By Vasudev Ram
I saw this article on Scientific American about almost-primes today:
What Is an “Almost Prime” Number?
HN thread about it.
I commented, mentioning that groups, rings and fields of mathematics are cool, and underlie many other mathematical areas.
- Vasudev Ram - Online Python training and consultingHit the ground running with my vi quickstart tutorial, vetted by two Windows system administrator friends.Jump to posts: Python * DLang * xtopdfInterested in a Python, SQL or Linux course?Get WP Engine, powerful managed WordPress hosting.Subscribe to my blog (jugad2.blogspot.com) by emailMy ActiveState Code recipes
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Showing posts with label puzzles. Show all posts
Showing posts with label puzzles. Show all posts
Monday, November 5, 2018
Monday, October 22, 2018
Solution for A Python email signature puzzle
By Vasudev Ram
Hi, readers,
Here is the answer to the puzzle in my recent post titled A Python email signature puzzle:
The answer is that the program prints this output:
I'll first mention that there was a mistake in the code in the post, and the fix for it, and will then describe how the code works, below:
In the 5th line of the code, i.e. in the line below the one in which the print keyword appears, the fragment:
Sorry about that.
I''ve reproduced the full (corrected) code below for your convenience:
The outer for loop starts with:
So we can start with the argument to enumerate().
It is a list of 3 tuples.
Each tuple has two items.
The first tuple is:
The second tuple is:
Now that we have evaluated the list of tuples, let's see what the outer for loop does with it. This bit:
Within the outer for loop, the first (and only) statement is the inner for loop, which goes like this:
Since it[1] is successively 1, then 5, then 2, the first time, the inner for loop has 1 iteration, then it has 5 iterations, and finally it has 2 iterations.
For the last part that needs to be explained, i.e. the print statement that is controlled by the inner for statement, I'll reverse direction temporarily, i.e. I'll first go outside in, for the main components of the print statement, then for each detailed part, I'll again go inside out.
The print statement prints the evaluated value of a Python conditional expression. See later in this post for background information about conditional expressions in Python. We can describe the statement and its embedded conditional expression like this in English:
Print some item if a condition is True, else print some other item.
That was the outside in part. Now the inside out part, for the conditional expression in the print statement:
This is the "some item" part:
chr(ord(it[0][::-1][0]) - 2 ** 5) +
it[0][::-1][(1 >> 8) - (2 ** 8 - 1):]
(For display here, I've removed the backslashes that were there at the ends of some lines, since they are only Python syntax to indicate the continuation of a logical line across physical lines.)
The above "some item" can be evaluated like this:
In each of the 3 iterations of the outer loop, it[0] becomes the string which is the first item of each of the 3 tuples.
So it[0] is successively "\n", "larur ylurt", and "\n".
The chr() function returns the ASCII character for its ASCII code (integer) argument, and the ord() function (the inverse of the chr() function), returns the ASCII code for its ASCII character argument. So chr(65) is 'A' and ord('A') is 65, for example.
Also, in the ASCII code, the uppercase letters A-Z are separated from the corresponding lowercase letters 32 positions each.
That is, ord('t') - ord('T') = 32. The same goes for any other lowercase letter and its corresponding uppercase one.
2 ** 5 is 32.
For a given string s, the expression s[::-1] uses Python string slicing to reverse the string.
1 >> 8 is 256, as is 2 ** 8.
The part x % 2 == 1 makes one part of the conditional expression get evaluated in one case,
when the condition is True ((when ix is 1), and the other part get evaluated in the other two cases,
when the condition is False (when ix is 0 or 2).
bin() is a Python built-in function which converts its argument to binary:
The last fragment of the expression for the else part (of the conditional expression), uses string repetition, i.e. the * operator used with a string on the left and an integer on the right, to repeat the string that many times.
Given all the above information, a reader should be able to see (some assembly required) that the program prints the output as shown near the top of the post above, i.e. the string "Truly rural" 5 times, with some number of newlines before and after those 5 lines :)
Here is some background material on conditional expressions in Python:
Python 2 - conditional expressions
Python 3 - conditional expressions
PEP 308
Some examples of the use of conditional expressions, run in the Python shell:
Classifying characters using nested conditional expressionsThe same code on my blog:Using nested conditional expressions to classify characters
- Enjoy.
- Vasudev Ram - Online Python training and consulting
I conduct online courses on Python programming, Unix/Linux (commands and shell scripting) and SQL programming and database design, with personal coaching sessions. See the Training page on my blog.
Contact me for details of course content, terms and schedule.
DPD: Digital Publishing for Ebooks and Downloads.
