programming-for-dummies

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Comparing Sorting Algorithms
The quick sort algorithm works nearly identically to merge sort, but quick sort
uses a pivot value to pre-sort values into two different lists. Sorting values by
this pivot value alone makes quick sort generally faster than merge sort.
Basically, the quick sort algorithm works likes this:
1. Pick a pivot value from the list.
2. Divide the list in two, placing values less than the pivot value in the
first list and values greater than the pivot value in the second list.
3. Repeat Steps 1 and 2 until the lists contain only one item.
4. Combine these smaller lists into a larger, sorted list.
The key to speeding up the quick sort algorithm is to choose the proper
pivot for dividing each list. The pivot value must be a middle value in a list.
Notice that the merge sort algorithm (see Figure 1-10) still sorts values
through every step whereas pivot values make the quick sort algorithm
(see Figure 1-11) sort the entire list in far fewer steps.
Comparing Sorting Algorithms
To compare the speed of sorting algorithms, computer scientists consider
the following scenarios:
✦ Best-case
✦ Worst-case
✦ Average-case
A best-case scenario measures the speed of different algorithms sorting a
list of values that are already completely sorted. The worst-case scenario
measures the speed of different algorithms sorting a list that’s completely
unsorted. The average-case scenario measures the speed of different algorithms
sorting random values in a list.
To measure the speed and efficiency of an algorithm, computer scientists
measure how much time an algorithm needs to run based on different sizes
of input, which is designated by the letter (n). A small value of (n) means the
input is short whereas a large value of (n) means the input is large.
An algorithm’s efficiency (how fast it runs) is thus based on its input size (n).
In mathematical terms, this is referred to as an order of (n). If an algorithm
runs at the same speed no matter how much data it receives, it’s said to run
at constant time, which can be written in Big-O notation as O(1).