From 91613683c2767aabdde767c6448b84ce53dfa4b1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Mike=20Schw=C3=B6rer?= Date: Fri, 26 Jan 2018 22:27:22 +0100 Subject: [PATCH] euler - bestof --- www/fragments/blogview_euler_list.php | 17 +++ www/fragments/blogview_euler_single.php | 2 +- www/index.php | 1 - www/pages/blog_view.php | 26 ++-- .../euler/Euler_Problem-043_explanation.md | 116 +++++++++++++++++- 5 files changed, 145 insertions(+), 17 deletions(-) diff --git a/www/fragments/blogview_euler_list.php b/www/fragments/blogview_euler_list.php index 04a5345..781783b 100644 --- a/www/fragments/blogview_euler_list.php +++ b/www/fragments/blogview_euler_list.php @@ -52,6 +52,23 @@ $problems = Euler::listAll(); I recommend using BefunExec. I specially made that interpreter for this project. It can run befunge code with around 6.5 MHz (on my machine)

+

My favorites:

+ + + +

All solved problems

diff --git a/www/fragments/blogview_euler_single.php b/www/fragments/blogview_euler_single.php index 4792acd..f39fbd3 100644 --- a/www/fragments/blogview_euler_single.php +++ b/www/fragments/blogview_euler_single.php @@ -53,7 +53,7 @@ $max = ceil($max / 20) * 20; 'code' => file_get_contents($problem['file_code']), 'url' => $problem['url_raw'], 'interactive' => !$problem['abbreviated'], - 'speed' => $problem['steps'] < 500000 ? 2 : 3, + 'speed' => $problem['steps'] < 15000 ? 1 : ($problem['steps'] < 500000 ? 2 : 3), 'editable' => false, ]; echo require (__DIR__ . '/../fragments/widget_befunge93.php'); diff --git a/www/index.php b/www/index.php index f400d49..0ea2b99 100644 --- a/www/index.php +++ b/www/index.php @@ -185,7 +185,6 @@ try { //TODO better gh widget //TODO remove db table prefixes //TODO euler insert+show 32bit | 64bit mode -//TODO euler best of on top of list (?) //TODO optimize image sizes for display/download (? - auto?) //TODO send cache header (?) //TODO global uncached error logger -> send by mail diff --git a/www/pages/blog_view.php b/www/pages/blog_view.php index 946b69d..daf8842 100644 --- a/www/pages/blog_view.php +++ b/www/pages/blog_view.php @@ -12,31 +12,29 @@ $post = Blog::getBlogpost($id); if ($post === NULL) httpError(404, 'Blogpost not found'); +$isSubEuler = ($post['type'] === 'euler' && $subview !== ''); +$eulerproblem = null; +if ($isSubEuler) +{ + require_once(__DIR__ . '/../internals/euler.php'); + $eulerproblem = Euler::getEulerProblemFromStrIdent($subview); +} +if ($eulerproblem === null) $isSubEuler = false; + ?> - Mikescher.com - Blog + Mikescher.com - <?php echo ($isSubEuler ? $eulerproblem['title'] : $post['title']); ?> - '; - } - else - { - echo ''; - } - ?> + '; ?>
- +
diff --git a/www/statics/euler/Euler_Problem-043_explanation.md b/www/statics/euler/Euler_Problem-043_explanation.md index 4e00d4e..0001ff0 100644 --- a/www/statics/euler/Euler_Problem-043_explanation.md +++ b/www/statics/euler/Euler_Problem-043_explanation.md @@ -7,4 +7,118 @@ The code here was a tight fit into the Befunge-93 80x25 grid, not because of som Here we generate all combinations from the last digit to the first, we significantly limit the amount of possible combinations by checking the constraints for every number. For example we are at `???????410`, we then don't need to evaluate the first 7 digits because constraint 7 is violated (divisibility of d_789 by 17). -This way instead of evaluating `3,628,800` possibilities we only have to look at `1702`. \ No newline at end of file +This way instead of evaluating `3,628,800` possibilities we only have to look at `1702`. + +Pen-and-paper solution +====================== + + +We can rule out a lot of combinations by simply looking at our rules. I divided my thought processes into steps: + +**Step 1:** + + - d_1 != d_2 != d_3 != d_4 != d_5 != d_6 != d_7 != d_8 != d_9 *(palindromic)* + - d_1 is not `0` + - d_234 is divisible by 2 => d_4 is even + - d_345 is divisible by 3 => `(d_3 + d_4 + d_5) % 3 = 0` + - d_456 is divisible by 5 => d_6 is `0` or `5` + - d_567 is divisible by 7 + - d_678 is divisible by 11 + - d_789 is divisible by 13 + - d_89A is divisible by 17 + +**Step 2:** + +if d_6 is `0` then d_678 starts with a `0`, and because d_678 is divisible by 11: `d_7 == d_8`. This conflicts with our palindrome rule. + +Therefore d_6 = `5`. + +**Step 3:** + +d_6 is `5` and d_678 is divisible by 11. There are only 8 possibilities for d_678: + +~~~ +506, 517, 528, 539, 561, 572, 583, 594 +~~~ + +**Step 4:** + +d_789 is divisible by 13, together with the possibilities for d_78 there are only 4 possibilities left for d_6789: + +~~~ +5286, 5390, 5728, 5832 +~~~ + +**Step 5:** + +d_89A is divisible by 17, then we can again - together with the previous result - look at the possibilities for d_6789A: + +~~~ +52867, 53901, 57289 +~~~ + +**Step 6:** + +d_567 is divisible by 7, d_6 is `5` and d_7 is `2`, `3` or `7`. There are now only 2 possible values for d_56789A left: + +~~~ +357289, 952867 +~~~ + +**Step 7:** + +Both values contain `2`, `5`, `7`, `8`, `9`, so d_1 - d_4 can't be any of those + +**Step 8:** + +d_345 is divisible by 3. d_5 is `3 or 9` and d_4 is even and the possible digits are `0`, `1`, `2`, `3`, `4`, `6` and `9` (`9` only for d_5). +The possible values for d_345 are therefore: + +~~~ +063, 069, 309, 603, 609 +~~~ + +And so the possible values for d_3456789A: + +~~~ +06357289, 06952867, 30952867, 60357289, 60952867 +~~~ + +number 2 and 5 are not palindromic, so the numbers left are: + +~~~ +06357289, 30952867, 60357289 +~~~ + +**Step 9:** + +The only numbers left are now `1` and `4` and there are no rules left to consider. +We can now list the resulting numbers by using the 3 numbers from before and every combination of `1` and `4`: + + - 14 06357289 + - 41 06357289 + +---- + + - 14 30952867 + - 41 30952867 + +---- + + - 14 60357289 + - 41 60357289 + +**Step 10:** + +The final step is now to calculate the sum of these numbers: + +~~~ + 1406357289 ++ 4106357289 ++ 1430952867 ++ 4130952867 ++ 1460357289 ++ 4160357289 + += 16695334890 +~~~ \ No newline at end of file