Powerful numbers: Difference between revisions
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{{libheader|Phix/mpfr}} |
{{libheader|Phix/mpfr}} |
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===priority queue=== |
===priority queue=== |
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Tried a slightly different approach, but it gets 7/10 at best on performance |
Tried a slightly different approach, but it gets 7/10 at best on performance, and simply not worth attempting under pwa/p2js |
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<lang Phix> |
<!--<lang Phix>(notonline)--> |
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<span style="color: #008080;">without</span> <span style="color: #008080;">javascript_semantics</span> |
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<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> |
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integer pq = NULL -- data is the prime powers, eg {2,2} for 2^2*3^2 |
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-- priority is the mpz of that, eg/ie 36 |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">pq</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">NULL</span> <span style="color: #000080;font-style:italic;">-- data is the prime powers, eg {2,2} for 2^2*3^2 |
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-- priority is the mpz of that, eg/ie 36</span> |
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procedure padd(mpz n, np, sequence s) |
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if pq=NULL then |
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">padd</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">np</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> |
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pq = pq_new(MIN_HEAP,routine_id("mpz_cmp")) |
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<span style="color: #008080;">if</span> <span style="color: #000000;">pq</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span> |
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end if |
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<span style="color: #000000;">pq</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">pq_new</span><span style="color: #0000FF;">(</span><span style="color: #004600;">MIN_HEAP</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">routine_id</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"mpz_cmp"</span><span style="color: #0000FF;">))</span> |
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if mpz_cmp(np,n)<=0 then |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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pq_add({s,mpz_init_set(np)},pq) |
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)<=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> |
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end if |
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<span style="color: #7060A8;">pq_add</span><span style="color: #0000FF;">({</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">)},</span><span style="color: #000000;">pq</span><span style="color: #0000FF;">)</span> |
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end procedure |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span> |
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procedure add_next(integer k, mpz n, p, sequence s) |
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mpz np = mpz_init() |
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">add_next</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> |
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integer l = length(s) |
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">np</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span> |
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for i=1 to l do |
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<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> |
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integer ki = iff(s[i]=0?k:1) |
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<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: #000000;">l</span> <span style="color: #008080;">do</span> |
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mpz_ui_pow_ui(np,get_prime(i),ki) |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">ki</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</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: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #000000;">k</span><span style="color: #0000FF;">:</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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mpz_mul(np,np,p) |
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<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</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: #000000;">ki</span><span style="color: #0000FF;">)</span> |
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s[i] += ki |
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<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> |
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padd(n,np,s) |
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<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;">ki</span> |
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s[i] -= ki |
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<span style="color: #000000;">padd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> |
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end for |
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<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;">ki</span> |
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mpz_ui_pow_ui(np,get_prime(l+1),k) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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if l>0 and s[l]=k and s[1..l-1]==repeat(0,l-1) then |
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<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span> |
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padd(n,np,0&s) |
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<span style="color: #008080;">if</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">k</span> <span style="color: #008080;">and</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]==</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
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elsif s={} then |
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<span style="color: #000000;">padd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">np</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> |
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mpz_mul(np,np,p) |
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<span style="color: #008080;">elsif</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">={}</span> <span style="color: #008080;">then</span> |
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padd(n,np,s&k) |
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<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #000000;">np</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> |
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end if |
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<span style="color: #000000;">padd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">np</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> |
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end procedure |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span> |
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function powerful(integer k, mpz n) |
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mpz prevp = mpz_init(1) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">powerful</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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sequence res = {prevp} |
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">prevp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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add_next(k,n,prevp,{}) |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">prevp</span><span style="color: #0000FF;">}</span> |
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while pq_size(pq) do |
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<span style="color: #000000;">add_next</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prevp</span><span style="color: #0000FF;">,{})</span> |
