Help needed with matrix in for-loop and output of matrix

Hi, i have a question regarding some tasks to change the content of a matrix. The goal of this operation is to 'clear' a matrix consisting out of 2 columns and a random amount of rows. The operation has to be done using a function-file. The input has to be x = [:,1] and y = [:,2]. After that the first step is to put them together in a matrix A = [x,y] and the rows need to be sorted from lowest to highest value from the first column, B = sortrows(A,1). The problem however is that in the first column the x-values are supposed to be unique with it's matching y-values (2nd column).

So let's say you got a x = [1;3;4;3;2;2;4] and y = [5;1;3;2;9;6;1] which will then transfer into the matrix B = [1,5;2,9;2,6;3,1;3,2;4,3;4,1]. Now as you can see there are several x-values that aren't unique in the first column. The result of this operation should be the next matrix C = [1,5;2,6;3,1;4,1].

1. If an x-value is unique, then it's y-value is the one to be taking.
2. If an x-value is not unique, then the y-value should be the lowest value matching with these x-values.

How can i write a code into a for-loop(?) with these 2 conditions so it can be used for any matrix with n x 2 dimension? This is what i had so far, yet i have no idea if this is anywhere near the solution..

function [ new_matrix ] = matrix( x,y )
 A = [x,y];
 B = sortrows(A,1);
 n = size(B,1);
 for i = 1:1:n
  if B(i,1) == B(i+1,1) && B(i,2) <= B(i+1,2)
      B(i+1,:) = [];
  elseif B(i,1) == B(i+1,1) && B(i,2) >= B(i+1,2)
      B(i,:) = [];
  end
  end

This is an example of how it's supposed to work, but for any matrix with n x 2 dimensions.

%

Answer 1

[Sara]

With x,y column vectors:

 A = [x,y];
 B = sortrows(A,1);
 unique_x = unique(B(:,1));
 new_matrix = zeros(numel(unique_x),2);
 new_matrix(:,1) = unique_x;
 for i = 1:numel(unique_x)
    k = find(B(:,1) == unique_x(i));
    new_matrix(i,2) = min(B(k,2));
 end

[Karsten]

Well that doe seem to work! Thanks alot Sara, much appreciated!