SORTING ALGORITHMS
bubble sort algorithm
steps
- compare the first two items in the queue
- put the smaller value in extra bin
- move the largest value among the two to the right and replace the value in the bin to the left
why algorithms
- gives us an idea of running time
- helps us decide on the hardware requirements
- helps us decide on what is feasible vs what's not
compare the two
time complexity
time complexity explained
- algorithm working on smaller no of elements = less time taken
- e.g 1 millisecond to work on 5data items 2 (thereabout) milliseconds on 11 data items
- what is the order of growth of an algorithm
how to measure time
- 100 - 10ms
| ITEMS | ALGORITHM1(ms) | ALGORITHM2(ms) |
|---|---|---|
| 200 | 20 | 40 |
| 1000 | 100 | 1000 |
| 10000 | 1000 | 100000 |
prev slide explained
| items | algorithm1(ms) | algorithm2(ms) |
|---|---|---|
| 200 | 20 | 40 |
| 1000 | 100 | 1000 |
| 10000 | 1000 | 100000 |
| linear growth | quadratic growth |
types of time complexity
- Best case
- Average case
- Worst case
ram model of computation
Assumptions made are:
- we have infinite memory
- each operation takes one unit of time
- for each mem access unit time is consumed
Time complexity of bubble sort algorithm (wc)
| 12 | 8 | 7 | 5 | 2 |
|---|
| 8 | 7 | 5 | 2 | 12 |
|---|
| comparison | swap |
|---|---|
| 1 | 3 |
| 1 | 3 |
| 1 | 3 |
| 1 | 3 |
total ops: 16
first pass
| 7 | 5 | 2 | 8 | 12 |
|---|
| comparison | swap |
|---|---|
| 1 | 3 |
| 1 | 3 |
| 1 | 3 |
total ops: 12
second pass
| 5 | 2 | 7 | 8 | 12 |
|---|
| comparison | swap |
|---|---|
| 1 | 3 |
| 1 | 3 |
total ops: 8
third pass
| 2 | 5 | 7 | 8 | 12 |
|---|
| comparison | swap |
|---|---|
| 1 | 3 |
total ops: 4
third pass
16+12+8+4
= 4(4+3+2+1)
= 4 (n-1+ n-2 + ... 3 + 2 + 1)
= 2 * n * (n - 1)
= pn^2 + qn + r