What to read for the programmer to improve serious algorithmic basis in the corporate sector?

Cormen. Algorithms. The construction and analysis of
S. McConnell.Perfect code.
Bentley. Art of computer programming
Tannenbaum. Computer networks

Whip. The art of computer programming.

Normal program

and
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the best book I can advise on parts of the basic algorithms

Excuse me, please, smile :)
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You very correctly advised. Get a job now. Even for a penny. Books will help you, but only if you have experience. Otherwise, no matter how much you read, no matter how much I studied, when you get — will only response a La: "raise it. College boy". There is nothing wrong, but the programmer theorist with no experience is much less valuable than a programmer, read poloniecki, and even that is only about syntax, but rattled off five years in the relevant post.
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You need to read "the literature" but you don't know on what subject. That's the problem.

E. Gamma, R. Helm, R. Johnson, J. Vlissides
Techniques of object-oriented design. Design patterns

The famous "Refactoring" of Fowler — no comments and additional recommendations. "Pearls of programming" Bentley — easy to read and not too bulky a book about serious and interesting things.

Martin. Clean code.
Fowler. Templates of corporate applications

Basic algorithms and concepts:
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Aho, Hopcroft, Ullman. Algorithms and data structures.
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Virt. Algorithms + data Structures = Programs
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Classics on BD:
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Deyt. Introduction to database systems.