# Questions tagged [list-manipulation]

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

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### Shuffle product of two lists

I want to do the following: I have two lists {a_1,...a_n}, {b_1,...,b_n} and I would like to build now all shuffles out of this. This means all unions of these ...
11k 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 ...
3k views

### Looking for a way to insert multiple elements into multiple positions simultaneously in a list

I would like to take the following data: insertValues = {r, x}; insertPositions = {{1}, {5}}; originalList = {a, b, c, d, e, f, g}; and generate output that ...
937 views

### Make a huge vector in a wise way

I need to construct a vector similar to: v[x_]:={0, 0, x, 0, 0, 2*x, 0, 0, 3*x, ....., 0, 0, n*x}; where n=10^9. How can I ...
6k views

### Map and Apply a function on a nested list

I have a list like this: {{1,2}, {4,2}, {6,4} ... } I want to replace every second number with a function of that number. For e.g. ...
1k views

### Combining values in one column (or part) when values in another column (or part) match

Consider the following: ...
1k views

### How do I obtain an intersection of two or more list of lists conditioned on the first element of each sub-list?

Given two lists like list1 = {{1, 1}, {2, 4}, {3, 9}, {4, 16}}; list2 = {{2, 6}, {3, 9}, {4, 12}, {5, 15}}; I would like to produce an output like ...
1k views

### Solving word search puzzles

I am trying to create a code that can identify the following terms in a grid of letters: MATHEMATICA, STACK, EXCHANGE and USERS. ...
4k views

### How to zero (or replace) the diagonal of a square matrix?

Zeroing the diagonal of a square matrix is an operation I need frequently, but somehow I still haven't managed to find an elegant solution that satisfies all these requirements: works with both ...
2k views

### Instruct a Table to only evaluate until a condition is fulfilled

I am looking for the way of building a Table of pairs of numbers in a fast way. My true table evaluates huge functions, and I see no way and reason to show those cumbersome expressions here. Let us ...
3k views

### How do I split up a curve into chords of equal length?

I have a curve that is defined as f[x] and what I'm attempting to do is to divide the curve into equal straight lengths for a number of segments of my choosing that I've defined as nSeg. I've created ...
4k views

### What is the right way to rotate an array?

Suppose I have an array, not necessarily square: a = $\left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} \right)$ I want to rotate it like one ...
4k views

### Pretty way to group elements at odd and even positions

How to make a function that splits list elements by odd and even positions? Shortest implementation wins. I myself came up with: ...
2k views

### Moving maximum function?

How can I construct a moving maximum function? For example, if I have a list of 12 values: { 5, 6, 9, 3, 2, 6, 7, 8, 1, 1, 4, 7 } and I want to maximize over 3 ...
652 views

### How to generate all possible orderless partitions of a list according to another list?

This question is hard to describe in plain text. So I will post an example and a working code (brute force) to illustrate. For example I have a list: ...
1k views

### Implementing a function which generalizes the merging step in merge sort

One of the key steps in merge sort is the merging step. Given two sorted lists sorted1={2,6,10,13,16,17,19}; sorted2={1,3,4,5,7,8,9,11,12,14,15,18,20}; of ...
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### How to use Union on list of lists without sorting them first?

If I do ClearAll[a, d] lsts = {{a, d}, {a, d}}; Union[lsts] I get the expected answer {{a, d}} but if I do ...
2k views

### Accessing list elements by name

First, a bit of a long introduction to my problem: I only have a few weeks of Mathematica experience. I am creating a mathematica application that calculates some material properties of steel based ...
7k views

### How do I use Map for a function with two arguments?

I'm a newbie who tries to be a good boy, and use Map instead of writing out a list of functions. I have a table I want to Map ...
722 views

### What is the best way to flatten a linked list with lists as values?

By following the advice on this site I have ended up with a linked list like the following: acc = {{1, 2}, {{2, 3}, {{3, 4}, {{4, 5}, {{5, 6}, {}}}}}}; This was ...
2k views

### Efficient way to combine SparseArray objects?

I have several SparseArray objects, say sa11, sa12, sa21, sa22, which I would like to combine into the equivalent of {{sa11, sa12}, {sa21, sa22}}. As an example, I ...
2k views

### How to monitor the progress of Map?

I have a function doSomethingComplicated[...] that takes about 10s on average to evaluate. My list, listOfArgs has about 10000 ...
1k views

### Generating Tuples with restrictions

I am interested in a certain subset of all tuples. Generating all with Tuples and then filtering is wasteful, and will "blow up" very quickly. For a concrete ...
5k views

### How do I convert an argument list to a sequence of arguments?

I think this is a basic question, but I am having difficulty finding the answer in the documentation. Thread is not what I am looking for, I think. Suppose that I ...
1k views

