Given a graph with $ n$ nodes . The adjacency matrix of the graph is given. We do $ k$ operations on this graph. In each operation we choose two distinct nodes $ i$ and $ j$ (there are $ (n*(n-1))/2$ such choices) equiprobably (all choices are equiprobable) and if there exists a edge between $ i$ and $ j$ we delete that edge or else we draw an edge between the chosen pair of nodes.

We have to output a $ n*n$ matrix where the element at $ (i,j)th$ position denotes the probability of occurrence of edge connecting the nodes $ i$ and $ j$ in the final resulting graph.

The constraints on n and k are $ n<=50$ and $ k<=50$ .

I tried it using dynamic programming but could figure out transitions properly.

Can you please help me out.

# Tag: each

## What is the upper bound on the number of nodes in a tree with n leaves where each internal node has at least two children?

The pieces of information available to us are the number of leaves in a tree and that each internal node must have at least two children. Is there a way to find the upper bound on the total number of nodes in the tree?

## How to estimate the complexity of sequential algorithm given that we know the complexity of each step?

First case: I was stumble upon a two step sequential algorithm where the big O complexity of each step is O(N^9).

Second case: Also if the algorithm have three steps where the complexity of step 1 is O(N^2), the complexity of step 2 is O(N^3) and the complexity of step 3 is O(N^9)

What would be the complexity of the first case and second case ?

## What Illusion spell would allow me to trick two enemies into fighting each other?

Is there a good spell or combination of spells that will allow me to cause opponents to see their allies as the enemies they are fighting? Either one on one or in groups? The intention is to make them fight their allies thinking that the allies are the enemy.

The best i can think of is using Major Image and placing it over another creature, so that his companions see him as the bad guy. Then through concentration I can manipulate the illusion to make it look like its fighting… Unfortunately that would only work for one attack because once the illusion is touched the opponent can see through it… Any other options?

## Having a backdoor password for each user to allow impersonation

For some context, I want my api to be able to ‘impersonate’ (or connect as) a user on my ldap database as most of the api’s access controls are on the ldap database and tied to the user you are connected as.

In order to do this I have an idea where I will generate a random password for each user. The random password will then be encrypted with a key only the api has access to. The encrypted string will then be stored under the user’s entry. Now when the api wants to impersonate a user, it will get the encrypted string, decrypt it and then connect as that user.

How bad of an idea is this?

## Construct a grammar for the expression of each of the following language [closed]

Construct a grammar for the expression of each of the following language: E = The set of all strings of 0’s and 1’s not containing 101 as a substring. a. C Language b. Java Language

## Is it a bug or intended that Unarmored defense from barbarian and monk overwrite each other?

For science I made a level 1 monk and level 1 barbarian character. Set all the stats to 18. So according to monks unarmored defense your ac = 10 + dex + wis. Then with the barbarian it adds con. Yet the ac was still only 18. Is this intended or is this a bug with dndbeyond?

## Oracle PL-SQL “Regular expression” to replace each “(space)and(space)” with ‘,’ in a string

I have a string like this `x=y and g=h and u=1`

and I need to replace each `(space)and(space)`

with `,`

. I’m using the powerful `regular_expression`

for this but it does not give me the desired result.

`select regexp_replace('x=y and g=h and u=1','(^[[:space:]]*)AND(^[[:space:]]*)', ',') from dual; `

I was wondering if you could help me out here. thanks in advance.

## Does Moonbeam damage get re-rolled each turn?

Moonbeam is cast, a creature starts its turn within it, and the damage is rolled. The creature moves out of the beam. On the caster’s turn, they move the moonbeam back onto the creature. The creature starts its next turn in the moonbeam…does the caster roll again for the damage, or use the damage roll from the previous turn?

## Creating image box below each other.

How can i create something like this, where the image on is on the left and i can add text, and then the next image is on the right, and so on

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