title: Maximum Sum Subarray Removing One Element
signature: function maximum_sum_subarray_removing_one_element(arr, n)
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, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(arr, n) 
      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({2, 8, 14, 17, 19, 35, 38, 45, 50, 53, 55, 70, 82, 88, 92, 96}, 13, 488)
      print(string.format("TEST-0...%s",result))
  
      result = driver({-64, -56, -80, -82, 72, 62, -8, 48, -96, 34, 64, -38, -60, 80, 4, -64, -62, 34, 94, -16, 38, 62, -84, 48, 42, -40}, 22, 344)
      print(string.format("TEST-1...%s",result))
  
      result = driver({0, 0, 0, 0, 1, 1, 1}, 6, 2)
      print(string.format("TEST-2...%s",result))
  
      result = driver({3, 7, 50, 53, 72, 14, 18, 74, 27, 65, 41, 20, 54, 17, 87, 40, 63, 15, 47}, 11, 424)
      print(string.format("TEST-3...%s",result))
  
      result = driver({-96, -96, -94, -80, -74, -74, -74, -74, -70, -64, -60, -58, -52, -52, -44, -42, -40, -38, -36, -34, -30, -14, -12, -8, -2, 6, 12, 16, 24, 24, 48, 48, 66, 76, 76, 84, 90}, 32, 178)
      print(string.format("TEST-4...%s",result))
  
      result = driver({1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0}, 8, 7)
      print(string.format("TEST-5...%s",result))
  
      result = driver({4, 4, 5, 9, 11, 13, 13, 15, 16, 21, 23, 25, 27, 30, 31, 35, 35, 43, 43, 47, 49, 50, 52, 54, 55, 55, 57, 57, 57, 59, 62, 64, 66, 68, 69, 71, 73, 76, 80, 84, 88, 88, 90, 90, 97, 97, 99}, 34, 1255)
      print(string.format("TEST-6...%s",result))
  
      result = driver({-86, -60, 4, 14, 6, -6, -50, 46, -50, -62, -56, 16, -76, 90, 40, 2, 36, 48, -26, 34, 78, 84, 2, -54, 94, 60, -26, 60, 84, 2, -98, 2, -74}, 25, 482)
      print(string.format("TEST-7...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1}, 9, 1)
      print(string.format("TEST-8...%s",result))
  
      result = driver({36, 99, 27, 8, 90, 74, 67, 77, 49, 23, 43, 25, 68, 56, 85, 6}, 12, 646)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
source_py: def maximum_sum_subarray_removing_one_element(arr, n):
      fw = [0 for k in range(n)]
      bw = [0 for k in range(n)]
      (cur_max, max_so_far) = (arr[0], arr[0])
      for i in range(n):
          cur_max = max(arr[i], (cur_max + arr[i]))
          max_so_far = max(max_so_far, cur_max)
          fw[i] = cur_max
      cur_max = max_so_far = bw[(n - 1)] = arr[(n - 1)]
      i = (n - 2)
      while (i >= 0):
          cur_max = max(arr[i], (cur_max + arr[i]))
          max_so_far = max(max_so_far, cur_max)
          bw[i] = cur_max
          i -= 1
      fans = max_so_far
      for i in range(1, (n - 1)):
          fans = max(fans, (fw[(i - 1)] + bw[(i + 1)]))
      return fans
source_cpp: int maximum_sum_subarray_removing_one_element(vector<int> arr, int n) {
    int fw [ n ], bw [ n ];
    int cur_max = arr [ 0 ], max_so_far = arr [ 0 ];
    fw [ 0 ] = arr [ 0 ];
    for ( int i = 1;
    i < n;
    i ++ ) {
      cur_max = max ( arr [ i ], cur_max + arr [ i ] );
      max_so_far = max ( max_so_far, cur_max );
      fw [ i ] = cur_max;
    }
    cur_max = max_so_far = bw [ n - 1 ] = arr [ n - 1 ];
    for ( int i = n - 2;
    i >= 0;
    i -- ) {
      cur_max = max ( arr [ i ], cur_max + arr [ i ] );
      max_so_far = max ( max_so_far, cur_max );
      bw [ i ] = cur_max;
    }
    int fans = max_so_far;
    for ( int i = 1;
    i < n - 1;
    i ++ ) fans = max ( fans, fw [ i - 1 ] + bw [ i + 1 ] );
    return fans;
  }