Randomized Algorithm
A randomized algorithm is an algorithm that employs randomness as part of its logic, typically using random numbers to make decisions during execution. This approach can lead to simpler, faster, or more practical solutions compared to deterministic algorithms, especially for complex problems like optimization, approximation, or in distributed systems. Common examples include quicksort with random pivot selection, Monte Carlo methods for numerical integration, and randomized data structures like skip lists.
Developers should learn randomized algorithms when dealing with problems where deterministic solutions are inefficient, intractable, or overly complex, such as in machine learning for stochastic gradient descent, cryptography for generating secure keys, or network protocols for load balancing. They are particularly useful in scenarios where average-case performance is acceptable and worst-case scenarios are rare, offering probabilistic guarantees on correctness or runtime, as seen in algorithms for primality testing or graph algorithms like min-cut.