Pick out elements from a list of lists using criteria

Consider a list of lists in this form (with a shape $ m \times n \times 3 $ ):

{  {{a1, R1, c11}, {a2, R1, c12}, {a3, R1, c13}, ..., {an, R1, c1n}},  {{a1, R2, c21}, {a2, R2, c22}, {a3, R2, c23}, ..., {an, R2, c2n}},  ...,  {{a1, Rm, cm1}, {a2, Rm, cm2}, {a3, Rm, cm3}, ..., {an, Rm, cmn}} } 

where in each outer list, the 2nd element $ R_i $ is fixed ($ i = 1, 2, …, m $ ), and the 1st element changes from $ a_1 $ to $ a_n $ , the 3rd element $ c_{ij} $ is normally a complex and its imaginary part can change from positive to negative or from negative to positive for several times. Here is a sample data for test.

I want to pick out the neighbor lists whenever the imaginary part of $ c_{ij} $ changes its sign, say, for $ R_2 $ , the selected lists are something like $ \{a_j, R_2, c_{2j}\} $ and $ \{a_{j+1}, R_2, c_{2,j+1}\} $ , where $ \text{Im} c_{2,j} < 0 $ and $ \text{Im} c_{2,j+1} > 0 $ . More generally, for $ R_p $ I pick out $ \{a_j, R_p, c_{pj}\} $ and $ \{a_{j+1}, R_p, c_{p,j+1}\} $ , and then to plot a curve with ListLinePlot[{{R1, a01}, {R2, a02}, ..., {Rp, a0p}, ..., {Rm, a0m}}], in which $ a_{0j} = (a_j + a_{j+1}) / 2 $ . In other words, I what to plot a parameter curve w.r.t the 1st and 2nd elements, across which the imaginary part of the 3rd element changes sign.

I tried Cases, Select and ParametricPlot, but I am still having trouble to find all the pairs of the neighboring lists when the imaginary part of $ c_{ij} $ changes its sign.

Are there price lists for magic items, such as the Bag of Holding?

We are playing Hoard of the Dragon Queen. My PC’s are only at level 3. They stumbled into a magic shop and asked for a Bag of Holding. I made the asker roll to beat a 15 and if he did I said that he could buy one. (He rolled a 17.) So then I proceeded to look for for how much one costs in the DMG, PHB & HotDQ. Magic item creation and endless tables were all I found. Someone found a D&D Wiki and said it was 2500 GP. I ended the game (about 15 minutes early) to do my homework. Am I missing something?

My question is:

Why is the Bag of Holding not listed in the Index of any book?

Where do I get price lists for magic items? Or if the answer is “It’s at my discretion”, what should I use as a guide?

How to construct simultaneous equations from two lists?

Assume that I want to solve a simultaneous equation below.

\begin{cases} 2x_1+3x_2=5\ x_1-x_2=0 \end{cases}

First I construct two lists

coefs = {{2, 3, 5}, {1, -1, 0}}; vars = Array[x, 2]; 

Note that I feel more comfortable to put the constants 5 and 0 in the coefficient list rather than separating them into another list.

Because I don’t know how to construct equ from the above lists, I manually construct as follows.

equ = 2 x[1] + 3 x[2] == 5 && x[1] - x[2] == 0 

Finally equ is passed to Solve[equ, vars].

Question

What is the simplest way to construct equ from the available two list coefs and vars?

Minimal Working Example

The following template will save your typing time.

coefs = {{2, 3, 5}, {1, -1, 0}}; vars = Array[x, 2]; equ = 2 x[1] + 3 x[2] == 5 && x[1] - x[2] == 0 Solve[equ, vars] 

Time complexity of removing duplicates in lists


Question

I am wondering what is the minimum time complexity of get the unique value of a array in two conditions: keep the order or not.

I think time complexity of not keeping the order is $ O(n)$ using a hashtable. Keeping order has a time complexity $ O(n^2)$ .

So, Am I right? Can someone give a detailed prove the time complexity of the best in each condition?

For more infomation:

I use Python, I find 2 python code for drop dumplicates in a list.

  1. How do you remove duplicates from a list whilst preserving order?
  2. removing duplicates in lists

combining 2 or more password lists with crunch

how can i combine 2 or more password lists together like for example i have a passlist with names and a passlist with numbers so i wanna combine them like putting all the numbers in front or after the names

passlist1 contains too many names for example david-larry-kevin … passlist2 contains numbers 123-347-897672 and … then combine these 2 password lists together for something like dadvid123 david347 david897672 larry123 larry347 and … this is clear i want to combine two or more password lists together in crunch ,also no need to scripting tnx in advance

Faculty for binary trees instead of lists

i know how to count permutations within a list (–> n!), but what about binary trees? Subtrees from “siblings” are allowed to have their own order, otherwise it would be trivial.

here is an example for n=5

the root has 5 possibilities

each of the 2 children has 4 possibilities

each of the 4 grandchildren has 3 possibilities

each of the 8 grandgrandchildren has 2 possibilities

and the grandgrandgrandchildren have no choice

how to calculate the total number for n?

Are Paid GSASER Lists From Third-Parties To Be Used In A Certain Way?

Like…what Tier should I point the links at, that are on the list?
Like…Are certain types of links better for different tiers?
Like…What is the site quality like of the links on these lists?
Like…What are longevity of the links on these lists?
Are there ever posting opportunities on these lists on sites that are banned from Googel?