programming-for-dummies

Sequential Search 415
Fibonacci numbers are a series of numbers that are calculated by adding the
last two numbers in a series to determine the next number in the series. So
the first Fibonacci number is 0, the second is 1, the third is 1 (0 + 1), the fourth
is 2 (1 + 1), the fifth is 3 (1 + 2), the sixth is 5 (2 + 3), and so on like this:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on . . . .
Fibonacci numbers tend to occur in nature, such as measuring the branching
of trees or the curves of waves. So the idea behind Fibonacci searching is
rather than divide a list in half, like binary searching, Fibonacci searching
divides a sorted list into progressively smaller lists, based on Fibonacci numbers,
until it finally finds the data or confirms that the data doesn’t exist.
Surprisingly, this method works consistently faster than binary searching.
Fibonacci searching works like this, as shown in Figure 2-6:
Divide list by five (5) items.
18 46 89 93
102 146 198
18 46 89 93 102
Divide list by three (3) items.
Figure 2-6:
Fibonacci
numbers
divide and
search a list
more
efficiently
than a
binary
search.
18 46 89
93 102
93
Divide list by one (1) item.
Fibonacci searching divides a list into parts that correspond to
Fibonacci numbers starting with 5, 3, and finally 1.
Book IV
Chapter 2
1. Determine the size of the sorted list (dubbed n).
2. Find the largest Fibonacci number that’s less than the size of the
sorted list (dubbed p).
3. Examine the value stored at the pth location of the sorted list.
If this value is the one you want to find, stop.
Searching
Algorithms