# Questions tagged [sorting]

Questions on the sorting/ordering functions of Mathematica (Sort, SortBy, Ordering, etc.).

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### Character edge finding

The following line of code finds the edge of a character: ...
• 64.4k
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### Sort lists according to the order of another

I have three parallel lists (i.e. the elements in position i of each list are related). I want to sort the first list using the function Sort and make the same ...
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### How to sort colors properly?

I can't seem to be able to sort colors by their hue and perceptual brightness correctly. Here's my current solution, but it's not right; there are all these dark bands: ...
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### Is there a "precedence table" for the canonical Sort ordering?

This answer in which I wrote about the Operator Precedence Table was unexpectedly popular. That got me thinking about similar things, and I am wondering: Does an "ordering table" exist for the ...
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### How do I reassign canonical ordering of symbols?

I have a big polynomial that evaluates to: $$A^2 e^2 \phi ^- \phi ^++A e \phi ^- \phi ^+ c_{2 w} g_Z+\frac{1}{2} A e g h W^- \phi ^+ +\ll13\gg,$$ which is supposed to represent some terms in the ...
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### Sort data after specific ordering (ascending/descending) in multiple columns

I have some data: ...
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### Sort strings by natural ordering

Is there an easy way to sort strings according to their natural ordering? For example a list of file names ...
• 383
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### Sorting a list with secondary criterion

Is there an easy way to sort a list on multiple levels of criteria? By this I mean, first the list should be sorted according by criteria A (the same as using the usual sort function, ...
• 1,227
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### Ordering problem

Let's look at the following example. Ordering[{0, 20 Sqrt[5], 40 Sqrt[5], 20 Sqrt[5], 20 Sqrt[10]} // N] gives the right answer ...
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### Generating an ordered list of pairs of elements from ordered lists

I have a pair of ordered lists. I want to generate a new ordered list (using the same ordering) of length n by applying a binary operator to pairs of elements, one from each list, along with the index ...
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### Unexpected result {".a", "co", ".m"} from Sort[{".m", ".a", "co"}]

I came across the following situation: Evaluating Sort[{".m", ".a", "co"}] Results in {".a", "co", ".m"} I wondering: ...
• 321
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### How to find rows that have maximum value?

Suppose if I have following list { {10,b,30}, {100,a,40}, {1000,b,10}, {1000,b,70}, {100,b,20}, {10,b,70} } How to find rows that have max value in ...
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### Retaining and reusing a one-to-one mapping from a sort

Imagine I sort the elements of an array $Q$ by some means. Perhaps I sort strictly by the elements in the first column, perhaps I use SortBy[...] to sequentially sort by the elements in successive ...
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394 views

### Ordering function with recognition of duplicates

Fairly often I have a need to get the Ordering of an expression but with recognition of duplicates. For example: ...
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### Reproducing a ranking function that behaves like Excel's RANK

I tried to find a function or expression in Mathematica that produces the same output as the RANK function in Excel (see its description here), but unfortunately I ...
• 507
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### FindCurvePath for lines (rather than points)

I have need of a function to find a good ordering for a series of lines, as FindCurvePath does for points. Sample data: ...
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### 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: ...
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496 views

### ls Ordering[Ordering[list]] optimal?

Given a list list with unique elements, the task is to replace each element by its position in Sort[list]. For example, ...
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### Rearrange the list in a specific way

Suppose I have a list like {"e", "c", "a", "d", "b"} and list of rules {1 -> 5, 2 -> 3, 3 -> 1, 4 -> 4, 5 -> 2}. ...
887 views

### Better way to sort course grades

I use the following code to create a histogram of grades. Grades are provided as a List of strings such as "A-", "D+", "E" (don't ask), etc. The +/- substitution hack is necessary to sort the grades ...
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### How can we implement "Sleep Sort"?

Inspired by Implement Sleep Sort: Sleep Sort is an integer sorting algorithm I found on the Internet. It opens an output stream, and for each input numbers in parallel, delay for the number seconds ...
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### Simple algorithm to find cycles in edge list

I have the edge list of an undirected graph which consists of disjoint "cycles" only. Example: {{1, 2}, {2, 3}, {3, 4}, {4, 1}, {5, 6}, {6, 7}, {7, 5}} Each ...
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### Fastest way to combine pre-sorted lists?

I need to combine two long, already-sorted lists into one sorted list. My effort below takes advantage of the fact that the lists are already sorted; but it's far slower than just using Join and Sort,...
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### Lexicographic ordering of lists-of-lists?

