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MATLAB Puzzler: Finding the two closest points

Here is a new MATLAB Puzzler.

Given two vectors representing the X and Y coordinates of some points, find the two closest points in Cartesian space.

n = 10;
x = rand(1,n);
y = rand(1,n);

Brett and I took very different paths to solving this problem, he knows more about the statistics toolbox than I do and found a much shorter solution because there is a function that basically does this. As a benchmark. sticking with base MATLAB, I solved this in seven lines of code.

Post your solutions in the comments area along with how long it took you to solve.

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