Lef counting aeries (n): he Champernowne word 1234567891011121314151617181920212223., also kno ounting series, is an infinitely long string of digits made up of all positive integers writ scending order without any separators. This function should return the digit at positio hampernowne word. Position counting again starts from zero for us budding computer se f course, the automated tester will throw at your function values of n huge enough that t onstruct the Champernowne word as an explicit string will run out of both time ands efore receiving the answer. Instead, note how the fractal structure of this infinite seque vith 9 single-digit numbers, followed by 90 two-digit numbers, followed by 900 t umbers, and so on. This observation gifts you a pair of seven league boots that allow the kip prefixes of this series in exponential leaps and bounds, instead of having to crawl th he desired position one step at the time with the rest of us. Once you reach the block umbers that contains the position n. the digit there is best determined with integer a erhaps aided by an str conversion for access to digit positions. Expected result

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Up for the count
def counting_series (n):
The Champernowme word 1234567891011121314151617181920212223., also known as the
counting series, is an infinitely long string of digits made up of all positive integers written out in
ascending order without any separators. This function should return the digit at position n of the
Champernowne word. Position counting again starts from zero for us budding computer scientists.
Of course, the automated tester will throw at your function values of n huge enough that those who
construct the Champernowne word as an explicit string will run out of both time and space long
before receiving the answer. Instead, note how the fractal structure of this infinite sequence starts
with 9 single-digit numbers, followed by 90 two-digit numbers, followed by 900 three-digit
numbers, and so on. This observation gifts you a pair of seven league boots that allow their wearer
skip prefixes of this series in exponential leaps and bounds, instead of having to crawl their way to
the desired position one step at the time with the rest of us. Once you reach the block of k-digit
numbers that contains the position n, the digit there is best determined with integer arithmetic,
perhaps aided by an str conversion for access to digit positions.
Expected result
1
10
100
10000
10**100
6
This favourite problem of many past students segues into a more difficult but also more awesome
side quest problem. Define "shy" integers to appear inside the Champernowne word for the first
time only at their first "official appearance", whereas "eager" integers make earlier appearances in
the digit sequence as Frankennumbers stitched together from pieces of lesser numbers. Can you
think up a rule that establishes at a glance that the eight-digit integer 92021222 is muy eager,
whereas its shy successor 92021223 does not reveal her face to the world before her quinceañera?
Transcribed Image Text:Up for the count def counting_series (n): The Champernowme word 1234567891011121314151617181920212223., also known as the counting series, is an infinitely long string of digits made up of all positive integers written out in ascending order without any separators. This function should return the digit at position n of the Champernowne word. Position counting again starts from zero for us budding computer scientists. Of course, the automated tester will throw at your function values of n huge enough that those who construct the Champernowne word as an explicit string will run out of both time and space long before receiving the answer. Instead, note how the fractal structure of this infinite sequence starts with 9 single-digit numbers, followed by 90 two-digit numbers, followed by 900 three-digit numbers, and so on. This observation gifts you a pair of seven league boots that allow their wearer skip prefixes of this series in exponential leaps and bounds, instead of having to crawl their way to the desired position one step at the time with the rest of us. Once you reach the block of k-digit numbers that contains the position n, the digit there is best determined with integer arithmetic, perhaps aided by an str conversion for access to digit positions. Expected result 1 10 100 10000 10**100 6 This favourite problem of many past students segues into a more difficult but also more awesome side quest problem. Define "shy" integers to appear inside the Champernowne word for the first time only at their first "official appearance", whereas "eager" integers make earlier appearances in the digit sequence as Frankennumbers stitched together from pieces of lesser numbers. Can you think up a rule that establishes at a glance that the eight-digit integer 92021222 is muy eager, whereas its shy successor 92021223 does not reveal her face to the world before her quinceañera?
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