title: Position Element Stable Sort
signature: function position_element_stable_sort(arr, n, idx)
test_code: 
  
  -- SOLUTION CODE
  -- ============================================
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  function isCorrect(actual, expected)
      if type(expected) ~= type(actual) then
          return false
      end
      
      if type(expected) == 'table' then
          for k,v_expected in pairs(expected) do
              
              if actual[k] == nil then
                  return false
              end
              local v_actual = actual[k]
              if not isCorrect(v_actual, v_expected) then
                  return false
              end
              actual[k]=nil
          end
      
          if next(actual) then 
              return false
          end
          return true
      else
          return actual == expected
      end
  end
  
  function validateSolution(actual, expected)
      return isCorrect(actual,expected)
  end
  
  function driver(arr, n, idx, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(arr, n, idx) 
      end)
      if status then
          if validateSolution(exec_result,expected) then
              return "PASSED"
          end
          return "FAILED"
      else
          return string.format("ERROR=%s",string.gsub(error_msg,".*:[%d]+: ",""))
      end
  end
      
  function main()
      result = driver({4, 8, 9, 12, 15, 16, 18, 28, 28, 31, 33, 36, 36, 37, 40, 41, 44, 44, 46, 50, 50, 50, 52, 52, 54, 55, 60, 61, 65, 68, 71, 75, 75, 78, 81, 84, 87, 89, 90, 92, 94, 97, 97, 98, 98, 99}, 37, 32, 32)
      print(string.format("TEST-0...%s",result))
  
      result = driver({-16, 86, 94, -86, -38, 64, 96, -64, 94, 10, -10, -62, -50, -46, -62, -32, -4, 72, 14, 36, 74, -66, 46, 82, -44, -22, -26, 16, -8, 0, -90, 94, -50, 22, -82, 8, 92, -84, -34, -36, -66}, 31, 27, 20)
      print(string.format("TEST-1...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 30, 34, 30)
      print(string.format("TEST-2...%s",result))
  
      result = driver({66, 8, 30, 84, 36, 96, 45, 63, 23, 23, 14, 34, 86, 51, 18, 97, 21, 39, 96, 70, 28, 96, 78, 68, 88, 66, 13, 24, 74, 94}, 26, 21, 24)
      print(string.format("TEST-3...%s",result))
  
      result = driver({-94, -90, -86, -86, -72, -72, -58, -50, -32, -22, -18, -10, -4, -2, -2, 0, 0, 6, 14, 22, 22, 36, 36, 40, 44, 58, 60, 70, 70, 76, 82, 82, 84, 88, 96}, 17, 31, 17)
      print(string.format("TEST-4...%s",result))
  
      result = driver({1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1}, 30, 36, 14)
      print(string.format("TEST-5...%s",result))
  
      result = driver({3, 5, 6, 7, 8, 10, 17, 20, 20, 26, 27, 27, 27, 32, 32, 38, 40, 44, 45, 45, 45, 45, 47, 50, 57, 57, 57, 58, 62, 63, 63, 67, 68, 73, 75, 76, 77, 79, 79, 80, 85, 88, 89, 89, 89, 94, 96, 98}, 42, 35, 35)
      print(string.format("TEST-6...%s",result))
  
      result = driver({98, -92, 18, -18, 44, -88, -90, -66, -38, 78, -22, -46, -20, 64, -10, 54}, 14, 12, 7)
      print(string.format("TEST-7...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 19, 31, 19)
      print(string.format("TEST-8...%s",result))
  
      result = driver({14, 17}, 1, 1, 1)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
source_py: def position_element_stable_sort(arr, n, idx):
      result = 0
      for i in range(n):
          if (arr[i] < arr[idx]):
              result += 1
          if ((arr[i] == arr[idx]) and (i < idx)):
              result += 1
      return result
source_cpp: int position_element_stable_sort(vector<int> arr, int n, int idx) {
    int result = 0;
    for ( int i = 0;
    i < n;
    i ++ ) {
      if ( arr [ i ] < arr [ idx ] ) result ++;
      if ( arr [ i ] == arr [ idx ] && i < idx ) result ++;
    }
    return result;
  }