How to compare the pairs of coordinates most efficiently without using nested loops in Matlab?

问题

If I have 20 pairs of coordinates, whose x and y values are say :

x   y
27  182
180 81
154 52
183 24
124 168
146 11
16  90
184 153
138 133
122 79
192 183
39  25
194 63
129 107
115 161
33  14
47  65
65  2
1   124
93  79

Now if I randomly generate 15 pairs of coordinates (x,y) and want to compare with these 20 pairs of coordinates given above, how can I do that most efficiently without nested loops?

回答1:

If you're trying to see if any of your 15 randomly generated coordinate pairs are equal to any of your 20 original coordinate pairs, an easy solution is to use the function ISMEMBER like so:

oldPts = [...];  %# A 20-by-2 matrix with x values in column 1
                 %#   and y values in column 2
newPts = randi(200,[15 2]);  %# Create a 15-by-2 matrix of random
                             %#   values from 1 to 200
isRepeated = ismember(newPts,oldPts,'rows');

And isRepeated will be a 15-by-1 logical array with ones where a row of newPts exists in oldPts and zeroes otherwise.

回答2:

If your coordinates are 1) actually integers and 2) their span is reasonable (otherwise use sparse matrix), I'll utilize a simple truth table. Like

x_0= [27 180 ...
y_0= [182 81 ...
s= [200 200]; %# span of coordinates
T= false(s);
T(sub2ind(s, x_0, y_0))= true;
%# now obtain some other coordinates
x_1= [...
y_1= [...
%# and common coordinates of (x_0, y_0) and (x_1, y_1) are just
T(sub2ind(s, x_1, y_1))

回答3:

If your original twenty points aren't going to change, you'd get better efficiency if you sorted them O(n log n); then you could see if each random point was in the list with a O(log n) search.

If your "original" points list changes (insertions / deletions), you could get equivalent performance with a binary tree.

BUT: If the number of points you're working with is really as low as in your question, your double loop might just be the fastest method! Algorithms with low Big-O curves will be faster as the amount of data gets really big, but it's often at the cost of a one-time slowdown (in your case, the sort) - and with only 15x20 data points... There won't be a human-perceptible difference; you might see one if you're timing it on your system clock. Or you might not.

Hope this helps!

来源：https://stackoverflow.com/questions/5874105/how-to-compare-the-pairs-of-coordinates-most-efficiently-without-using-nested-lo