Improving Quicksort

1. Improving Quicksort

2. Quicksort stack size • Each tree element is the partitioning element • The tree structure does not change with the order of partitioning • However, to traverse the tree the size of the stack may grow significantly in degenerate cases

3. Quicksort stack size • Stack size for 2 random cases and for one degenerate

4. Quicksort stack size Naïve quicksort implementation similar to preorder traversal private void traverseS(Node h) { NodeStack s = new NodeStack(max); s.push(h); while (!s.empty()) { h = s.pop(); h.item.visit(); if (h.r != null) s.push(h.r); if (h.l != null) s.push(h.l); } }

5. Quicksort stack size Naïve case - preorder Stack output A - CB A CED B CEGF D CEGIH F …. Visit the smallest sub-tree first Stack output A - BC A B C DE B D E FG D ….

6. Quicksort stack size (modified book code) static void quicksort(ITEM[] a, int l, int r) { intStack S = new intStack(50); S.push(l); S.push(r); while (!S.empty()) { r = S.pop(); l = S.pop(); if (r <= l) continue; int i = partition(a, l, r); if (i-l > r-i) { S.push(l); S.push(i-1); S.push(i+1); S.push(r);} else { S.push(i+1); S.push(r); S.push(l); S.push(i-1); } } }

7. Small input • It is guaranteed that a recursive sorting method will be called many times with a small input • Goal: become efficient for small inputs • Recursions can be an overhead for small input and do not offer much gain • Observation: insert sort can be efficient for small inputs

8. Small input • Code modifications • Call insert sort when small input if (r-l <= M) insertion(a, l, r); • Leave unsorted (temporarily) if (r-l <= M) return; A partially sorted input will be created O(N) for insert sort

9. Small input • Experimental decision of cutoff threshold M