Skip to main content

Finding a subsequence in a list


I have a list and I want to find (in this particular case the first) appearance of a any of some subsequences, of possible different lengths. None of the subsequences is a subsequence of each other. In my particular case I could do this translating the list to a string and using StringPosition. But I could do it because all elements on my list were one-character-long. Before realizing this I had implemented a not-nearly-one-liner that did the trick without recurring to Strings. It didn't do any useless comparison but it did lots of useless coping of the list as a whole, and it turned out to be 50 times slower than the StringPosition version. It can be improved, avoiding that issue, making it even less one-liner. The task just seems too easy to describe so as to be so not-easy to program well... Is there an efficient way to do it for the general case? "Find the first appearance of one of many subsequences (possible different lengths, perhaps could be patterns, or not) in a list"


(Wow, I think I just thought of a good way, I'll give it a shot... If it works I'll auto-answer. But I'd still like your input, I'm afraid I'm missing some options)



Answer




I asked the same question on StackOverflow recently, and the answer that is now my favourite came from Jan Pöschko (modified):


findSubsequence[list_, {ss__}] := 
ReplaceList[list, {pre___, ss, ___} :> Length[{pre}] + 1]

This will find all positions of ss in list. Example:


findSubsequence[Range[50] ~Mod~ 17, {4, 5, 6}]


{4, 21, 38}




Despite using patterns, this solution runs very quickly, even for packed arrays. Please see the question I linked to for more possibilities.




A potentially useful generalization to other heads may be had with:


findSubsequence[list : h_[__], _[ss__]] :=
ReplaceList[list, h[pre___, ss, ___] :> Length[{pre}] + 1]

Allowing such forms as:


x = Hold[1 + 1, 2 + 1, 3 + 1, 4 + 1, 2 + 1, 3 + 1, 1 + 1, 2 + 1, 3 + 1];

findSubsequence[x, Hold[2 + 1, 3 + 1]]



{2, 5, 8}



Comments

Popular posts from this blog

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.