Wednesday, August 8, 2007

additional space requirement of quicksort

In-place sorting like quicksort has low space requirement. O(log N) space complexity is considered low. I think it's probably the minimum for comparison-sorts.
Iterative is an alternative to recursive. Iterative lets first call complete before starting 2nd call -- no call stack. Recursive is characterized by a deep call stack (of depth log N). Think onion. Think LIFO.
For any resursive sort, you usually need O(s) space where s = stack-depth. Since most (?) well-known divide-and-conquer sorts involve log N divisions and log N nested calls, space complexity is presumably O(log N)?
Now what's the constant factor in O(log N)? At least the number of local variables defined in the subroutine. Each call on the stack maintains that number of local variables.
"additional" means besides space for the N elements.

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