Hit the ground running with my vi quickstart tutorial. I wrote it at the request of two Windows system administrator friends who were given additional charge of some Unix systems. They later told me that it helped them to quickly start using vi to edit text files on Unix.
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Hi, readers,
Here is the answer to the puzzle in my recent post titled A Python email signature puzzle:
The answer is that the program prints this output:
Truly rural Truly rural Truly rural Truly rural Truly ruralThere are a few blank lines in the output, so I intentionally included them above.
I'll first mention that there was a mistake in the code in the post, and the fix for it, and will then describe how the code works, below:
In the 5th line of the code, i.e. in the line below the one in which the print keyword appears, the fragment:
1 >> 8was a typo; it should really be:
1 << 8i.e. 1 left-shifted by 8, not 1 right-shifted by 8.
Sorry about that.
I''ve reproduced the full (corrected) code below for your convenience:
for ix, it in enumerate([('\n', 2 >> 1), \
("larur ylurt", (8 >> 1) + 1), ('\n', 1 << 1),]):
for tm in range(it[1]):
print chr(ord(it[0][::-1][0]) - 2 ** 5) + \
it[0][::-1][(1 << 8) - (2 ** 8 - 1):] \
if ix % 2 == 1 else it[0] * int(bin(4) \
and bin(1), 2) * ix
Now let's dissect the code a piece at a time to understand how it works:The outer for loop starts with:
for ix, it in enumerate([('\n', 2 >> 1), \
("larur ylurt", (8 >> 1) + 1), ('\n', 1 << 1),]):
When evaluating or figuring out what nested expressions mean, we have to evaluate them from the inside out, because the inner expressions' values need to be first computed in order to be used as terms or arguments in outer ones.So we can start with the argument to enumerate().
It is a list of 3 tuples.
Each tuple has two items.
The first tuple is:
('\n', 2 >> 1)
which evaluates to:('\n', 1)
because2 >> 1equals
1(Right-shifting a number by 1 is the same as dividing it by 2, BTW, and left-shifting a number by 1 is the same as multiplying it by 2. This is for integers. See Arithmetic shift.)
The second tuple is:
("larur ylurt", (8 >> 1) + 1)
which evaluates to:("larur ylurt", 5)
because (8 >> 1) + 1equals
4 + 1The third tuple is:
('\n', 1 << 1)
which evaluates to:('\n', 2)
because1 << 1equals
2So the list of tuples evaluates to:
[('\n', 1), ("larur ylurt", 5), ('\n', 2)]
(BTW, in Python, it is legal (although optional), to put a comma after the last item in a list, before the closing square bracket, as I did in the code. It is a convenience, so that when adding another item to the list later, maybe on the next line, if won't matter if you forget to add a comma before that new item. A bit of defensive programming there. Putting two consecutive commas is illegal, though.)Now that we have evaluated the list of tuples, let's see what the outer for loop does with it. This bit:
for ix, it in enumerate(...)where the ... is a placeholder for the argument to enumerate() (i.e. list of tuples), causes Python to run the block controlled by the outer loop, 3 times (since the list has 3 items), with ix and it set to the successive indices and item of the list, with i going from 0 to 2.
Within the outer for loop, the first (and only) statement is the inner for loop, which goes like this:
for tm in range(it[1]):That creates a loop with tm going from 0 to it[1] - 1 (for each time the outer loop executes), where it[1] is the 2nd item of each tuple, i.e. the number that follows the string. But it[1] varies with each iteration of the outer loop.So the inner for statement effectively runs 3 times (which is not the same as a for loop having 3 iterations). This is because there are 3 tuples in the list looped over by the outer for statement. The index for the inner for loop start at 0 each time, and goes up to the value of it[1] - 1 each time. This is because range(n) gives us 0 to n - 1.
Since it[1] is successively 1, then 5, then 2, the first time, the inner for loop has 1 iteration, then it has 5 iterations, and finally it has 2 iterations.
For the last part that needs to be explained, i.e. the print statement that is controlled by the inner for statement, I'll reverse direction temporarily, i.e. I'll first go outside in, for the main components of the print statement, then for each detailed part, I'll again go inside out.
The print statement prints the evaluated value of a Python conditional expression. See later in this post for background information about conditional expressions in Python. We can describe the statement and its embedded conditional expression like this in English:
Print some item if a condition is True, else print some other item.
That was the outside in part. Now the inside out part, for the conditional expression in the print statement:
This is the "some item" part:
chr(ord(it[0][::-1][0]) - 2 ** 5) +
it[0][::-1][(1 >> 8) - (2 ** 8 - 1):]
(For display here, I've removed the backslashes that were there at the ends of some lines, since they are only Python syntax to indicate the continuation of a logical line across physical lines.)
