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Identify nearest location and calculate distance

There is probably a simple solution to this but I haven't figure it out yet. I have a table of location ID's with X and Y locations. I need to identify the nearest location and calculate the Euclidean distance to that location.  The distance seems not too onerous but I'm struggling with finding the nearest location. File is attached. Thanks.

Re: Identify nearest location and calculate distance

KD Table() is probably what you need.

 

 @Craige_Hales  has a blog post:Neighbors 

 

Re: Identify nearest location and calculate distance

Picking up on 'KDTable()' mentioned by @Jeff_Perkinson, here's an example:

Names Default To Here( 1 );

n = 100;  // Size of square

// Make a table of x and y locations
dtx = AsTable((1::n)`, << Invisible);
dty = AsTable((1::n)`, << Invisible);
dt = dty << Join( With( dtx ), Cartesian Join );
Close(dtx, NoSave);
Close(dty, NoSave);
Column(dt, 1) << setName("x");
Column(dt, 2) << setName("y");
dt << deleteProperty("Source");
dt << setName("xy Locations");

// Put these locations into a matrix
mat = dt << getAsMatrix;
tbl = KDTable( mat );

// Pick a point in the interior, so we don't need to decide on any boundary conditions
myX = RandomInteger(2, n-1);
myY = RandomInteger(2, n-1);
myRow = Loc(mat[0, 1] == myX & mat[0, 2] == myY);
myRow = myRow[1];

// Find the 8 nearest neighbours to the chosen point
{rows, dist} = tbl << K nearest rows( 8, myRow ); 
Show( myRow, rows );

// Check it worked
myXvals = Column(dt, "x")[myRow];
myYvals = Column(dt, "y")[myRow];
dt << NewColumn("Distance", Numeric, Continuous, Formula(sqrt((:x - myXvals)^2 +(:y - myYvals)^2)));
dt << selectRows(VConcat(myRow, rows`));
gb = dt << Graph Builder(
      Size( 529, 453 ),
      Show Control Panel( 0 ),
      Variables( X( :x ), Y( :y ), Color( :Distance ) ),
      Elements( Points( X, Y, Legend( 5 ) ) )
     );