Logarithmic Algorithms, O(log N)

1. A logarithm is the exponent to which a base number must be raised to equal a given number.

2. A log₂N algorithm, seen in line B on the Order of Algorithms graph, is one where the number of steps increases as a function of log₂N. If the number of data was 1024, the number of steps equals log₂1024, or 10 steps since 2¹⁰ = 1024.

3. Algorithms in this category involve splitting the data set in half repeatedly. Several examples will be encountered later in the course.

4. Algorithms that fit in this category are classed as O(log N), regardless of the numerical base used in the analysis.