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Sum to 100 (view source)

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→‎{{header|Phix}}: added syntax colouring the hard way, phix/basics
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=={{header|Phix}}==
{{libheader|Phix/basics}}
This is just a trivial count in base 3, with a leading '+' being irrelevant, so from 0(3)000_000_000 to 0(3)122_222_222 which is only (in decimal) 13,122 ...<br>
Admittedly, categorising them into 3429 bins is slightly more effort, but otherwise I am somewhat bemused by all the applescript/javascript/Haskell shenanegins.<br>
<lang Phix>enum SUB=-1, NOP=0, ADD=1
 
<!--<lang Phix>-->
function eval(sequence s)
<span style="color: #008080;">enum</span> <span style="color: #000000;">SUB</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">NOP</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ADD</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span>
integer res = 0, this = 0, op = ADD
for i=1 to length(s) do
<span style="color: #008080;">function</span> <span style="color: #000000;">eval</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
if s[i]=NOP then
<span style="color: #004080;">integer</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tmp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">op</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ADD</span>
this = this*10+i
<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;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
else
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">NOP</span> <span style="color: #008080;">then</span>
res += op*this
<span style="color: #000000;">tmp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tmp</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">+</span><span style="color: #000000;">i</span>
this = i
<span op style="color: s[i]#008080;">else</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">op</span><span style="color: #0000FF;">*</span><span style="color: #000000;">tmp</span>
end if
<span style="color: #000000;">tmp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
end for
<span style="color: #000000;">op</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
return res + op*this
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">op</span><span style="color: #0000FF;">*</span><span style="color: #000000;">tmp</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">show</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</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;">s</span><span style="color: #0000FF;">)</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;">i</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">NOP</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">','</span><span style="color: #0000FF;">-</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">'0'</span><span style="color: #0000FF;">+</span><span style="color: #000000;">i</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;">"%s = %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">eval</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;">procedure</span>
<span style="color: #000080;font-style:italic;">-- Logically this intersperses -/nop/+ between each digit, but you do not actually need the digit.</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">SUB</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (==&gt; ..nop+add*8)</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">done</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">maxl</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">maxr</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">while</span> <span style="color: #008080;">not</span> <span style="color: #000000;">done</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">eval</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd_index</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">solns</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">}:</span><span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">getd_by_index</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">),</span><span style="color: #000000;">s</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">setd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">solns</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">maxl</span><span style="color: #0000FF;"><</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solns</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">maxl</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">maxr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</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;">s</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: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">NOP</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">done</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">ADD</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">SUB</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</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;">"%d solutions considered (dictionary size: %d)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">dict_size</span><span style="color: #0000FF;">()})</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s100</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">100</span><span style="color: #0000FF;">)</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;">"There are %d sums to 100:\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s100</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">papply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">show</span><span style="color: #0000FF;">)</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;">"The positive sum of %d has the maximum number of solutions: %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">maxr</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxl</span><span style="color: #0000FF;">})</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">prev</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">missing</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">key</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000080;font-style:italic;">/*data*/</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000080;font-style:italic;">/*pkey*/</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000080;font-style:italic;">/*user_data=-2*/</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">key</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">prev</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">prev</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">key</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #7060A8;">traverse_dict_partial_key</span><span style="color: #0000FF;">(</span><span style="color: #000000;">missing</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</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;">"The lowest positive sum that cannot be expressed: %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">prev</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">highest</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">top10</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">key</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000080;font-style:italic;">/*data*/</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000080;font-style:italic;">/*user_data*/</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">highest</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">key</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">highest</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">10</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #7060A8;">traverse_dict</span><span style="color: #0000FF;">(</span><span style="color: #000000;">top10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rev</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</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;">"The 10 highest sums: %v\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">highest</span><span style="color: #0000FF;">})</span>
<!--</lang>-->
 
procedure show(sequence s)
string res = ""
for i=1 to length(s) do
if s[i]!=NOP then
res &= ','-s[i]
end if
res &= '0'+i
end for
puts(1,res&" = ")
end procedure
 
-- Logically this intersperses -/nop/+ between each digit, but you do not actually need the digit.
sequence s = repeat(SUB,9) -- (==> ..nop+add*8)
 
bool done = false
integer maxl = 0, maxr
integer count = 0
while not done do
count += 1
integer r = eval(s), k = getd_index(r)
sequence solns = iff(k=0?{s}:append(getd_by_index(k),s))
setd(r,solns)
if r>0 and maxl<length(solns) then
maxl = length(solns)
maxr = r
end if
for i=length(s) to 1 by -1 do
if i=1 and s[i]=NOP then
done = true
exit
elsif s[i]!=ADD then
s[i] += 1
exit
end if
s[i] = SUB
end for
end while
 
printf(1,"%d solutions considered (dictionary size: %d)\n",{count,dict_size()})
 
sequence s100 = getd(100)
printf(1,"There are %d sums to 100:\n",{length(s100)})
for i=1 to length(s100) do
show(s100[i])
?100
end for
 
printf(1,"The positive sum of %d has the maximum number of solutions: %d\n",{maxr,maxl})
 
integer prev = 0
function missing(integer key, sequence /*data*/, integer /*pkey*/, object /*user_data=-2*/)
if key!=prev+1 then
return 0
end if
prev = key
return 1
end function
traverse_dict_partial_key(routine_id("missing"),1)
printf(1,"The lowest positive sum that cannot be expressed: %d\n",{prev+1})
 
sequence highest = {}
function top10(integer key, sequence /*data*/, object /*user_data*/)
highest &= key
return length(highest)<10
end function
traverse_dict(routine_id("top10"),rev:=1)
printf(1,"The 10 highest sums: ") ?highest</lang>
{{Out}}
<pre>
Petelomax
7,804

edits

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