Get indices of all rows containing a value - repeated or not

Say I have the following

id = (1:5)';
rng(1);
x = randperm(10,5)';
y = randperm(10,5)';
nodes = table(id,x,y)
connections = [1,2 ; 1,3 ; 2,4 ; 2,5 ; 3,5]

nodes =

  5×3 table

    id    x    y
    __    _    _

    1     3    6
    2     4    2
    3     7    5
    4     1    3
    5     2    1
    

connections =

     1     2
     1     3
     2     4
     2     5
     3     5

I want to find the distances between the node pairs mentioned in connections (like between nodes 1 and 2, nodes 1 and 3, etc), based on their (x,y) values given in nodes table. And since the original data I have contains about 85000 connections, I'm looking to do this more efficiently than using a for loop for every pair. It works in the following way when the connections are unique:

connections = [1,3 ; 4,5];
x1 = nodes.x(ismember(nodes.id,connections(:,1)));
x2 = nodes.x(ismember(nodes.id,connections(:,2)));
y1 = nodes.y(ismember(nodes.id,connections(:,1)));
y2 = nodes.y(ismember(nodes.id,connections(:,2)));
% Chebyshev distance
dist = max([abs(x2-x1),abs(y2-y1)],[],2);

dist =

     4
     2
     

Thus, distance between nodes 1 and 3, and nodes 4 and 5, is 4 and 2 respectively. How can I do this as efficiently when there are repeated nodes in connections array? In the original case, I believe I should get

dist =

     4
     4
     3
     2
     5

Answer 1

[Bruno Luong]

[c,~,J] = unique(sort(connections,2),'rows');
[i,~,I] = unique(c);
[~,j] = ismember(i, id);
xy = [x(j) y(j)];
I = reshape(I,[],2);
d = max(abs(xy(I(:,1),:)-xy(I(:,2),:)),[],2);
dist = d(J);

[Tejas]

That works great for me. Much faster than a for loop. Thanks!