Problem using big O notation

• MHB
• rayari
In summary, Big O notation is a way to measure the efficiency of an algorithm in terms of time or space as the input size increases. It is important for problem-solving in computer science as it helps us choose the most efficient algorithm for a given problem. It is calculated by looking at the number of operations in relation to the input size and is represented using the uppercase letter "O" followed by parentheses. Some common time complexities include constant, logarithmic, linear, quadratic, and factorial. The time complexity of an algorithm can be determined by counting nested loops or looking at arithmetic/logical operations. The main advantage of Big O notation is the ability to compare algorithms, but it may not consider other factors that can impact performance.
rayari
Functions defines on the plane $\mathbb{R}^2$ or open subsets , using $X=(x_1,x_2)\in\mathbb{R}^2$ asthe coordinates
Find all $\alpha \in \mathbb{R}$ such that $(\ln x_1)(x_2^2+x_2)=O(||X||^{\alpha})$ as $||X||\to 0$.
and $|X|| \to \infty$ (note that $x_1>0)$

It might help to be clear on notation. For instance I assume $||X||^\alpha = (x_1^2 + x_2^2)^{\alpha/2}$. In any case this is interesting, anyone got any ideas?

What is big O notation?

Big O notation is a mathematical notation used to describe the time complexity of an algorithm. It represents the upper bound on the time it takes for an algorithm to run, in terms of the input size.

Why is big O notation important?

Big O notation allows us to analyze the efficiency of an algorithm and compare it to other algorithms. It helps us understand how the algorithm will perform as the input size increases, and allows us to make informed decisions when choosing between different algorithms.

How is big O notation calculated?

Big O notation is calculated by looking at the number of operations an algorithm performs in relation to the input size. It is represented by the letter "O" followed by an expression, such as O(n) or O(n^2), where n is the input size.

What is the difference between best case, worst case, and average case in big O notation?

Best case refers to the minimum number of operations an algorithm will perform for a given input size. Worst case refers to the maximum number of operations an algorithm will perform for a given input size. Average case refers to the average number of operations an algorithm will perform for a given input size. Big O notation typically represents the worst case scenario.

Can big O notation be used for all algorithms?

Big O notation can be used for most algorithms, but there are some cases where it may not accurately represent the time complexity. For example, it may not be suitable for recursive algorithms or algorithms with multiple input variables. In these cases, other notations such as big Omega and big Theta may be more appropriate.

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