Binary logarithm
Logarithms in the form log2n are called Binary logarithms or Base 2 logarithms. Base 2 logarithms are frequently written lg n.Algorithms and data structures that are binary in nature, like Binary search trees and binary partition halving, make use of the lg n property. For BSTs, basic dynamic set algorithms can be designed to operate on BSTs in lg n time.
Binary partition halving can split an array in lg n time. As an example, a recursive algorithm can split an array of size n into 2 n/2 arrays. The algorithm can call itself and split those 2 n/2 arrays into 4 n/4 arrays, and so forth. During each iteration i, the size of the input array is n/2i. Assuming that the algorithm ends at array of size 1 (the base case), 2i = n. Using the binary logarithm on 2i, we see that i iterations takes lg n time.
Also, binary algorithms that are multiplied by a linear term are sometimes called linearithmic (n lg n).
Many algorithms grow in lg n or n lg n time. Some examples include:
- average time quicksort
- Binary search trees
- merge sort
- Monge array calculation
- ... many others.
Compare: natural logarithm (Base e), common logarithm (Base 10)
J. K. Henderson of New York, having danced repeatedly with
following Wednesday, when he again danced repeatedly with the same
a four hours' journey during an afternoon in the middle of the week,
began to wonder if a concrete formation, associated with the name of
energetic assault of this nature, supposing it were to be constantly
corner parlor. Dorothy sat in a cane armchair, while Katherine threw
gazed through the open window at the misty infinity beyond.
"Well," sighed Katherine, "this has been the most enjoyable evening I
creditably."
"I didn't know but you might have forgotten the Prince."
"No, I haven't exactly forgotten him, but-- I do think he might have
rather, was our topic of conversation. Still, he might have
you."
"Yes, I suppose it was. I hadn't thought of that."
"Then again, Kate, Russian notions regarding writing to young ladies
live wire."
"Yes, there are many possibilities," murmured Katherine.
On
wordlookup.net
All is still licensed under the GNU FDL.
It uses material from the wikipedia.
|
|