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### Re: Re (tilly) 1: Finding sum of all digits from 1 to 1 million.

by PrakashK (Pilgrim)
 on Jan 24, 2002 at 00:59 UTC ( #141024=note: print w/replies, xml ) Need Help??

a good exercise would be to write Perl code that efficiently calculates the sum of all of the digits in a range of integers.
Assuming sum(n) is the sum of all digits from 1 to n, sum_range(m, n) is the sum of all digits from m to n, and m < n, isn't the following true?
```sum_range(m,n) = sum(n) - sum(m)
Or, did I totally get you wrong? /prakash

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Re (tilly) 3: Finding sum of all digits from 1 to 1 million.
by tilly (Archbishop) on Jan 24, 2002 at 01:06 UTC
Off by one error again, your formula drops m from the answer. (And the obvious fix will need more cases if your range potentially includes negative integers.)

But still, you are essentially correct. After some wrapper logic, the problem really does boil down to being able to efficiently calculate the sum of the digits from 1 to n for any positive integer n.

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