How to take a list and build sets of 2 elements without duplicates?

Question

I am new to Mathematica so the answer to this question is probably easy.

I have a list of 2D-points in the form {{x1, y1}, {x2, y2}, ...} Then I have a function that will take two points and test some condition based on their distance. I want to test all points against each other, without duplicates.

How can you do that?

Look up DistanceMatrix[]. "Without duplicates" means you'll only need the strict upper triangle of that matrix. — J. M.'s missing motivation, Jun 25 '16 at 17:28
What about yourCondition/@yourDistanceFunction@@@Permutations[list]? — JungHwan Min, Jun 25 '16 at 17:31
Following @J.M. 's solution, UpperTriangularize[] would be appropriate to use with DistanceMatrix[]. — JungHwan Min, Jun 25 '16 at 17:34
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The answer to the question in the title is given by yode - look at the output from Subsets[Range[4], {2}] — Jason B., Jun 25 '16 at 17:39
Thank you all for your answers. I am going with yodes answer because it seems to be the simplest method for solving this problem. — user41279, Jun 25 '16 at 18:18
related q/a: Calculating the distance between the coordinates in a list and this answer — kglr, Jun 25 '16 at 18:55

score 4 · Answer 1 · edited Apr 13 '17 at 12:55

Based on comment from yode

Let us suppose a list:

list = {{1, 1}, {2, 1}, {7, 8}, {8, 9}}

$\left( \begin{array}{cc} 1 & 1 \\ 2 & 1 \\ 7 & 8 \\ 8 & 9 \\ \end{array} \right)$

With this function you can calculate the distances of each point without repetitions:

EuclideanDistance @@@ Subsets[list, {2}]

$\left\{1,\sqrt{85},\sqrt{113},\sqrt{74},10,\sqrt{2}\right\}$

Here below only a presentation of the steps

EuclideanDistance[list[[2]], list[[1]]]

$1$

EuclideanDistance[list[[3]], list[[1]]]

$\sqrt{85}$

EuclideanDistance[list[[4]], list[[1]]]

$\sqrt{113}$

EuclideanDistance[list[[2]], list[[3]]]

$\sqrt{74}$

EuclideanDistance[list[[2]], list[[4]]]

$10$

EuclideanDistance[list[[3]], list[[4]]]

$\sqrt{2}$

How to take a list and build sets of 2 elements without duplicates?

1 Answers1