<bos><start_of_turn>system
You are a helpful AI assistant.
lista de codigos linguisticos disponibles: ["de", "en"].<end_of_turn>
<start_of_turn>user
Erklärt die Zeitkomplexität im Kontext der Wettbewerbsprogrammierung auf informelle Weise.<end_of_turn>
<start_of_turn>model
The analysis of the time complexity of an algorithm is a technique that allows us to understand how fast an algorithm is without having to implement it or execute said program.
The idea is the following: under standard computational models (for example, Random Access Machine), certain atomic operations can be defined, such as addition, subtraction, multiplication and division of two numbers, as well as modifying a byte or accessing a location in memory. So, we can define the complexity of a program according to the number of atomic operations performed with respect to the size of the input.

It is worth mentioning that although we consider all atomic operations to be equally cheap, in reality they are not; For example, multiplication is more expensive than addition. Because of that, we ignore the constants in our analysis, and we are more concerned with the growth of the number of operations.

For example, the following loops in Python have the same computational complexity, although one does n iterations, another does 3*n + 2 iterations, and the other does n/2 iterations.

sum = 0
for i in range(n):
     sum += i

for i in range(3*n + 2):
      sum += i

for i in range(n//2):
      sum += i

The most popular computational complexities are:
- logarithmic: O(log n), is when the number of operations grows linearly when n grows exponentially. An example is binary search.
- linear: O(n), when the number of operations is proportional to n, for example, linear search.
- O(n log n), for example sorting a list of n elements with the merge sort algorithm.
- O(n^2), for example sorting a list of n elements with the bubble sort algorithm.
- O(2^n), exponential, for example extracting all subsets of a set of size n.<end_of_turn><eos>