The above "some item" can be evaluated like this:
In each of the 3 iterations of the outer loop, it[0] becomes the string which is the first item of each of the 3 tuples.
So it[0] is successively "\n", "larur ylurt", and "\n".
The chr() function returns the ASCII character for its ASCII code (integer) argument, and the ord() function (the inverse of the chr() function), returns the ASCII code for its ASCII character argument. So chr(65) is 'A' and ord('A') is 65, for example.
Also, in the ASCII code, the uppercase letters A-Z are separated from the corresponding lowercase letters 32 positions each.
That is, ord('t') - ord('T') = 32. The same goes for any other lowercase letter and its corresponding uppercase one.
2 ** 5 is 32.
For a given string s, the expression s[::-1] uses Python string slicing to reverse the string.
1 >> 8 is 256, as is 2 ** 8.
The part x % 2 == 1 makes one part of the conditional expression get evaluated in one case,
when the condition is True ((when ix is 1), and the other part get evaluated in the other two cases,
when the condition is False (when ix is 0 or 2).
bin() is a Python built-in function which converts its argument to binary:
>>> print bin.__doc__ bin(number) -> string Return the binary representation of an integer or long integer.The values of bin(4) and bin(1) are as below:
>>> bin(4) '0b100' >>> bin(1) '0b1'If you need a clue as to why the and operator in the above expression works the way it does, see the below code snippets:
>>> def foo(n): ... print "in foo, n =", n ... return n ... >>> def bar(m): ... print "in bar, m =", m ... return m ... >>> foo(1) in foo, n = 1 1 >>> bar(2) in bar, m = 2 2 >>> foo(1) and bar(2) in foo, n = 1 in bar, m = 2 2 >>> foo(1) or bar(2) in foo, n = 1 1
The last fragment of the expression for the else part (of the conditional expression), uses string repetition, i.e. the * operator used with a string on the left and an integer on the right, to repeat the string that many times.
Given all the above information, a reader should be able to see (some assembly required) that the program prints the output as shown near the top of the post above, i.e. the string "Truly rural" 5 times, with some number of newlines before and after those 5 lines :)
Here is some background material on conditional expressions in Python:
Python 2 - conditional expressions
Python 3 - conditional expressions
PEP 308
Some examples of the use of conditional expressions, run in the Python shell:
>>> a = 1 >>> b = 1 >>> print 1 if a == b else 2 1 >>> b = 2 >>> print 1 if a == b else 2 2 >>> # A dummy function that considers even-numbered days as fine weather. ... >>> def fine_weather(day): ... return day % 2 == 0 ... >>> for i in range(4): print i, fine_weather(i) ... 0 True 1 False 2 True 3 False >>> for i in range(4): print 'Go out' if fine_weather(i) else 'Stay in' ... Go out Stay in Go out Stay inA Python code recipe example for conditional expressions on my ActiveState Code recipes page (over 90 Python recipes there):
Classifying characters using nested conditional expressionsThe same code on my blog:Using nested conditional expressions to classify characters
- Enjoy.
- Vasudev Ram - Online Python training and consulting
I conduct online courses on Python programming, Unix/Linux (commands and shell scripting) and SQL programming and database design, with personal coaching sessions. See the Training page on my blog.
Contact me for details of course content, terms and schedule.
DPD: Digital Publishing for Ebooks and Downloads.
Hit the ground running with my vi quickstart tutorial. I wrote it at the request of two Windows system administrator friends who were given additional charge of some Unix systems. They later told me that it helped them to quickly start using vi to edit text files on Unix.
Check out WP Engine, powerful WordPress hosting.
Get a fast web site with A2 Hosting.
Creating or want to create online products for sale? Check out ConvertKit, email marketing for online creators.
Own a piece of history:
Legendary American Cookware
Teachable: feature-packed course creation platform, with unlimited video, courses and students.
Posts about: Python * DLang * xtopdf
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Follow me on:
Saturday, October 13, 2018
A Python email signature puzzle
By Vasudev Ram
[ UPDATE: I forgot to escape the less than and greater than signs in the code, so the code was a bit garbled.
Fixed now. My apologies to readers seeing the post twice as a result, via blog aggregators like Planet Python. ]
Hi, readers,
I sometimes use slightly cryptic Python code snippets in my email signature.
Can you figure out what output this Python program produces, and how it works, without running the code?
I folded some logical lines to multiple physical lines so the code does not get truncated.
for ix, it in enumerate([('\n', 2 >> 1), \
("larur ylurt", (8 >> 1) + 1), ('\n', 1 << 1),]):
for tm in range(it[1]):
print chr(ord(it[0][::-1][0]) - 2 ** 5) + \
it[0][::-1][(1 >> 8) - (2 ** 8 - 1):] \
if ix % 2 == 1 else it[0] * int(bin(4) \
and bin(1), 2) * ix
If you could, how long did it take you to solve it?I'll publish the answer in my next post, for those who could not get it.
