Questions on the manipulation of List objects in Mathematica, and the functions used for these manipulations.

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13
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6answers
1k views

Building a continued fraction

I've completed a problem that involves approximating $e$ by a continued fraction: $$\frac{N_1}{D_1+\frac{N_2}{D_2+\frac{N_3}{\ddots+\frac{N_k}{D_k}}}}$$ with the $N_i$ being the list ...
13
votes
4answers
370 views

How to evaluate the second argument of Cases only once

I'd like to find a fast but readable way to achieve the following: ...
13
votes
6answers
1k views

Splitting up delimited data in lists

One task that I frequently find myself doing in Mathematica is splitting lists into lists of sublists, using specific elements to define the break-points. This is particularly useful with imported ...
13
votes
7answers
428 views

Concatenation of lists in a Fibonacci-like pattern

I am trying to create a List of elements that follow the general pattern: $$X_{n+1} = X_n X_{n-1}$$ where the operation on the right hand side is concatenation, i.e., joining. I want to achieve the ...
13
votes
3answers
883 views

Subtracting two plots from each other after shifting one

I have the following lists representing energy spectra that need to be subtracted from each other to produce a difference spectrum. ...
13
votes
6answers
719 views

Sort+Union on a list

Probably this is too trivial question for this forum but for some reason I am not getting it on my Mathematica 7 so far. I have a list ...
13
votes
2answers
372 views

Bad performance of LengthWhile?

A friend of mine showed me this example, it's a test comparing LengthWhile to a self-made lengthwhile written in a direct and ...
13
votes
4answers
2k views

Reshape vectors exactly like in MATLAB

This gives a 64×1 column vector in Mathematica: ...
13
votes
6answers
3k views

Selecting every n-th element from a list

I have a list: data = {4, 5, 7, 8, 9, 5, 3, 2, 1, 2, 13, 12}; I want to take those elements in the list which are located at equal distances, say, every third ...
13
votes
1answer
477 views

How can I collect data for visualization of quick sort?

I know how to implement quick sort in Mathematica. But I don't know how to get the temp data for visualization, because I used recursion. I want the effect similar to this: ...
13
votes
2answers
2k views

How do I find the elements in a list that return the highest value for a function?

Suppose we have a list of values and a function f. I want to find which of the elements maximizes the return value of the function in Mathematica. Let call the ...
13
votes
4answers
389 views

The gap between MapAt and ReplacePart for 2D data tables with headers

Consider a relational table derived from survey data, where each column ("001-01" ...) represents a responder and each row (...
13
votes
3answers
1k views

What is the most efficient way to map a linked list?

In order to work with lists effectively using common recursive patterns from functional programming, it's often most convenient to worked with the "linked list" representation, that looks like this: <...
13
votes
2answers
392 views

Simple way to concatenate Dataset columns

Consider these two datasets: d1 = Transpose@Dataset[<|"a" -> Range[5]|>]; d2 = Transpose@Dataset[<|"b" -> Range[5, 1, -1]|>]; {d1, d2} What's ...
13
votes
1answer
223 views

Unexpected slowness checking for empty list?

I thought I had a firm understanding of the differences between Equal and SameQ, but this has me puzzled: ...
13
votes
2answers
555 views

What is the fastest way to get the nth distinct permutation of a list?

What is the fastest way to write a function nthPermutation[xs_List, n_Integer] which is equivalent to Permutations[xs][[n]] but ...
13
votes
2answers
840 views

Vlookup function as Excel in Mathematica

How can we create a Vlookup function, similar to what we have in Excel? So if we have a table a and another b, we could add ...
12
votes
7answers
644 views

Brackets around each item in matrix

I have a matrix where every item in the matrix has its own brackets that I do not want. How can I remove the brackets around each item?
12
votes
12answers
644 views

How to group each element with each consecutive elements in one head

Suppose I have the following list: list = {a, b, c, d} I want to generate this result: ...
12
votes
5answers
863 views

Is there a way to riffle more than two lists?

I thought Riffle would generalize such that Riffle[{a,b,c},{1,2,3},{x,y,z}] would return ...
12
votes
10answers
598 views

How to pick increasing numbers from the list

How to pick increasing numbers from the list. lst = {5, 3, 6, 2, 7, 4, 8}; out: {5,6,7,8} So many interesting ...
12
votes
5answers
344 views

Make a ragged list rectangular by trimming instead of padding

I have a ragged list ragged = {{a,b,c,d,e},{x,y,z}} that I would like to trim (on the right) to be rectangular. The desired result is ...
12
votes
3answers
3k views

Most Efficient Way to Calculate the Product of All Items in a List?

Say that I have a list of returns on a financial asset over time and want to know the total compounded return. To get the answer, I need to add 1 to each return and then calculate the product of all ...
12
votes
5answers
693 views

Filtering elements from a list that appear only once

I want to be able to select elements from a list that only appear once. I originally had this: Select[Table[Count[list, i], {i, list}], # == 1] But the issue is ...
12
votes
7answers
3k views

Combination and Permutation

How could I obtain the list of all the groups of 5 numbers taken from Range[12] such that the 2 lists have an empty intersection : ...
12
votes
7answers
486 views

Product of elements of a list

Sum is for functions; Total is for a list. Product is for a function; what is the command ...
12
votes
7answers
1k views

How can I Flatten this List with Inner List of Lists?

