1. Sorting Problem Definition Silly Sort Bubble Sort Selection Sort
Insertion Sort
4/3/2019
CS 303 – Sorting
Lecture 14

2. Sorting Given A sequence of records – V[i]
Key - field to sort on - V[i].key
‘<=‘ - Linear Ordering Relationship (on Keys)
Problem
Arrange records so that Keys are non-decreasing
Generalizations
usually best to sort a list of pointers
system should provide a facility to define ‘<=‘
we’ll use <, <=, >, >= as needed, i.e., V[i].key > V[i+1].key
even better...let’s use Compare(i,j) (and CompareAndSwap(i,j))
4/3/2019
CS 303 – Sorting
Lecture 14

3. Silly Sorts ReallySilly(n) Repeat i  rand(1,i); j  rand(i+1,n)
CompareAndSwap(i,j)
Until Sorted
O(???)
Silly(n)
for i  1 to n /* for each slot */
for j  n downto /* find correct x */
CompareAndSwap(j-1,j)
O(n2)
we can improve this one a bit, to get...
4/3/2019
CS 303 – Sorting
Lecture 14

4. Bubble Sort BubbleSort(n) for i  1 to n-1 /* for each slot */
for j  n downto i /* find correct x */
CompareAndSwap(j-1,j)
O(n2)
Notice that all sorts (so far) have used CompareAndSwap, and have
not taken note of the result of the Compare. They all do the
same comparisons, no matter what the input data.
They are “oblivious”.
4/3/2019
CS 303 – Sorting
Lecture 14

5. Selection Sort SelectionSort(n) for i  0 to n-2
{ /* i are correct */
Best  i
for j  i+1 to n-1 if Compare(j,Best) Best  j
Swap(i,Best) } or
ExchangeSort(n)
for j  i+1 to n-1 CompareAndSwap(i,j)
Which is better? [depends on architecture!]
Which is oblivious?
4/3/2019
CS 303 – Sorting
Lecture 14

6. Insertion Sort InsertionSort(n) for i  1 to n-1
{ /* i-1 are sorted (not “correct”) */
j  i
while CompareAndSwap(j,j-1) j  j-1 }
Beware! This program does not work! Why not?
Demonstrate!
Fix by:
sentinel (use V[0], if available)
add test for j >1 to inner loop (ouch!)
add 1 pass of (say) BubbleSort to swap Min with V[1]
4/3/2019
CS 303 – Sorting
Lecture 14