### Data Table Manipulation in Mathematica: Step 2

In this previous post (Data Table Manipulation in Mathematica) we find the brilliant suggestion proposed by Leonid Shifrin that allows to select specific rows identified by the header name. I'm now ...
517 views

### Upper bound “Vicious nearest neighbour” algorithm suggestions

I am asking a question based on this question from the sister site MSE. In an effort to make this a self-contained question, I include the fiorst documented posing of the problem by Robert Abilock in ...
1k views

### On generalizing Partition[] (with offsets) to sublists of unequal length

The usual Partition[] function is a very handy little thing: ...
7k views

### Generating a list of numbers that are not multiples of 4

I want to write simple code that will list all numbers from $1$ to $n$ that are not multiples of $4$. And in this case I consider that ...
930 views

### Any built-in function to generate successive sublists from a list?

Given lst = {a, b, c, d} I'd like to generate {{a}, {a, b}, {a, b, c}, {a, b, c, d}} but using built-in functions only, ...
802 views

### How can I remove B -> A from a list if A -> B is in the list?

I have a list of transformations like this: list = {"A" -> "B", "B" -> "A", "C" -> "D"} As this is used to plot an undirected graph with ...
2k views

### How to replace an element in a list based on the value of the next element?

I use Mathematica a little bit. I try to understand it, but it is hard I have a list of 5 numbers selected randomly from 0 and -1. I have to replace a 0 with a 1 when the 0 is followed by -1. My ...
917 views

### How to construct a list of lengths efficiently

Say I have a sorted list of integers RandomInteger[{1, 100000}, 10000] // Sort // Short I want to construct another list whose $m$-th element is the number of ...
4k views

### Finding the period of an array of integers

A simple array of integers is given. The problem is to detect if a pattern is repeatedly occurring in the array, and find the length of that pattern. For example, for ...
3k views

### Recursively appending elements to a list

In wanting to demonstrate the power of Mathematica, I wanted to show my 11-year-old son how we could validate that his sequences homework was correct. We could generate the next value in sequence in a ...
493 views

### Find duplicates in list of InfiniteLine

MMA 10 introduced a new function, which can be very convenient: InfiniteLine. Of course, two infinite lines can be described by different arguments: for example <...
2k views

### How to Set parts of indexed lists?

I would like to assign a list to an indexed variable and then change it using Part and Set like this: ...
576 views

### Is it possible to avoid unpacking when merging Association?

For example, if we have assoc = AssociationThread[{1, 2, 3} -> RandomReal[1., {3, 10}]]; and ...
1k views

### How to delete subsets quickly?

I have some data like this: ...
655 views

### How to enumerate all possible binary associations?

Suppose I have a list of symbols like: {a,b,c,d} I would like to enumerate all possible binary associations (combining symbols and/or sublists pairwise): ...
1k views

### How to remove duplicates from set of machine precision 2D points?

I have a set of 2D points with machine precision coordinates. I need to remove all duplicates. Performance is important. This is the most obvious fast solution: ...
493 views

### Make MapIndexed listable

My goal is to apply MapIndexed to every element of a nested list without destroying the arithmetic operations within the elements. For example, let's start with ...
673 views

### Partition on sublists beginning with a certain marker elements

Say I have the list {{a}, {0, 2, 5}, {5, 4, 1}, {a}, {1, 1, 0}, {1, 4, 2}, {3, 3, 0}, {a}, {3, 2, 0}, {1, 4, 1}} I would like to make sublists of everything ...
2k views

### Generating an Ulam spiral

An Ulam Spiral is quite an interesting construction, revealing unexpected features in the distribution of primes. Here is a related topic with one answer by Pinguin Dirk, who has provided one ...
728 views

### How to find longest monotonic sequence?

I have a list, for example list = {2, 1, 3, 5, 4, 6} How to find longest ascending sequence of this list? There are two meanings of this question: Find the ...
2k views

### Optimising 2D binning code

I have a set of (x,y,z) data, 45,000 to be precise and I want to bin the z values in 256 equidistant bins based on their (x,y) values. The final array should be a set of 256x256 array with each slot ...
517 views

### How do I understand ListCorrelate(contains $\{k_L,k_R\}$) when it works for 2-dimensional data?

Two months ago, I asked a question here And @nikie give me a solution: The intuitive way to understand ListCorrelate is that the kernel is "moved" to every ...
440 views

### Using Sequence to delete a part of an expression

I thought that assigning Sequence[] to a part of an expression is an effective way to remove it. For example, the following code yields ...
744 views

### Simulation of diffusion in a grid

I want to simulate a diffusive process in a 2D grid, for a central initial value of 1 to the adjacent cells initially at 0. At each time step, the value of the +1 level adjacent cells are increased ...