1. 在the same as... 结构中，the same 属于主句里面的成分，as 是连词，引导比较从句。

2. as they did = as they slept。

3. the same 既可以是副词作状语（同样地），也可以是代词作宾语或表语（同样的人或物）。本句，由于sleep 是不及物动词，不接宾语，所以the same 用作副词作状语。例如：

作状语：

He behaves the same as before.

作宾语：

I will do the same as you told me to.

作表语：

Driving a boat is not the same as driving a car.  

作定语：(the same 后接名词时)

I have the same idea as you (do).