CS 261 - Fall 2009

Sorted List Sets

What is the use of sorting?

• Remember we sorted a dynamic array so that we could use binary search.

• There would seem to be little reason to kept a list is sorted order, since searching still requires an O(n) traversal of all links.

Forshadowing of next topic

• Think carefully about this.• Why can’t we do a binary search on a

list?• (What if we COULD??? Would it be any

better than a binary search on a dynamic array? Why???)

But there was another reason

• But, if you think about it, there is another reason why you might want to keep a collection in order

• That is, an ordered collection allows us to do a very rapid merge operation.

Merge

Idea of merge

• Run down both lists in order• Keep a “finger” pointing to each list.• Always advance the finger that points to

the smaller element• Creates a merge in O(n) time

Set Operations are merge-like

• Each of the set operations are merge-like• Intersection - keep only if found in both lists• Union - keep if found in either, keep only one

copy if found in both• Difference - keep only if found in one• Subset - test each value to see if in second

Example: Intersectionvoid listIntersection (struct list *list1, struct list

*list2, struct list * result) { /* assumes list1 and list2 are sorted and result is

empty */ struct ptr1 = list1->frontSentinel->next; struct ptr2 = list2->frontSentinel->next; while (ptr1 != list1->backSentinel && ptr2 != list2-

>backSentinel) { if (LT(ptr1->value, ptr2->value)) { ptr1 = ptr1->next; } else if (EQ(ptr1->value, ptr2->value)) { listAddBack(result, ptr1->value); ptr1 = ptr1->next; ptr2 = ptr2->next; } else { ptr2 = ptr2->next; }}}

Union just a bit more work

• Union has some extra loops at the end• Can anybody explain why?• What other operations need to do this?

Short day today

• Think about what would be involved in writing the set operations (union, intersection, difference, subset) as a type of merge.

• Not going to do the worksheet today, but maybe a future assignment….