What textbook on algorithms should be given to a high school student?

Question

Algorithms

Interested in a textbook on the basic primitive algorithms and their implementation on any PL:
- conditions, cycles
- working with arrays (search, sorting)
- counting rows
- recursions
What programming language is used in the book is not important.

Answer 1

"Conditions and cycles" are, nevertheless, not algorithms, but the theory of PL.
And, for the rest, without hesitation, I will recommend the super-classic "Algorithms and Data Structures" by Niklaus Wirth. For fun, in between times, you can throw Warren's Algorithmic Tricks for Programmers.
Well, if it tramples, then move on to heavy artillery, like Cormen and / or Sedgwick. :)

Answer 2

Well, or heavy artillery in the form of Donald Knuth)