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Rank of root in AVL tree

Find a function that bounds from above and below (asymptotic) the rank of the root r in an AVL tree,
i.e. find a function $ f(n)$ so there exists a constant $ c>0$ that for every AVL tree with $ n$ nodes so $ c * f(n)\le rank(r)\le n-c*f(n) $ .

$ rank(r)$ gets his maximum value when his sub-left tree contains maximal number of nodes and because it’s an AVL tree, for tree with height $ h$ the sub left tree will be with height of $ h-1$ and the number of nodes will be maximal when the sub tree is a full tree with $ 2^{h-2}-1$ nodes hence we get:
$ rank(r)\leq 2^{h-2}-1+1=2^{h-2}$

On the other hand, $ rank(r)$ gets his minimal value when his sub left tree contains a minimal number of nodes and it happens when the sub left tree is a fibonacci tree with height of $ h-2$ , therefore
$ rank(r) \geq \phi ^{h-2}+1$ .

Now I need to find f as a function of the number of nodes $ n$ and not the height $ h$ . Am I in the right direction?
Would apricciate any help how to continue, Thanks.

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Why is finding square root of perfect square $O(M(n))$

I saw this question and its answer on Theoretical Computer Science stack exchange and I can’t understand why the complexity of finding the root is the same as that of a multiplication. My thought was that we may need more than $ O(1)$ multiplications to find the root (using Newton’s Iteration as stated in the answer, since the method may need more than $ O(1)$ steps).

Is there an upper limit not depending on $ n$ to the amount of multiplications we may need? Or a method to find the root with enough accuracy(which means finding the actual root) after $ O(1)$ steps? Am I missing something?

Note: I didn’t ask this on theoretical CS stack exchange, since it is supposed to be for professional researchers in CS and no one asked about this in the comments so assume it isn’t a research level question even if it is about an explanation of one (research level question).

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Rate my idea: NodeJS as root behind Apache as a proxy with password

I’m the admin of a small Linux server owned by a relative of mine. He’s fairly tech savvy, but more at a level of a power user than an expert. I want to make a handy visual tool for him that would allow to do some simple server tasks: add/remove users and change their passwords; set up/remove websites; set up/remove mailboxes (I’ve decoupled those from system users so it’s a separate task if needed); and perhaps something else as needed.

Most of these things can be done from command line and some require the editing of some config files, but lengthy incantations with a lot of changing parts is just asking for trouble. I’d rather have a handy script.

The trouble is: most of these tasks require superuser permissions. He already has that, so I could make a textmode tool (which requires to be run as root), but a website would be so much nicer.

There’s already an apache webserver in place on port 80, bit running that as root would obviously be a lousy idea. Similarly, I don’t want to store root password anywhere.

So I had the idea of making the website in NodeJS and running the Node process as root, listening only on a specific port which only accepts incoming connections from localhost. Then Apache would be a non-elevated proxy in front of the NodeJS app. In addition, both Apache and NodeJS would ask for a password (taken from the same .htpasswd file).

If you can’t enter the password to Apache, you can’t even get to Node. If you hack Apache (or have access to some local account) you still need the password to get the Node app to cooperate.

Would this be safe enough? Ok, that’s kinda subjective, but considering that I’m more worried about opportunistic hackers from outside than malicious local users, would this be ok? There’s really nothing of much value stored on the server; I don’t expect anyone to do targeted hacking because there’s not much to gain (Wanna see pictures of my kids? You’re welcome…) I consider automated scanners and hackers trying to add to their botnets/db leaks the main threat. Any other suggestions on how to achieve this maybe?

How to determine whether the certificate is a root certificate

My understanding is that if Issuer and Subject fields for same, the certificate is self-signed and must be a root certificate. I’m trying to do this comparison in code but facing issues.

  m_X509_NAME *R_CDECL2 =  X509_get_subject_name( ps_X509Cert);   X509_NAME *R_CDECL2_issuer = X509_get_issuer_name((X509*) ps_X509Cert);     X509_NAME_get_text_by_NID( R_CDECL2, NID_commonName, subjectName, MAX_BUF_SIZE);    printf("\n-------------\n subjectName: %s \n--------------\n", subjectName);    b_X509_NAME_get_text_by_NID( R_CDECL2_issuer, NID_commonName, issuerName, MAX_BUF_SIZE);    printf("\n-------------\n issuerName: %s \n--------------\n", issuerName); 

With the above code, subject name is printing as expected. But the code crashes when executing b_X509_NAME_get_text_by_NID for issuer name. Any mistake in this code?

Certificate checking with OCSP and root CA not trusted

I have a root certificate authority, an sub CA and an server.

The root ca delivers a certificate for the sub CA.

The sub CA delivers a certificate for the server.

I want to check all the certification chain, from the server to the root CA with OCSP.

The command

openssl ocsp -issuer chain.pem -cert server.pem -CAfile root_ca.crt -text -url http://ipa-ca.sub.berettadomaine.fr/ca/ocsp 

gives the result:

Response Verify Failure  140376105273232:error:27069070:OCSP routines:OCSP_basic_verify:root ca not trusted:ocsp_vfy.c:166:  server.pem: good 

chain.pem contains all the certificates (root ca, sub ca and server).

So, root ca is not trusted but, however, I put the option “-CAfile root_ca.crt…

Do you know where is my fault, how can I check all the chain please?

Thank you very much.

Certificate check works with root but fails with Intermediate CA [duplicate]

I have 3 certificates, server.crt issued by Intermediate CA which is issued by Root. The server.crt is configured on apache2 (version 2.4.29-1) on Ubuntu 18.04.

However when I am trying to connect to the server URL through openssl (version 1.1.1) using the intermediate CA as the CAfile parameter, I receive error as Verify return code: 2 (unable to get issuer certificate) Command used : openssl s_client -connect server_URL:443 -CAfile Intermediate.pem

But when I try to connect the same URL using the root certificate it works with return code 0. Command used : openssl s_client -connect server_URL:443 -CAfile Root.pem — Works fine

How can I make the the certificate check work using the intermediate CA and not Root certificate.

Note that the below certificate chain verification are all successful.

openssl verify -CAfile root.pem Internal_CA.pem — OK

openssl verify -CAfile root_and_intemediate_combined.pem server.pem — OK

Also I got same results for using both pem and crt formats for all certificates.