ANALYSIS OF ALGORITHMS

This provides an upper bound on the growth rate. This means f(n) grows at most as fast as g(n), up to a constant factor.

• BIG-O NOTATION

• Big-Omega (ΩΩ) Notation

• Big-Theta (ΘΘ) Notation

This provides a lower bound. This means f(n) grows at least as fast as g(n), up to a constant factor

• BIG-O NOTATION

• Big-Omega (ΩΩ) Notation

• Big-Theta (ΘΘ) Notation

This indicates that two functions grow at the same rate.

• BIG-O NOTATION

• Big-Omega (ΩΩ) Notation

• Big-Theta (ΘΘ) Notation

is to evaluate and compare the efficiency of algorithms, particularly in terms of their performance and scalability as the size of the input data increases.

• TIME AND SPACE COMPLEXITY

• RANDOMIZED AND CIRCUIT COMPLEXITY

• PARAMETER AND DESCRIPTIVE COMPLEXITY

• UNCOMPUTABILITY

an algorithm that incorporates randomness into its decision-making process. This randomness might involve random choices or probabilistic calculations to solve the problem.

• Circuit Algorithm.

• Randomized Algorithm.

• Parameter Algorithm.

• Descriptive Algorithm.

a circuit that represents the problem and minimizes its size or depth. This involves cleverly combining logic gates to achieve the desired computation with the fewest resources.

• Circuit Algorithm.

• Randomized Algorithm.

• Parameter Algorithm

• Descriptive Algorithm.

an algorithm that takes into account a parameter of the problem. This algorithm should run in polynomial time with respect to the size of the input and be efficient with respect to the parameter.

• Circuit Algorithm.

• Randomized Algorithm.

• Parameter Algorithm.

• Descriptive Algorithm.

This translates a computational problem into logical statements using descriptive logic. Then, checks whether these logical statements can be satisfied, indicating a solution to the problem.

• Descriptive Algorithm.

• Parameter Algorithm.

• Randomized Algorithm.

• Circuit Algorithm.