merge_sort.m

%% Merge sorting Algorithm:
function y = merge_sort(x)
% function to sort vector 'x' with using the merge sort algorithm
% INPUT: 'x' array
% OUTPUT: sorted array
n = length(x);
if n==1
    y = x;
else
    m = floor(n/2);
    left = merge_sort(x(1:m))    % sorting left part of vector
    right = merge_sort(x(m+1:n)) % sorting right part of vector
    y = merge(left,right)        % with using 'merge' function, 2 part will be merged
end

%% Merge Algorithm:
function z = merge(x,y)
n = length(x); m = length(y); z = zeros(1,n+m);
ix = 1; 
iy = 1; 
for iz=1:(n+m)
    % Deteremin the iz-th value for the merged array.
    if ix > n
        % All done with x-values. Select the next y-value.
        z(iz) = y(iy); iy = iy+1;
    elseif iy > m
        % All done with y-values. Select the next x-value.
        z(iz) = x(ix); ix = ix + 1;
    elseif x(ix) <= y(iy)
        % The next x-value is less than or equal to the next y-value
        z(iz) = x(ix); ix = ix + 1;
    else
        % The next y-value is less than the next x-value
        z(iz) = y(iy); iy = iy + 1;
    end
end