$\star$ We wish to implement a dictionary by using direct addressing on a huge array. At the start, the array entries may contain garbage, and initializing the entire array is impractical because of its size. Describe a scheme for implementing a direct-address dictionary on a huge array. Each stored object should use $\O(1)$ space; the operations
DELETEshould take $\O(1)$ time. (Hint: Use an additional array, treated somewhat like a stack whose size is the number of keys actually stored in the dictionary, to help determine whether a given entry in the huge array is valid or not.)
I don't really understand why this is an exercise - it's far to tricky for the common good. Anyhow.
As the hint suggests, we use an addition stack. Each stack item will contain a pointer in the huge array. Each cell in the huge array will contain the index of the stack item.
INSERT a new item, we push the pointer address in the huge array on
the stack and set the value of that cell to the stack index.
SEARCH, we get the value in the array. If it is a valid stack index
(that is, if the value is $n$, the stack has at most $n$ items) and the value
at that position of the stack is the original pointer, then we have a match.
Otherwise, we don't.
DELETE there would be a hole in the stack. We can fix it by moving
the top item to the hole and updating the value in the huge array.
If we need satellite data, we can keep it in a parallel stack that we also modify on those operations.
There is an elaboration on this algorithm in the Instructor's Manual.