someone could explain it for me, thanks.
In Lua, # is the length operator. for i = 1, #npc essentially loops from 1 to the length of the npc array.
As was already pointed out, it gets the length of a list. However, there's another thing worth pointing out: that for loop is suboptimal and unidiomatic. It would be better written as for i, v in ipairs(npc) do. In general, using # in a for loop is almost always the wrong thing to do.

Algorithm design manual solution to 1-8

I'm currently reading through The Algorithm Design Manual by Steven S. Skiena. Some of the concepts in the book I haven't used in almost 7 years. Even while I was in college it was difficult for me to understand how some of my classmates came up with some of these proofs. Now, I'm completely stuck on one of the exercises. Please help.
Will you please answer this question and explain how you came up with what to use for your Base case and why each step proves why it is valid and correct. I know this might be asking a lot, but I really need help understanding how to do these.
Thank you in advance!
Proofs of Correctness
Question:
1-8. Proove the correctness of the following algorithm for evaluating a polynomial.
$$P(x) = a_nx_n+a_n−1x_n−1+⋯+a_1x+a_0$$
&function horner(A,x)
p=A_n
for i from n−1 to 0
p=p∗x+Ai
return p$
btw, off topic: Sorry guys, I'm not sure how to correctly add the mathematical formatting for the formula. I tried by addign '$' around each section. Not sure why that isn't working.
https://cs.stackexchange.com/ is probably better for this. Also I'm pretty sure that $$ formatting only works on some StackExchange sites. But anyways, think about what this algorithm is doing at each step.
We start with p = A_n.
Then we take p = p*x + A_{n-1}. So what is this doing? We now have p = x*A_n + A_{n-1}.
I'll try one more step. p = p*x + A_{n-2} so now p = (x^2)*A_n + x*A_{n-1} + A{n-2} (here x^2 means x to the power 2, of course).
You should be able to take it from here.

How to represent one variable in terms of others in an equation set in Mathematicas?

I have an pretty complex equation set enter image description here
I want to solve Vo in terms of Vin.
But when I clicked Ctrl+Enter (a.k.a Evaluate Cell), nothing happened.
How to fix it? Thanks for your help
Simplify[Reduce[eqn, Vo]]
works.
If you can include any assumptions (as a second argument to Simplify or by giving those along with your equations to Reduce) that you have about some variables not being zero then the result might be simpler. In any case, you look through each of the terms returned from Simplify to try to find the case that matches your real world problem.

What are "d-smooth sequences?"

I have a homework problem that tells me this:
I can't seem to make sense of what d-smooth means. Can someone please help explain it in a more understandable way? Thanks!
A sequence is d-smooth if you can increment/decrement each number at most d times to obtain a (strictly) increasing sequence.

backtracking line search in R

why backtracking(step halving) line serach get fail? actually sometimes in my R code i have an ascent direction and step size $t = 1e-21$ which means that Error: Line search failed (tol=1e-10) and i chose alpha=0.3 and beta=0.5.
I'm going to make a wild guess and say that thanks to floating point round off, you can't reliably make steps that small.
But really I don't know. Nor will anyone else until you follow the suggestion to actually show us what is not working.

Resources