Upside-down numbers: Difference between revisions
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=={{header|Phix}}==
Finishes instantly
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">get_counts</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">first</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">d</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">first</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">last</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">even</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">*=</span><span style="color: #000000;">9</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">first</span><span style="color: #0000FF;">+</span><span style="color: #000000;">count</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">first</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">first</span><span style="color: #0000FF;">),</span><span style="color: #000000;">last</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">last</span><span style="color: #0000FF;">)}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #008000;">""</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (might as well check)</span>
<span style="color: #008080;">return</span> <span style="color: #008000;">"5"</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">9</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">((</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">kth</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">*</span><span style="color: #000000;">count</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #008000;">'1'</span><span style="color: #0000FF;">+</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">&</span> <span style="color: #0000FF;">(</span><span style="color: #008000;">'9'</span><span style="color: #0000FF;">-</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">get_which</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">nth</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">digits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">first</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">nth</span><span style="color: #0000FF;">></span><span style="color: #000000;">last</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">first</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">last</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #000000;">digits</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">even</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">*=</span><span style="color: #000000;">9</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">first</span><span style="color: #0000FF;">+</span><span style="color: #000000;">count</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">kth</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nth</span><span style="color: #0000FF;">-</span><span style="color: #000000;">first</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">nth</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nth</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"The first 50 upside down numbers:\n%s\n"</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">50</span><span style="color: #0000FF;">),</span><span style="color: #000000;">get_which</span><span style="color: #0000FF;">),</span><span style="color: #000000;">6</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%4s"</span><span style="color: #0000FF;">))</span>
<span style="color: #000080;font-style:italic;">-- Let's just spell it out for you...</span>
<span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"There are %,d %d-digit upside down numbers (the %,d%s to %,d%s)\n"</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">7</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">get_counts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"(etc...)\n\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"The %,d%s upside down number is the %,d%s %d-digit number (%s)\n"</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">w</span> <span style="color: #008080;">in</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">182</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500</span><span style="color: #0000FF;">,</span><span style="color: #000000;">910</span><span style="color: #0000FF;">,</span><span style="color: #000000;">911</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50000000</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">500000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5000000000000</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">50000000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500000000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5000000000000000</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">get_which</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"The total time taken for this onerous and difficult task: %s\n"</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">))</span>
<!--</syntaxhighlight>-->
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<pre>
The first 50 upside down numbers:
5 19 28 37 46 55 64 73 82 91
159 258 357 456 555 654 753 852 951 1199
1289 1379 1469 1559 1649 1739 1829 1919 2198 2288
2378 2468 2558 2648 2738 2828 2918 3197 3287 3377
3467 3557 3647 3737 3827 3917 4196 4286 4376 4466
There are 1 1-digit upside down numbers (the 1st to 1st)
There are 9 2-digit upside down numbers (the 2nd to 10th)
There are 9 3-digit upside down numbers (the 11th to 19th)
There are 81 4-digit upside down numbers (the 20th to 100th)
There are 81 5-digit upside down numbers (the 101st to 181st)
There are 729 6-digit upside down numbers (the 182nd to 910th)
There are 729 7-digit upside down numbers (the 911th to 1,639th)
(etc...)
The 1st upside down number is the 1st 1-digit number (5)
The 2nd upside down number is the 1st 2-digit number (19)
The 10th upside down number is the 9th 2-digit number (91)
The 11th upside down number is the 1st 3-digit number (159)
The 182nd upside down number is the 1st 6-digit number (111999)
The 500th upside down number is the 319th 6-digit number (494616)
The 910th upside down number is the 729th 6-digit number (999111)
The 911th upside down number is the 1st 7-digit number (1115999)
The 5,000th upside down number is the 3,361st 8-digit number (56546545)
The 50,000th upside down number is the 35,239th 10-digit number (6441469664)
The 500,000th upside down number is the 367,141st 12-digit number (729664644183)
The 5,000,000th upside down number is the 3,804,259th 14-digit number (82485246852682)
The 50,000,000th upside down number is the 39,238,321st 16-digit number (9285587463255281)
The 500,000,000th upside down number is the 15,724,390th 19-digit number (1436368345672474769)
The 5,000,000,000th upside down number is the 641,519,500th 21-digit number (269222738456273888148)
The 50,000,000,000th upside down number is the 10,773,675,490th 23-digit number (41835623444566678457296)
The 500,000,000,000th upside down number is the 146,963,079,400th 25-digit number (5724139689945611241796835)
The 5,000,000,000,000th upside down number is the 1,822,667,714,590th 27-digit number (751766588225456588225443953)
The 50,000,000,000,000th upside down number is the 21,404,009,431,300th 29-digit number (94816546925914569158146549261)
The 500,000,000,000,000th upside down number is the 36,744,952,787,041st 32-digit number (12651942383972646483172786195489)
The 5,000,000,000,000,000th upside down number is the 830,704,575,083,359th 34-digit number (1513835774459212468981566335727959)
The total time taken for this onerous and difficult task: 0s
</pre>
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