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{sequence s, mpz p} = pq_pop(pq) |
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<span style="color: #008080;">while</span> <span style="color: #7060A8;">pq_size</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pq</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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if mpz_cmp(p,prevp)!=0 then |
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<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;">mpz</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">pq_pop</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pq</span><span style="color: #0000FF;">)</span> |
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res &= p |
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prevp</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> |
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add_next(k,n,p,s) |
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<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">p</span> |
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prevp = p |
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<span style="color: #000000;">add_next</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</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> |
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end if |
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<span style="color: #000000;">prevp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span> |
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end while |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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return res |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">res</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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mpz p = mpz_init(10) |
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for k=2 to 10 do |
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span> |
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mpz_mul_si(p,p,10) |
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span> |
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sequence s = powerful(k,p) |
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<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span> |
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integer l = length(s) |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">powerful</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> |
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for i=1 to 5 do |
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<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> |
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s[i] = mpz_get_str(s[i]) |
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<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: #000000;">5</span> <span style="color: #008080;">do</span> |
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s[-i] = mpz_get_str(s[-i]) |
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<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: #7060A8;">mpz_get_str</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> |
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end for |
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<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: #7060A8;">mpz_get_str</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> |
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s[6..-6] = {"..."} |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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s = join(s,",") |
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<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">6</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"..."</span><span style="color: #0000FF;">}</span> |
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printf(1,"%d %2d-powerful numbers <= 10^%-2d : %s\n",{l,k,k,s}) |
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<span style="color: #000000;">s</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: #008000;">","</span><span style="color: #0000FF;">)</span> |
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end for |
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<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 %2d-powerful numbers <= 10^%-2d : %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</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> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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puts(1,"\n") |
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--Not really fast enough, so only doing to k+5..k+8 for the first 4, but k+9 for last 5 |
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<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span> |
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for k=2 to 10 do |
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<span style="color: #000080;font-style:italic;">--Not really fast enough, so only doing to k+5..k+8 for the first 4, but k+9 for last 5</span> |
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sequence counts = {} |
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span> |
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integer lim = k+min(k+3,9) |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">counts</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
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mpz_set_si(p,1) |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span> |
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for j=0 to lim do |
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<span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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printf(1,"counting (%d/%d)...\r",{j,lim}) |
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lim</span> <span style="color: #008080;">do</span> |
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counts &= length(powerful(k,p)) |
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<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;">"counting (%d/%d)...\r"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">})</span> |
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mpz_mul_si(p,p,10) |
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<span style="color: #000000;">counts</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">powerful</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">))</span> |
|||
end for |
|||
<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span> |
|||
printf(1,"Counts of %2d-powerful numbers <= 10^(0..%d) : %v\n",{k,lim,counts}) |
|||
<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;">"Counts of %2d-powerful numbers <= 10^(0..%d) : %v\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">,</span><span style="color: #000000;">counts</span><span style="color: #0000FF;">})</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
<!--</lang>--> |
|||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 788: | Line 791: | ||
{{trans|Go}} {{trans|Sidef}} |
{{trans|Go}} {{trans|Sidef}} |
||
Significantly faster. The last few counts were wrong when using native ints/atoms, so I went gmp, which means it also works on 32-bit. |
Significantly faster. The last few counts were wrong when using native ints/atoms, so I went gmp, which means it also works on 32-bit. |
||
<lang Phix> |
<!--<lang Phix>(phixonline)--> |
||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
|||
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">powerful</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">k</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: #004080;">mpz</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> |
|||
function powerful(mpz n, integer k, sequence res={}, mpz m=NULL, integer r=0) |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span> |
|||
if m=NULL then |
|||
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
|||
m = mpz_init(1) |
|||
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> |
|||
r = 2*k-1 |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
end if |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;"><</span><span style="color: #000000;">k</span> <span style="color: #008080;">then</span> |