Given the following List ...
12
votes
5answers
2k views

How can I simulate this animation of checking for prime numbers?

I can only implement a very simple one, I want to make my code look like that. Any better ideas? ...
12
votes
9answers
1k views

How to partition a list of numbers in two lists of numbers such that each lists elements sums up to the same number?

I have the following list of squares. {1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256} Their sum is $1496$, I want to make two partitions ...
12
votes
5answers
5k views

How to create a list of pairs from 1d list(s)?

Say I've got two 1-dimensional lists A = {1,2,3} B = {a,b,c} How do I create a list of all pairs from list A such that the ...
12
votes
6answers
837 views

Deleting Lonely Numbers From a List

Suppose I have a list of integers like so: list = {1,2,5,6,8,10,11,12,14,16,17,18,19}; I'd like a function that will take this list and return a new list with ...
12
votes
3answers
264 views

Using 0 to create new columns in a list with Part

I just discovered a nice way to create intermediary columns in a list, and I would like to know if I can have some problem with it. It Works like this: Imagine I have this list, 5x3: ...
12
votes
4answers
945 views

Using Position (which requires a pattern) in the same manner as Select (which requires a criterion)

I am using Mathematica7. I have a list of lists (creatively named list in the following sample code) containing data. I would like to find the positions of the ...
12
votes
5answers
475 views

How would you efficiently implement BinListsBy?

Let's say I have a list like this: data = {{21, "Alice"}, {27, "Bob"}, {22, "Charles"}, {34, "Dora"}, {75, "Eliza"}} containing ages and names of persons. What I ...
12
votes
3answers
847 views

How to add lists with unequal length?

Given lists of unequal lengths, I want to add them together element-wise, treating missing elements as zero. For example, {1, 2, 3} + {a, b} + {x} should give ...
12
votes
4answers
648 views

What's the function that takes X[Y[z___]] to Y[X[z___]]? (“swap heads”)

I've seen the operation described in the title before (basically, swap the heads of the first two levels of an expression), but I can't find it... Does anyone know the function (or idiom/incantation) ...
12
votes
3answers
917 views

Specifying string patterns in DeleteCases

It seems that DeleteCases is not compatible with string patterns, at least directly (see, for example, this question). Is this true? If so, why is this the case? ...
12
votes
3answers
231 views

Exclude overlapping lists while keeping disjoint- and sub-lists?

Consider a function f[l1_List,l2_List] which is given lists of integers. Whenever two of the lists contain completely disjoint sets of integers OR one of the lists ...
12
votes
4answers
5k views

Removing empty sets from lists

If I had a list, say, names= {"Andy", "Bob", "Carly", "Sandy", "Jeff", "Tim", "Tom", "Zach"} and I decide to pick a characteristic only a certain of them have, ...
12
votes
2answers
429 views

How to fill a grid make its total be largest

I have a blank grid whose dimension is 5*5. I want to fill it with some number using 1, 2, 3 and 4. But in every blank space if you fill 2, its neighbor (include four direction, such as left, right,...
12
votes
3answers
357 views

Taking Top K Occurrences

Having millions of numbers in a list, I want to take top K occurrences. MMA Commonest is very slow so I write my own versions: <...
12
votes
3answers
523 views

Map a function of several arguments

I have three lists, e.g. list1 = {{a,b,...}}; list2 = {{1,2},{3,4},...}; list3 = {{x,y},{z,w},...}; and a function ...
12
votes
4answers
400 views

Thread a function over a list and with a non-atomic 2nd parameter?

From the documentation, Thread's behavior on functions where the first parameter is a List and the second is an atomic expression, is this: ...
12
votes
4answers
505 views

How to pass a list of arguments into HoldAll

I have a list of arguments (which in reality is lengthy): arguments = {a, b, c} arguments2 = {a_, b_, c_} f[Sequence@@arguments2] := a + b + c Note: It seems ...
12
votes
5answers
434 views

Faster way to convert triangle list to edge list with no duplicates

I have a list of triangles returned by a Delaunay triangulator, in the following format: ...
12
votes
4answers
579 views

Calculate proportion of values for dates

At work, we were discussing when is it the best time to change to winter tires for bikes and/or cars. Using WeatherData[] and ...
12
votes
3answers
869 views

Delete duplicates in a list, depending on the sequence of numbers

Below, list is a representative sample of my list, which contains lists of integers. I would like to be able to input: ...
12
votes
1answer
609 views

When to use @@@ vs. /@ [duplicate]

So much thanks to Szabolcs in improving sequence.. for complete explanation. I am so glad to read all explanation which fundamentally remove the problem. But in number 4 of its explanation pointed to <...
12
votes
2answers
319 views

What does IndexBy do and how exactly does it work?

I just saw the function IndexBy in the autocomplete suggestions and I was curious to know exactly how it works. Unfortunately, there's no trace of it in the ...
12
votes
2answers
202 views

Faster trimming of leading/trailing zeroes in rectangular array

Given a (large) rectangular array, e.g. (small for example case): ...