Runtime analysis

It should be becoming clear that an important aspect to algorithm design is gauging the efficiency both in terms of space (memory) and time (number of operations). This second measure, called runtime performance, is the subject of this section. It should be mentioned that an identical metric is used to measure an algorithm's memory performance. There are a number of ways we could, conceivably, measure run time and probably the most obvious is simply to measure the time the algorithm takes to complete. The major problem with this approach is that the time it takes for an algorithm to run is very much dependent on the hardware it is run on. A platform-independent way to gauge an algorithm's runtime is to count the number of operations involved. However, this is also problematic in that there is no definitive way to quantify an operation. This is dependent on the programming language, the coding style, and how we decide to count operations. We can use this idea, though, of...