Earlier chapters described algorithms that solve common problems. Obviously, you will encounter challenges in your programming career that do not fit into any common category, so this chapter presents four algorithmic approaches to solving problems.
Another change in this chapter is its focus on randomness and probability. These were used in previous chapters when analyzing the average-case behavior of algorithms. Here the randomness can become an essential part of an algorithm. Indeed, the probabilistic algorithms we describe are interesting alternatives to deterministic algorithms. Running the same algorithm on the same input at two different times may provide very different answers. Sometimes we will tolerate wrong answers or even claims that no solution was found.
The earlier algorithms in this book solve instances of a problem by giving an exact answer on a sequential, deterministic computer. It is interesting to consider relaxing these three assumptions:
Instead of seeking an exact answer for a problem, accept solutions that are close to, but not necessarily as good as, the true answer.
Instead of being restricted to sequential computation, create multiple computational processes to work simultaneously on subproblem instances.
Instead of computing the same result for a problem instance, use randomized computations to compute an answer. ...
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