Numbers with prime digits whose sum is 13/Phix: Difference between revisions
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I decided to keep the main entry simple, and archived this OTT version here:
<!--<lang Phix>(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">unlucky</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">needed</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">={})</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">needed</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">needed</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">unlucky</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">,</span><span style="color: #000000;">needed</span><span style="color: #0000FF;">-</span><span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">+</span><span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">mult</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;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">6</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (see below)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unlucky</span><span style="color: #0000FF;">({</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)),</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"numbers"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">l</span><span style="color: #0000FF;"><</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (ie shortened?)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">m</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"..."</span> <span style="color: #008080;">then</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end for</lang>▼
<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;">"Prime_digit-only numbers summing to %d: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
Originally I thought I wouldn't need to sort the output of unlucky(), but it generates all numbers ending in 7 first, and alas (eg) 355 < 2227, not that it hurts any.
{{out}}
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Based on the algorthim suggested by Nigel Galloway on the [[Talk:Numbers_with_prime_digits_whose_sum_is_13|Talk page]]<br>
I am tempted to replace my original, as this is a bit cleaner and does not require a sort, but it is longer...
<!--<lang Phix>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">digits</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">unlucky</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">part</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">={},</span> <span style="color: #000000;">next</span><span style="color: #0000FF;">={}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">part</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">v</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">part</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">sn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">nv</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">+</span><span style="color: #000000;">d</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">sn</span><span style="color: #0000FF;">=</span><span style="color: #000000;">13</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">nv</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">sn</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">11</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">next</span> <span style="color: #0000FF;">&=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">nv</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sn</span><span style="color: #0000FF;">}}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">next</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">unlucky</span><span style="color: #0000FF;">(</span><span style="color: #000000;">next</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unlucky</span><span style="color: #0000FF;">({{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}}),{</span><span style="color: #004600;">pp_IntFmt</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%7d"</span><span style="color: #0000FF;">})</span>
<!--</lang>-->
<pre>
{ 337, 355, 373, 535, 553, 733, 2227, 2272, 2335,
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Revision as of 00:42, 7 June 2021
Extended Phix version of Numbers_with_prime_digits_whose_sum_is_13#Phix.
I decided to keep the main entry simple, and archived this OTT version here:
with javascript_semantics function unlucky(sequence set, integer needed, atom mult=1, v=0, sequence res={}) if needed=0 then res = append(res,v) elsif needed>0 then for i=length(set) to 1 by -1 do res = unlucky(set,needed-set[i],mult*10,v+set[i]*mult,res) end for end if return res end function for i=6 to 6 do -- (see below) integer p = get_prime(i) sequence r = sort(unlucky({2,3,5,7},p)), s = deep_copy(shorten(r,"numbers",3)) integer l = length(s), m = l<length(r) -- (ie shortened?) for j=1 to l-m do if s[j]!="..." then s[j] = sprintf("%d",s[j]) end if end for printf(1,"Prime_digit-only numbers summing to %d: %s\n",{p,join(s)}) end for
Originally I thought I wouldn't need to sort the output of unlucky(), but it generates all numbers ending in 7 first, and alas (eg) 355 < 2227, not that it hurts any.
- Output:
Prime_digit-only numbers summing to 13: 337 355 373 ... 223222 232222 322222 (43 numbers)
With "for i=1 to 11" you get:
Prime_digit-only numbers summing to 2: 2 Prime_digit-only numbers summing to 3: 3 Prime_digit-only numbers summing to 5: 5 23 32 Prime_digit-only numbers summing to 7: 7 25 52 223 232 322 Prime_digit-only numbers summing to 11: 227 272 335 ... 22322 23222 32222 (19 numbers) Prime_digit-only numbers summing to 13: 337 355 373 ... 223222 232222 322222 (43 numbers) Prime_digit-only numbers summing to 17: 377 557 575 ... 22322222 23222222 32222222 (221 numbers) Prime_digit-only numbers summing to 19: 577 757 775 ... 223222222 232222222 322222222 (468 numbers) Prime_digit-only numbers summing to 23: 2777 7277 7727 ... 22322222222 23222222222 32222222222 (2,098 numbers) Prime_digit-only numbers summing to 29: 35777 37577 37757 ... 22322222222222 23222222222222 32222222222222 (21,049 numbers) Prime_digit-only numbers summing to 31: 37777 55777 57577 ... 223222222222222 232222222222222 322222222222222 (45,148 numbers)
Note that the largest sum-to-37, 322222222222222222, being as it is 18 digits long, exceeds the capacity of a 64-bit float.
Alternative
Based on the algorthim suggested by Nigel Galloway on the Talk page
I am tempted to replace my original, as this is a bit cleaner and does not require a sort, but it is longer...
with javascript_semantics constant digits = {2,3,5,7} function unlucky(sequence part) sequence res={}, next={} for p=1 to length(part) do integer {v,s} = part[p] for i=1 to length(digits) do integer d = digits[i], sn = d+s, nv = v*10+d if sn=13 then res &= nv elsif sn<=11 then next &= {{nv,sn}} end if end for end for if length(next) then res &= unlucky(next) end if return res end function pp(unlucky({{0,0}}),{pp_IntFmt,"%7d"})
{ 337, 355, 373, 535, 553, 733, 2227, 2272, 2335, 2353, 2533, 2722, 3235, 3253, 3325, 3352, 3523, 3532, 5233, 5323, 5332, 7222, 22225, 22252, 22333, 22522, 23233, 23323, 23332, 25222, 32233, 32323, 32332, 33223, 33232, 33322, 52222, 222223, 222232, 222322, 223222, 232222, 322222}