Essential Algorithms: A Practical Approach to Computer Algorithms

CHAPTER 2

Numerical Algorithms

Numerical Algorithms calculate numbers. They perform such tasks as randomizing values, breaking numbers into their prime factors, finding greatest common divisors, and computing geometric areas.

All these algorithms are useful occasionally, but they also demonstrate useful algorithmic techniques such as adaptive algorithms, Monte Carlo simulation, and using tables to store intermediate results.

Randomizing Data

Randomization plays an important role in many applications. It lets a program simulate random processes, test algorithms to see how they behave with random inputs, and search for solutions to difficult problems. Monte Carlo integration, which is described in the later section “Performing Numerical Integration,” uses randomly selected points to estimate the size of a complex geometric area.

The first step in any randomized algorithm is generating random numbers.

Generating Random Values

Even though many programmers talk about “random” number generators, any algorithm used by a computer to produce numbers is not truly random. If you knew the details of the algorithm and its internal state, you could correctly predict the “random” numbers it generates.

To get truly unpredictable randomness, you need to use a source other than a computer program. For example, you could use a radiation detector that measures particles coming out of a radioactive sample to generate random numbers. Because no one can predict exactly when the particles will emerge, ...