Order of an Algorithm

Bubble sort is an example of an algorithm with quadratic order
- Bubble sort is to do with making comparisons. Therefore for a list of size \(n\), the first pass will take \((n-1)\) comparisons
- Assuming some swaps are made, the next pas will take \((n-2)\) comparisons. This trend continues, and when we expand this final expression out, we get a quadratic. Therefore it has quadratic order
- This means that if a list has size of 10 and it takes 2 seconds to solve, then a list of size 100 will take 200 seconds to solve.

If \(k\) is the factor of how much larger the size of the list is, then:
- Linear order will be \(k\)
- Quadratic order will be \(k^2\)
- Cubic order will be \(k^3\)

Bob's Algorithm: \(\frac{n^3}{100}-3n\) (cubic order)
Terry's Algorithm: \(7000000n^2+40000n\) (quadratic order)

When combining algorithms together, the order is only as big as the largest exponent in any of the orders in the seperate algorithms.