I am not a math genius, as any math genius who reviews my work is happy to tell me. Even so, when programming I’m often faced with math challenges where a math education would benefit. My most recent puzzle is how to count the number of digits in a value without first converting the value into a string.
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\nIf you visit this blog regularly, yes, this Lesson hints at an upcoming Exercise challenge. Still, the problem intrigued me: Does some mathematical trick exist that determines how a value such as 12345 contains five digits? Rather than research such a solution, I just started to code. Typical.<\/p>\n
Given the Power of the Computer, I devised a brute-force method to determine the number of digits in a value by subtracting successive powers of 10 from a given number. To ensure that large values are properly processed, I use long<\/em> integer types in the following code:<\/p>\n The Within the for<\/em> loop, a while<\/em> loop compares Within the while<\/em> loop, an if<\/em> statement compares the value submitted, This test works fine, but what I truly adore is generating random numbers to try the code. The problem here is that random values are typically and uniformly huge, so they must be pared down to a smaller length. Such an exercise requires more math magic, at which I confess to being a poor conjurer. Still, I took a stab at it in this update to the code:<\/p>\n Two random values are required to generate a random number of a random length. The first is the value itself, At Line 22, I would bet a whole donut that a better way exists to count the digits in a number. If not a better way, perhaps even a different way that makes more sense. If you know of one, please let me know. I’m not desperate, just curious.<\/p>\n","protected":false},"excerpt":{"rendered":" Does a way exist to count the number of digits in a value without converting the value into a string? Continue reading 2022_08_20-Lesson-a.c<\/a><\/h3>\n
\r\n#include <stdio.h>\r\n\r\nint main()\r\n{\r\n long d;\r\n int x,l;\r\n long value[10] = {\r\n 1, 12, 123, 1234, 12345,\r\n 123456, 1234567, 12345678,\r\n 123456789, 1234567890\r\n };\r\n\r\n for( x=0; x<10; x++ )\r\n {\r\n l=d=1;\r\n while( d<=10000000000 )\r\n {\r\n if( value[x]<d )\r\n {\r\n printf(\"%ld is %d digits long\\n\",value[x],l-1);\r\n break;\r\n }\r\n d*=10;\r\n l++;\r\n }\r\n }\r\n\r\n return(0);\r\n}<\/pre>\nvalue[]<\/code> array holds ten numbers progressing from 1 through 1234567890. A for<\/em> loop churns through each of the values.<\/p>\nvalue[x]<\/code> with successive powers of 10. The looping value d<\/code> starts at one, and multiplies itself by 10 each iteration until its value equals 10,000,000,000.<\/p>\nvalue[x]<\/code>, with d<\/code>, the power of 10. When the value is less, then digit counter variable l<\/code> (little L) determines the number of digits. Here is the output:<\/p>\n1 is 1 digits long
\n12 is 2 digits long
\n123 is 3 digits long
\n1234 is 4 digits long
\n12345 is 5 digits long
\n123456 is 6 digits long
\n1234567 is 7 digits long
\n12345678 is 8 digits long
\n123456789 is 9 digits long
\n1234567890 is 10 digits long<\/code><\/p>\n2022_08_20-Lesson-b.c<\/a><\/h3>\n
\r\n#include <stdio.h>\r\n#include <stdlib.h>\r\n#include <time.h>\r\n#include <math.h>\r\n\r\nint main()\r\n{\r\n long d;\r\n int l,r;\r\n long value;\r\n\r\n \/* seed the randomizer *\/<\/span>\r\n srand( (unsigned)time(NULL) );\r\n\r\n \/* obtain the random value *\/<\/span>\r\n value = rand();\r\n\r\n \/* obtain a random value length *\/<\/span>\r\n r = rand() % 11;\r\n\r\n \/* truncate the value *\/<\/span>\r\n value %= (int)pow(10,r);\r\n\r\n \/*\r\n now count the digits, which will end\r\n up being the same value as 'r', but\r\n what-the-hey\r\n *\/<\/span>\r\n l=d=1;\r\n while( d<=10000000000 )\r\n {\r\n if( value<d )\r\n {\r\n printf(\"%ld is %d digits long\\n\",value,l-1);\r\n break;\r\n }\r\n d*=10;\r\n l++;\r\n }\r\n\r\n return(0);\r\n}<\/pre>\nvalue<\/code> in the above code. The second is the truncating value, r<\/code> above.<\/p>\nvalue<\/code> is truncated by taking r<\/code> to the power of 10, typecasting it as an integer, and using the mod assignment operator, %=<\/code>. This expression reduces the random value<\/code> down to a digit range equal to the value of r<\/code> — which is what the remainder of the code attempts to discover. Still, the point is to try the technique on a random value, and it works:<\/p>\n36398 is 5 digits long
\n9070012 is 7 digits long
\n99086819 is 8 digits long
\n599137240 is 9 digits long
\n4 is 1 digits long<\/code><\/p>\n