Question

I’m trying to keep track of number of comparison between array elements being made in merge sort. The program is written in Lua. I am trying to use multiple result and keep track of the counter but it isn’t working out. Is there other suggestions?

This is my first post so sorry if it’s messy. Thank you!

function merge_sort (src_array)

  if #src_array <= 1 then 
    return src_array 
  else
   local a1, a2 = split_array(src_array)        -- splitting array to sort
   return merge(            -- merge the results recursively
         merge_sort(a1),    
         merge_sort(a2))
   end
end 

Answer 1

I am trying to use multiple result and keep track of the counter

If you want to do it using multiple results, you’ll need to change your recursive call.
Each function should return a sorted array together with the number of comparisons needed to sort it:

local s1, n1 = merge_sort(a1)
local s2, n2 = merge_sort(a2)
local s, n = merge(s1, s2)
return s, n1 + n2 + n

Your base case will look like

return src_array, 0

I think probably the extra result is not worth it and you are better off with a local counter and a nested merge function:

function merge_sort (src_array)

  local n = 0   -- number of comparisons

  local function merge(a1, a2)
    -- merge a1 and a2, incrementing n at each comparison
    -- return merged array
  end
  local function sort(a)
    if #a <= 1 then 
      return a
    else
      local a1, a2 = split_array(a)        -- splitting array to sort
      return merge(            -- merge the results recursively
            sort(a1),    
            sort(a2)) -- recursive call to `sort` *not* `merge_sort`
    end
  end
  local sorted = sort(src_array)
  return sorted, n
end