|||
if r<k then |
|||
<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: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_fits_atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)?</span><span style="color: #7060A8;">mpz_get_atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">):</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)))</span> |
|||
res = append(res,iff(mpz_fits_atom(m)?mpz_get_atom(m):mpz_get_str(m))) |
|||
<span style="color: #008080;">else</span> |
|||
else |
|||
<span style="color: #004080;">mpz</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span> |
|||
mpz t = mpz_init() |
|||
<span style="color: #7060A8;">mpz_fdiv_q</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- t := floor(n/m)</span> |
|||
mpz_fdiv_q(t, n, m) -- t := floor(n/m) |
|||
<span style="color: #7060A8;">mpz_nthroot</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- t = floor(rth root of t)</span> |
|||
{} = mpz_root(t,t,r) -- t = floor(rth root of t) |
|||
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">mpz_fits_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
if not mpz_fits_integer(t) then ?9/0 end if |
|||
<span style="color: #004080;">integer</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> |
|||
integer lim = mpz_get_integer(t) |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lim</span> <span style="color: #008080;">do</span> |
|||
for v=1 to lim do |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">k</span> |
|||
if r<=k |
|||
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">square_free</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">mpz_gcd_ui</span><span style="color: #0000FF;">(</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
|||
or (square_free(v) and mpz_gcd_ui(NULL,m,v)=1) then |
|||
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- t:= v^r</span> |
|||
mpz_ui_pow_ui(t,v,r) -- t:= v^r |
|||
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- t*= m</span> |
|||
mpz_mul(t,t,m) -- t*= m |
|||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">powerful</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
|||
res = powerful(n, k, res, t, r-1) |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
end if |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
end for |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
end if |
|||
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span> |
|||
return res |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
end function |
|||
function powercount(mpz n, integer k, mpz m=NULL, integer r=0) |
|||
atom res = 0 |
|||
if m=NULL then |
|||
m = mpz_init(1) |
|||
r = 2*k-1 |
|||
end if |
|||
mpz t = mpz_init() |
|||
mpz_fdiv_q(t, n, m) -- t := floor(n/m) |
|||
{} = mpz_root(t,t,r) -- t = floor(rth root of t) |
|||
if not mpz_fits_integer(t) then ?9/0 end if |
|||
integer lim = mpz_get_integer(t) |
|||
if r<=k then |
|||
res += lim |
|||
else |
|||
for v=1 to lim do |
|||
if square_free(v) and mpz_gcd_ui(NULL,m,v)=1 then |
|||
mpz_ui_pow_ui(t,v,r) -- t:= v^r |
|||
mpz_mul(t,t,m) -- t*= m |
|||
res += powercount(n, k, t, r-1) |
|||
end if |
|||
end for |
|||
end if |
|||
return res |
|||
end function |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">powercount</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">mpz</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> |
|||
atom t0 = time() |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> |
|||
mpz p = mpz_init(10) |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span> |
|||
for k=2 to 10 do |
|||
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
|||
mpz_mul_si(p,p,10) |
|||
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> |
|||
sequence s = sort(powerful(p, k)) |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
integer l = length(s) |
|||
<span style="color: #004080;">mpz</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span> |
|||
s[6..-6] = {"..."} |
|||
<span style="color: #7060A8;">mpz_fdiv_q</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- t := floor(n/m)</span> |
|||
s = ppf(s,{pp_FltFmt,"%d",pp_StrFmt,-1,pp_IntCh,false,pp_Maxlen,100}) |
|||
<span style="color: #7060A8;">mpz_nthroot</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- t = floor(rth root of t)</span> |
|||
printf(1,"%d %2d-powerful numbers <= 10^%-2d : %s\n",{l,k,k,s}) |
|||
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">mpz_fits_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
end for |
|||
<span style="color: #004080;">integer</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> |
|||
puts(1,"\n") |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">k</span> <span style="color: #008080;">then</span> |
|||
for k=2 to 10 do |
|||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">lim</span> |
|||
mpz_set_si(p,1) |
|||
<span style="color: #008080;">else</span> |
|||
sequence counts = {} |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lim</span> <span style="color: #008080;">do</span> |
|||
for j=0 to k+9 do |
|||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">square_free</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">mpz_gcd_ui</span><span style="color: #0000FF;">(</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> |
|||
counts = append(counts, powercount(p, k)) |
|||
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- t:= v^r</span> |
|||
mpz_mul_si(p,p,10) |
|||
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- t*= m</span> |
|||
end for |
|||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">powercount</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
|||
printf(1,"Counts of %2d-powerful numbers <= 10^(0..%d) : %v\n",{k,k+9,counts}) |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
end for |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
?elapsed(time()-t0)</lang> |
|||
<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: #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: #004080;">mpz</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span> |
|||
<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</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: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">powerful</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</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;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">6</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"..."</span><span style="color: #0000FF;">}</span> |
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<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">ppf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,{</span><span style="color: #004600;">pp_FltFmt</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_StrFmt</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_IntCh</span><span style="color: #0000FF;">,</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_Maxlen</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">})</span> |
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<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 %2d-powerful numbers <= 10^%-2d : %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</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> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span> |
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span> |
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<span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">counts</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> |
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">9</span> <span style="color: #008080;">do</span> |
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<span style="color: #000000;">counts</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">counts</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">powercount</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">))</span> |
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<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<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;">"Counts of %2d-powerful numbers <= 10^(0..%d) : %V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">counts</span><span style="color: #0000FF;">})</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<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> |
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<!--</lang>--> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |