This is a command line tool that searches a range of numbers to find the one requiring the most steps to reach a palindromic sum.
A palindromic sum is found by taking the reverse of a number, adding it to the original number, and seeing if the result is a palindrome (the same backwards as it is forwards). If the result is not a palindrome the process is repeated with the sum, until a palindrome is found.
The number 15, for example, requires only one step, since 15 + 51 = 66, which
is a palindrome.
The number 19, however, requires two steps, since 19 + 91 = 110, which is not
a palindrome, but 110 + 11 = 121, which is.
Boost Multiprecision is used for large number support.
C++11 or later is required for thread and lambda expression support.
Catch2 is used for unit testing.
palin [-t n-threads] start end step-limit
Where start is the first number in the range to be searched, end is the
last, and step-limit is the maximum number of steps to try before giving
up.
If start and end are the same number, step-limit will be ignored, and
the program will print out the steps for the number continually until a
palindromic sum is found, or the program is terminated.
The optional argument -t can be given, followed by a number indicating how
many threads should be used. If this argument is not given, the program will
attempt to detect how many threads are available and will use all of them.
The arguments -t 8 100 1000 500, for example, will produce the following
output:
Using 8 threads
100: 1 step
109: 2 steps
156: 3 steps
166: 5 steps
167: 11 steps
177: 15 steps
187: 23 steps
Gave up after 500 steps for 13 out of 901 numbers tested
Largest number of steps found: 23 for the number: 187
1: 187 + 781 = 968
2: 968 + 869 = 1837
3: 1837 + 7381 = 9218
4: 9218 + 8129 = 17347
5: 17347 + 74371 = 91718
6: 91718 + 81719 = 173437
7: 173437 + 734371 = 907808
8: 907808 + 808709 = 1716517
9: 1716517 + 7156171 = 8872688
10: 8872688 + 8862788 = 17735476
11: 17735476 + 67453771 = 85189247
12: 85189247 + 74298158 = 159487405
13: 159487405 + 504784951 = 664272356
14: 664272356 + 653272466 = 1317544822
15: 1317544822 + 2284457131 = 3602001953
16: 3602001953 + 3591002063 = 7193004016
17: 7193004016 + 6104003917 = 13297007933
18: 13297007933 + 33970079231 = 47267087164
19: 47267087164 + 46178076274 = 93445163438
20: 93445163438 + 83436154439 = 176881317877
21: 176881317877 + 778713188671 = 955594506548
22: 955594506548 + 845605495559 = 1801200002107
23: 1801200002107 + 7012000021081 = 8813200023188
Palindromic Sums Copyright © 2022 Steven Saunders
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
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