- Enjoy.
- Vasudev Ram - Online Python training and consulting
I conduct online courses on Python programming, Unix/Linux (commands and shell scripting) and SQL programming and database design, with personal coaching sessions.
Contact me for details of course content, terms and schedule.
Get DPD: Digital Publishing for Ebooks and Downloads.
Hit the ground running with my vi quickstart tutorial. I wrote it at the request of two Windows system administrator friends who were given additional charge of some Unix systems. They later told me that it helped them to quickly start using vi to edit text files on Unix.
Check out WP Engine, powerful WordPress hosting.
Own a piece of history:
Legendary American Cookware
Teachable: feature-packed course creation platform, with unlimited video, courses and students.
Track Conversions and Monitor Click Fraud with Improvely.
Posts about: Python * DLang * xtopdf
My ActiveState Code recipes
Follow me on:
Saturday, March 11, 2017
Analyse this Python code snippet
By Vasudev Ram
Hi reader [1],
Analyze the snippet of Python code below. See what you make of it.
I will discuss it in my next post.
>>> a = 1
>>> lis = [a, 2 ]
>>> lis
[1, 2]
>>> lis = [a, 2 ,
... "abc", False ]
>>>
>>> lis
[1, 2, 'abc', False]
>>> a
1
>>> b = 3
>>> lis
[1, 2, 'abc', False]
>>> a = b
>>> a
3
>>> lis
[1, 2, 'abc', False]
>>> lis = [a, 2 ]
>>> lis
[3, 2]
>>>
[1] This product is suitable for Pythonistas aged 1 to 2 (approximately). For those of higher age, the dose may have no effect :)
- Vasudev Ram - Online Python training and consulting
Are you a blogger with some traffic? Get Convertkit:Email marketing for professional bloggersGet updates (via Gumroad) on my forthcoming apps and content. Jump to posts: Python * DLang * xtopdf Subscribe to my blog by email My ActiveState Code recipesFollow me on: LinkedIn * Twitter
Hi reader [1],
Analyze the snippet of Python code below. See what you make of it.
I will discuss it in my next post.
>>> a = 1
>>> lis = [a, 2 ]
>>> lis
[1, 2]
>>> lis = [a, 2 ,
... "abc", False ]
>>>
>>> lis
[1, 2, 'abc', False]
>>> a
1
>>> b = 3
>>> lis
[1, 2, 'abc', False]
>>> a = b
>>> a
3
>>> lis
[1, 2, 'abc', False]
>>> lis = [a, 2 ]
>>> lis
[3, 2]
>>>
[1] This product is suitable for Pythonistas aged 1 to 2 (approximately). For those of higher age, the dose may have no effect :)
- Vasudev Ram - Online Python training and consulting
Are you a blogger with some traffic? Get Convertkit:Email marketing for professional bloggersGet updates (via Gumroad) on my forthcoming apps and content. Jump to posts: Python * DLang * xtopdf Subscribe to my blog by email My ActiveState Code recipesFollow me on: LinkedIn * Twitter
Saturday, June 20, 2015
What is the meaning of this number? 3735928559
By Vasudev Ram
Saw this tweet by Raymond Hettinger (@raymondh), Python core developer:
Pop quiz: Whenever you see the number 3735928559 in your output, there is probably an error in the code. What is special about this number?
So I took a guess: converted the number to hexadecimal:
How do you like that little critter at the top of the post?
I call him PyBug. Drawn impromptu, for this post, by:
- Yours truly,
- Vasudev Ram - Online Python training and programming Dancing Bison EnterprisesSignup to hear about new products or services that I create. Posts about Python Posts about xtopdf Contact Page
Saw this tweet by Raymond Hettinger (@raymondh), Python core developer:
Pop quiz: Whenever you see the number 3735928559 in your output, there is probably an error in the code. What is special about this number?
So I took a guess: converted the number to hexadecimal:
>>> print hex(3735928559)and sure enough, it printed out:
0xdeadbeefLHere is the reverse conversion, from hexadecimal to decimal:
>>> print int('0xDEADBEEF', 16)
3735928559
Also see: hexspeakHow do you like that little critter at the top of the post?
I call him PyBug. Drawn impromptu, for this post, by:
- Yours truly,
- Vasudev Ram - Online Python training and programming Dancing Bison EnterprisesSignup to hear about new products or services that I create. Posts about Python Posts about xtopdf Contact Page
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