A Fun Perfect Square Checker Using Integer Arithmetic Only... ;o) Post: 302952975

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Operating Systems OS X (Apple) A Fun Perfect Square Checker Using Integer Arithmetic Only... ;o) Post 302952975 by Don Cragun on Monday 24th of August 2015 04:50:14 PM

08-24-2015

Registered User

Quote:

Originally Posted by wisecracker

Hi Don...

Phew, that took some reading...

As 0^2 is 0, I never even considered it to be a perfect square so I stand corrected.
My error; however my code can very easily be changed to cater for it.

As you say it is slow, but it was coded from an observation not from any mathematical set of algorithms, that is, every _line_no_ is the perfect square of the odd number series...

Yes, it was a long post. I hope a few people found the narrative informative.

My code rejected 0 since your code didn't process it correctly. If you'd like to modify my script to accept 0, here is a diff showing the changes needed:

Code:

48,49c48,49
< 	    [[ num -lt 1 ]]
< 	then	printf "Out of range: 0 < x <= $LONG_MAX: x=$num\n"
---
> 	    [[ num -lt 0 ]]
> 	then	printf "Out of range: 0 <= x <= $LONG_MAX: x=$num\n"
58c58
< 		low=$((10 ** ((${#num} - 1) / 2)))
---
> 		low=$((10 ** ((${#num} - 1) / 2) - 1))

Your code used the observation that the sum of all of the odd numbers from 0 to x is a perfect square. My code used the observation that the square root of any positive x digit number has a square root between 10^((x-1)/2) and 10^(((x-1)/2)+1)-1 inclusive (except for the number 0 [since 10^0 is 1; not 0]).

Your code starts with the lowest perfect square and calculates successive perfect squares until it has a perfect square that is greater than or equal to the number being checked. My code performs a binary search of the possible square roots that could match the target number until it determines that there is a square root in range that is the square root of the target or determines that one does not exist.

For a 63-bit integer value, your code may need to loop through millions of possible perfect squares. A binary search like my code uses needs to loop through no more than 32 possible square roots. My code needs less than that since it restricts the high and low possible square roots based on the number of digits in the target number.

Don Cragun

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set_color

set_color(1)							       fish							      set_color(1)

NAME

       set_color - set_color - set the terminal color

set_color - set the terminal color
   Synopsis
       set_color [-v --version] [-h --help] [-b --background COLOR] [COLOR]

   Description
       Change the foreground and/or background color of the terminal. COLOR is one of black, red, green, brown, yellow, blue, magenta, purple,
       cyan, white and normal.

       o -b, --background Set the background color

       o -c, --print-colors Prints a list of all valid color names

       o -h, --help Display help message and exit

       o -o, --bold Set bold or extra bright mode

       o -u, --underline Set underlined mode

       o -v, --version Display version and exit

       Calling set_color normal will set the terminal color to whatever is the default color of the terminal.

       Some terminals use the --bold escape sequence to switch to a brighter color set. On such terminals, set_color white will result in a grey
       font color, while set_color --bold white will result in a white font color.

       Not all terminal emulators support all these features. This is not a bug in set_color but a missing feature in the terminal emulator.

       set_color uses the terminfo database to look up how to change terminal colors on whatever terminal is in use. Some systems have old and
       incomplete terminfo databases, and may lack color information for terminals that support it. Download and install the latest version of
       ncurses and recompile fish against it in order to fix this issue.

Version 1.23.1							  Sun Jan 8 2012						      set_color(1)