1. Presents a preliminary view of sorting algorithms
Sample Sorts
Presents a preliminary view of sorting algorithms
Bubble Sort
Selection Sort
Serial Sort
Bucket Sort
4/16/2019
CS 303 – Sample Sorts
Lecture 1

2. Bubble Sort for i = 0 to n-2 // not n-1? No!
for j = n-1 downto i // pay attention to limits!
if V[j-1] > V[j] SWAP(j-1,j) // CompareAndSwap
Inner loop is executed:
(n-1) + (n-2) + (n-3) + …
= (n-1)(n/2)
= n2/2 – n/2
= O(n2)
Prove it!
Experiments: [11150,11967]
4/16/2019
CS 303 – Sample Sorts
Lecture 1

3. Selection Sort for i = 0 to n-2 // for each output slot {
best = i // find the best item
for j = i+1 to n-1
if V[best] > V[j] best = j // CompareAndRememberBest??
SWAP(best,i) // put it there }
Optimized version of BubbleSort
Inner loop finds index of smallest element
Fewer SWAPs (exactly n-1), but still O(n2) comparisons
Experiments: [7933,8733]
4/16/2019
CS 303 – Sample Sorts
Lecture 1

4. Serial Sort i = 0 for k = 0 to m-1 // for each value for j = i to n-1
if k == V[j] SWAP(i++,j) // move to the front
Does not use <=
O(n*m)
m = range of values
n = size of input
Experiments: [666,784]
4/16/2019
CS 303 – Sample Sorts
Lecture 1

5. Bucket Sort for t = 0 to m-1 B[t] = 0 // O(m)
for i = 0 to n-1 B[V[i]] // O(n)
i = 0
for t = 0 to m // O(m*n)? no! O(n)
for u = 1 to B[t]
V[i++] = t
Does not use <=
Uses extra space
Does not carry along entire record
O(n+m)
Experiments: [50,67]
4/16/2019
CS 303 – Sample Sorts
Lecture 1

6. Sample Sort Recap Sorts that use <= Bubble, Selection -- O(n2)
Can we do better? Yes, we can get to O(nlogn)
Sorts that “cheat”
Serial -- O(m*n)
Bucket -- O(m+n) time; O(m) space
Experimental results
Bubble Selection Serial Bucket
$ $8300 $ $60
4/16/2019
CS 303 – Sample Sorts
Lecture 1