Grasping algorithmic notions utilizing a programming language, along with data structures are enough to engage into writing impeccable computer programs and applications.
With a little of experience, a thoughtful programmer would express the need to acquire an extra level of knowledge, so that s/he could assess the quality of the code s/he yields. "How can I prove this program is optimal? How can I criticize it? Can I improve it?" are all questions our talented programmer would pose.
The picturesque case is the previously cited problem "The Towers of Hanoi", which we ascertained it is not easily implementable when opting for an iterative solution, whereas its recursive version is definitely easy. Further, approaching mathematics to "computer algorithms" would allow us to find out that "The Towers of Hanoi" recursive version is extremely expensive in both time and space.
Also, a very fertile algorithm analysis area is the "sorting algorithms". Deducing the time complexity (and sometimes space complexity as well), and inferring if such an algorithm is stable or not, are all aspects discoverable within the field of Algorithm Analysis, indeed.
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