I was surprised to discover that Mathematica does not sort lists-of-lists (LLs) lexicographically by default. For example, applying Sort to ...
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I'm trying to use Dataset to explore some large data. I notice that the performance decrease more than 20X by adding heads to the columns. Here is an example: We ...
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### Difference between Sort and SortBy

I was playing with Sort. All examples I have come across so far, i.e Sort[{1, -1, 3, -3, 2, 5}, Abs[#1]<Abs[#2]&] can expressed in a shorter fashion ...
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### Terse Method to Swap Lowest for Highest?

I have built a solution to swap the lowest values with the highest values in a list. With ...
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### Quick QuickSort implementation

I am playing with julialang and loving it, but at the same time noticed that they have a benchmark comparison with Mathematica. I have already submited a better version of ...
• 1,599
284 views

### Ordering Problem With VoronoiMesh

Imagine I want to model 2D cells moving in a tissue. Consider, as an example, Lloyd's relaxation algorithm. Using VoronoiMesh I'm able to mimic some cell movement. ...
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### Sort date list in format DD/MM/YYYY

I have a list of dates (ranging from 2007 to 2012) in the DD/MM/YYYY format and I need to sort this list. My problem is, when I simply use Sort[] I get: ...
• 3,248
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### 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 ...
• 1,159
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### OrderedQ with string arguments

I don't find these results consistent: OrderedQ[{"a", "A"}] True ...
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### Efficiently searching a list for the position of the closest number to a specified number

Searching by closest and position I wasn't able to find an answer—but found Nearest by guessing. Nearest, however, returns ...
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### stable sort for association?

Should I be able to use the "list of functions" approach to getting a stable sort of an association? In 11.1 I see, ...
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### Gather list elements by labels

The following list has some elements that are labeled. For example {1, 2} -> 1, {-1, 3} -> 3, etc: ...
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### How to sort list of mixed types of elements with each type a specified canonical order?

For example, here is a list {{1, "u"}, {6, "d"}, {3, "u"}, {4, "d"}, {2, "u"}, {5, "u"}, {3, "d"}, {1, "d"}, {4, "u"}, {2, "d"}, {5, "d"}, {6, "u"}} The ...
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### Why does Sin[b-a] simplify to -Sin[a-b]?

As I understand it, Mathematica often uses alphabetical order when simplifying expressions. For example, b-a simplifies to -a+b. ...
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### Rearranging a List

I am trying to rearrange/sort a list i.e. {{1,2},{10,140},{43,10},{1,140},{43,2}} into ...
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### SortBy misbehaving?

It maybe a stupid thing in the end but I'm stuck a couple of hours now. I have a list of 2 points on the plane and I want to get the one with the biggest second coordinate. I thought I knew how ...
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### How to pass composite function list to SortBy?

In order to sort alphanumeric-as-string data of the form {"T3", "T14", "T1", "E2"}, so that "T14" comes after ...
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564 views

### Ranking Function Allowing for Ties

I have a list that I need to be able to assign ranks to individual elements in, giving it a number related to its position if the list were to be sorted, allowing for ties. For example, ...
• 111
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### Sorting function for non commuting bosons

I am trying to write a sorting function which will sort expressions involving products of bosonic objects which do not commute. For example, I can have objects like $a,\ a^\dagger,\ b,\ b^\dagger$ ...
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542 views

### Max element of a list with a custom ordering function

I need a function to find max element of a list according to some custom ordering function, assuming that the function implements a total order (elements being compared might not even be numbers). ...
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579 views

### How to generate Intervals from a given list?

If I have a list list={3,7,4,5,1} how to get the List of Intervals /Ranges result = {{1,3},{3,4},{4,5},{5,7}}
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### How to use Intersection[] but keep the original list order

I want to keep the original order of l1: ...
679 views

### Unexpected behavior when using SortBy as a dataset filter

I am still experimenting with datasets. Recently I tried to query the Titanic example to get info on the oldest passengers. Here is what I tried ...
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### Sorting Lists of lists of arbitrary length

I'm trying to sort a list of lists. The sublists are defined in length, but the length of the list containing it varies. A simplified set might be: ...
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### Wolfram Language symbols by their Ranks

I'd like to get the top 50, the bottom 50 and an ordered list of all Wolfram Language symbols based on their "Ranks". With ...
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### On the ordering of the vertices of a polygon

Writing: pts = {{1, 0}, {2, 0}, {2, 3}, {3, 3}, {3, 4}, {0, 4}, {0, 3}, {1, 3}, {1, 0}}; Graphics[{Red, Point[pts], Blue, Line[pts]}] we get: and all of this ...
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