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copied!<p>To reel of the digits from a number, we'd only ever need to do a costly string conversion if we couldnt do a mod, digits can most quickly be pushed of a number like this:</p> <pre><code>feed=number; do { digit=feed%10; feed/=10; //use digit... eg. digitTally[digit]++; } while(feed>0) </code></pre> <p>that loop should be very fast and can just be placed inside a loop of the start to end numbers for the simplest way to tally the digits.</p> <p>To go faster, for larger range of numbers, im looking for an optimised method of tallying all digits from 0 to number*10^significance (from a start to end bazzogles me)</p> <p>here is a table showing digit tallies of some single significant digits.. these are inclusive of 0, but not the top value itself, -that was an oversight but its maybe a bit easier to see patterns (having the top values digits absent here) These tallies dont include trailing zeros, </p> <pre><code> 1 10 100 1000 10000 2 20 30 40 60 90 200 600 2000 6000 0 1 1 10 190 2890 1 2 3 4 6 9 30 110 490 1690 1 0 1 20 300 4000 1 12 13 14 16 19 140 220 1600 2800 2 0 1 20 300 4000 0 2 13 14 16 19 40 220 600 2800 3 0 1 20 300 4000 0 2 3 14 16 19 40 220 600 2800 4 0 1 20 300 4000 0 2 3 4 16 19 40 220 600 2800 5 0 1 20 300 4000 0 2 3 4 16 19 40 220 600 2800 6 0 1 20 300 4000 0 2 3 4 6 19 40 120 600 1800 7 0 1 20 300 4000 0 2 3 4 6 19 40 120 600 1800 8 0 1 20 300 4000 0 2 3 4 6 19 40 120 600 1800 9 0 1 20 300 4000 0 2 3 4 6 9 40 120 600 1800 </code></pre> <blockquote> <p>edit: clearing up my origonal thoughts:</p> <p>from the brute force table showing tallies from 0 (included) to poweroTen(notinc) it is visible that a majordigit of tenpower:</p> </blockquote> <pre><code>increments tally[0 to 9] by md*tp*10^(tp-1) increments tally[1 to md-1] by 10^tp decrements tally[0] by (10^tp - 10) (to remove leading 0s if tp>leadingzeros) can increment tally[moresignificantdigits] by self(md*10^tp) (to complete an effect) </code></pre> <p>if these tally adjustments were applied for each significant digit, the tally should be modified as though counted from 0 to end-1</p> <p>the adjustments can be inverted to remove preceeding range (start number)</p> <p>Thanks Aaronaught for your complete and tested answer.</p>

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