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Complexity
General way to describe efficiency algorithms (linear vs exponential) indipendent from the computer architecture/speed.
The RAM - random-access machine
Model of computer used in this course.
Has random-access memory.
Basic types and basic operations
Has basic types (like int, float, 64bit words). A basic step is an operation on a basic type (load, store, add, sub, ...). A branch is a basic step. Invoking a function and returning is a basic step as well, but the entire execution takes longer.
Complexity is not measured by the input value but by the input size in bits.
Fibonacci(10) in linear in n (size of the value) but exponential in l
(number of bits in n, or size of the input).
By default, WORST complexity is considered.
Donald Knuth's A-notation
A(c) indicates a quantity that is absolutely at most c
Antonio's weight = (pronounced "is") A(100)
(big-) O-notation
f(n) = O(g(n))
Definition: if f(n) is such that f(n) = k * A(g(n)) for all n sufficiently large and for some constant k > 0, then we say that