MATLAB: How many times does each number appear

Question

Let a

 a = 
     1 4
     3 5
     4 7
     6 8

be integer intervals

    [1 2 3 4]
    [3 4 5]
    [4 5 6 7]
    [6 7 8]

I'm looking for an output b to count the number of times each element appears. It is clear that 1 appears one time, 2 appears one time, 3 appears twice, and so on…

So the output b would list the element and how many times it appears:

 b = 
     1 1
     2 1
     3 2
     4 3
     5 2
     6 2
     7 2
     8 1

The challenge is, a is an extremely large nx2 array, so using find even with parallel looping is inefficient. Is there a fast way to yield b given a? If it helps, we can be sure that the elements down the left-hand column of a are sorted, but not necessarily so for the right-hand column. Thanks in advance!

Answer 1

Assuming that the second column of a is always >= the first column of a, then this is an efficient solution.

 mA = max(a(:));
 b = (1:mA)';
 b = [b cumsum(accumarray(a(:,1),1,[mA 1]) + ...
               accumarray(min(a(:,2)+1,mA),-1,[mA 1]))];
 b(end) = b(end) +1;