Lecture No.16
5.3 Radix Sort
The main shortcoming of counting sort is that it is useful for small integers, i.e., 1..k
where k is small. If k were a million or more, the size of the rank array would also be a
million. Radix sort provides a nice work around this limitation by sorting numbers one
digit at a time.
Here is the algorithm that sorts A[1..n] where each number is d digits long.
Dynamic Programming
6.1 Fibonacci Sequence
Suppose we put a pair of rabbits in a place surrounded on all sides by a wall. How many
pairs of rabbits can be produced from that pair in a year if it is supposed that every month
each pair begets a new pair which from the second month on becomes productive?
Resulting sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, . . . where each number is the
sum of the two preceding numbers.
This problem was posed by Leonardo Pisano, better known by his nickname Fibonacci
(son of Bonacci, born 1170, died 1250). This problem and many others were in posed in
his book Liber abaci, published in 1202. The book was based on the arithmetic and
algebra that Fibonacci had accumulated during his travels. The book, which went on to be
widely copied and imitated, introduced the Hindu-Arabic place-valued decimal system
and the use of Arabic numerals into Europe. The rabbits problem in the third section of
Liber abaci led to the introduction of the Fibonacci numbers and the Fibonacci sequence
for which Fibonacci is best remembered today.
Docsity.com
