The Big O notation

Physics is not a topic in this book, but its influence is far-reaching and powerful enough to be obeyed everywhere, even by virtual constructs such as algorithms! However great their design, they still are constrained by two important factors: time and space.

Time? Whenever anything needs to be done, a sequence of steps is required. By multiplying the number of steps by the time for each step, the total—absolute—time is easy to calculate. Or so we think. For computers, this is mostly true, but many questions make it very hard to really know, since modern CPUs go way beyond what previous generations were able to achieve. Is that only thanks to higher clock rates? What about the additional cores? SIMD? Simply taking the absolute time won't achieve real comparability between algorithms. Maybe the number of steps is what we should use.

Space (as in memory) has become a commodity in many domains over the last few years, even in the embedded space. While the situation has improved...