Numbers of Armstong WP34s
07-30-2018, 12:58 AM
Post: #8
 Albert Chan Senior Member Posts: 914 Joined: Jul 2018
RE: Numbers of Armstong WP34s
I had solved Armstrong Numbers problem many years ago.

It searched all Armstrong Numbers (digits > 1) in 6 minutes on my laptop.
That is a huge 10^60 search space !

This is the gist of my routine:

If pattern 543 is checked, other permutations (345, 354, 435, 453, 534) can be skipped.
All permutations is going to produce the same sum anyway. So, 1 check = 3! = 6 tests

Digits pattern not reached 3 digits can be skipped: 100 110 111, 200, 210, 211, 220, ..., 432

Sum of over 3-digits can also be skipped: 964, 965, 966, 970, 971 ..., 988, 990, ... 999

Patterns to check = 433, 440, 441 ..., 963 (*)

The trick is to design how the pattern incremented.
You can guess the algorithm from above example.

Have you seen it ?
Combinatorial problem is fun ! :-)

(*) my code actually search to 988
To speed up the code, it need a simple test for endpoint.
So, the loop stop if the next pattern had too many 9's in it.
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 Messages In This Thread Numbers of Armstong WP34s - ggauny@live.fr - 11-30-2015, 07:02 PM RE: Numbers of Armstong WP34s - Thomas Klemm - 11-30-2015, 08:27 PM RE: Numbers of Armstong WP34s - Dave Frederickson - 11-30-2015, 09:21 PM RE: Numbers of Armstong WP34s - ggauny@live.fr - 12-01-2015, 06:35 AM RE: Numbers of Armstong WP34s - Thomas Klemm - 12-01-2015, 10:11 AM RE: Numbers of Armstong WP34s - ggauny@live.fr - 12-01-2015, 11:14 AM RE: Numbers of Armstong WP34s - Thomas Klemm - 12-01-2015, 01:07 PM RE: Numbers of Armstong WP34s - Albert Chan - 07-30-2018 12:58 AM

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