Improving Quicksort Quicksort stack size Each tree element

  • Slides: 9
Download presentation
Improving Quicksort

Improving Quicksort

Quicksort stack size • Each tree element is the partitioning element • The tree

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

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

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

Quicksort stack size Naïve quicksort implementation similar to preorder traversal private void traverse. S(Node

Quicksort stack size Naïve quicksort implementation similar to preorder traversal private void traverse. S(Node h) { Node. Stack s = new Node. Stack(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); } }

Quicksort stack size Naïve case preorder Visit the smallest sub-tree first Stack output A

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

Quicksort stack size (modified book code) static void quicksort(ITEM[] a, int l, int r)

Quicksort stack size (modified book code) static void quicksort(ITEM[] a, int l, int r) { int. Stack S = new int. Stack(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); } } }

Small input • It is guaranteed that a recursive sorting method will be called

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

Small input • Code modifications – Call insert sort when small input if (r-l

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

Small input • Experimental decision of cutoff threshold M

Small input • Experimental decision of cutoff threshold M