Early in my career, I got the first three volumes.
The volume on sorting and searching was the most useful, and there the most useful was AVL trees. Next, heap sort and the Gleason bound. Sort-merge? I'd known that already, but if don't then can learn it there. Radix sort? That's what the old punched card machines did; in some cases it's faster than heap sort (doesn't contradict the Gleason bound because that bound assumes that the sorting is from comparing pars, and radix sort doesn't do that). Radix sort could be still be useful in special cases. Lists, queues? Obvious.
The fast Fourier transform remains important, and some of what Knuth writes about it is good and tough to find elsewhere.
Somewhere in those first three volumes are some really good summaries of combinatorial formulas, with some results not easy to find elsewhere.
The volumes give some good examples of how to do the math to evaluate the performance of an algorithm -- might need to do that sometime, e.g., for some guaranteed performance in some embedded system -- and if need to do that then it's far easier to read at least the start on how from Knuth than reinvent it yourself and likely easier than from other sources.
The level of clarity, precision, and quality in Knuth is about as high as those go and a great example for others.
That's most of what I got from those three volumes.
For the later volumes, right, I didn't bother. But, if I have a question that might have an answer in one of those volumes, then, sure, I will eagerly look.
Early in my career, I got the first three volumes.
The volume on sorting and searching was the most useful, and there the most useful was AVL trees. Next, heap sort and the Gleason bound. Sort-merge? I'd known that already, but if don't then can learn it there. Radix sort? That's what the old punched card machines did; in some cases it's faster than heap sort (doesn't contradict the Gleason bound because that bound assumes that the sorting is from comparing pars, and radix sort doesn't do that). Radix sort could be still be useful in special cases. Lists, queues? Obvious.
The fast Fourier transform remains important, and some of what Knuth writes about it is good and tough to find elsewhere.
Somewhere in those first three volumes are some really good summaries of combinatorial formulas, with some results not easy to find elsewhere.
The volumes give some good examples of how to do the math to evaluate the performance of an algorithm -- might need to do that sometime, e.g., for some guaranteed performance in some embedded system -- and if need to do that then it's far easier to read at least the start on how from Knuth than reinvent it yourself and likely easier than from other sources.
The level of clarity, precision, and quality in Knuth is about as high as those go and a great example for others.
That's most of what I got from those three volumes.
For the later volumes, right, I didn't bother. But, if I have a question that might have an answer in one of those volumes, then, sure, I will eagerly look.