Permutations/Derangements: Difference between revisions
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=={{header|Phix}}== |
=={{header|Phix}}== |
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{{libheader|Phix/mpfr}} |
{{libheader|Phix/mpfr}} |
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<lang Phix> |
<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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for i=1 to length(s1) do |
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<span style="color: #008080;">function</span> <span style="color: #000000;">deranged</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s1</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">s2</span><span style="color: #0000FF;">)</span> |
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if s1[i]==s2[i] then return 0 end if |
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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: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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end for |
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<span style="color: #008080;">if</span> <span style="color: #000000;">s1</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">s2</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: #008080;">return</span> <span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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return 1 |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #000000;">1</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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function derangements(integer n) |
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sequence ts = tagset(n) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">derangements</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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sequence res = {} |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">ts</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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for i=1 to factorial(n) do |
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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> |
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sequence s = permute(i,ts) |
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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: #7060A8;">factorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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if deranged(s,ts) then |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">permute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ts</span><span style="color: #0000FF;">)</span> |
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res = append(res,s) |
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<span style="color: #008080;">if</span> <span style="color: #000000;">deranged</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ts</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
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end if |
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<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;">s</span><span style="color: #0000FF;">)</span> |
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end for |
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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;">for</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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function subfactorial(integer n) |
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if n<2 then return 1-n end if |
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<span style="color: #008080;">function</span> <span style="color: #000000;">subfactorial</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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return (n-1)*(subfactorial(n-1)+subfactorial(n-2)) |
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<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">n</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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end function |
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<span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)*(</span><span style="color: #000000;">subfactorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">subfactorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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?derangements(4) |
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for n=0 to 9 do |
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<span style="color: #0000FF;">?</span><span style="color: #000000;">derangements</span><span style="color: #0000FF;">(</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span> |
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printf(1,"%d: counted:%d, calculated:%d\n",{n,length(derangements(n)),subfactorial(n)}) |
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</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: counted:%d, calculated:%d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">derangements</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)),</span><span style="color: #000000;">subfactorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)})</span> |
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string msg = iff(machine_bits()=32?" (incorrect on 32-bit!)":"") -- (fine on 64-bit) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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printf(1,"!20=%d%s\n",{subfactorial(20),msg}) |
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<span style="color: #004080;">string</span> <span style="color: #000000;">msg</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">machine_bits</span><span style="color: #0000FF;">()=</span><span style="color: #000000;">32</span><span style="color: #0000FF;">?</span><span style="color: #008000;">" (incorrect on 32-bit!)"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">""</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (fine on 64-bit)</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;">"!20=%d%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">subfactorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">20</span><span style="color: #0000FF;">),</span><span style="color: #000000;">msg</span><span style="color: #0000FF;">})</span> |
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include mpfr.e |
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function mpz_sub_factorial(integer n) |
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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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-- probably not the most efficient way to do this! |
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<span style="color: #008080;">function</span> <span style="color: #000000;">mpz_sub_factorial</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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if n<2 then return sprintf("%d",{1-n}) end if |
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<span style="color: #000080;font-style:italic;">-- probably not the most efficient way to do this!</span> |
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mpz f = mpz_init(mpz_sub_factorial(n-1)), |
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<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</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;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">n</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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g = mpz_init(mpz_sub_factorial(n-2)) |
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mpz_sub_factorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)),</span> |
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mpz_add(f,f,g) |
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<span style="color: #000000;">g</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mpz_sub_factorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))</span> |
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mpz_mul_si(f,f,n-1) |
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<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">g</span><span style="color: #0000FF;">)</span> |
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string res = mpz_get_str(f) |
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<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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{f,g} = mpz_free({f,g}) |
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<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span> |
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return res |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">g</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_free</span><span style="color: #0000FF;">({</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">g</span><span style="color: #0000FF;">})</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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printf(1,"!20=%s (mpfr)\n",{mpz_sub_factorial(20)})</lang> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</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;">"!20=%s (mpfr)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mpz_sub_factorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">20</span><span style="color: #0000FF;">)})</span> |
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<!--</lang>--> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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| Line 2,541: | Line 2,544: | ||
!20=895014631192902121 (mpfr) |
!20=895014631192902121 (mpfr) |
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</pre> |
</pre> |
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<small>(under pwa/p2js you get a trailing "000" instead of "186" for the incorrect result)</small> |
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{{trans|FreeBASIC}} |
{{trans|FreeBASIC}} |
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A more efficient method of calculating subfactorials (0 should be handled separately, or obviously prepend a 1 and extract with idx+1).<br> |
A more efficient method of calculating subfactorials (0 should be handled separately, or obviously prepend a 1 and extract with idx+1).<br> |
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Should you instead of string results want an array of mpz for further calculations, use the mpz_init_set() call as shown: |
Should you instead of string results want an array of mpz for further calculations, use the mpz_init_set() call as shown: |
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<lang Phix> |
<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">with</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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function subfactorial(integer n) |
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sequence res = repeat(0,n) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">subfactorial</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> |
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mpz num = mpz_init(1) |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</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;">n</span><span style="color: #0000FF;">)</span> |
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<span style="color: #004080;">mpz</span> <span style="color: #000000;">num</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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for i=1 to n do |
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mpz_mul_si(num,num,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;">n</span> <span style="color: #008080;">do</span> |
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if mpz_odd(num) then |
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<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">num</span><span style="color: #0000FF;">,</span><span style="color: #000000;">num</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> |
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mpz_sub_ui(num,num,1) |
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_odd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">num</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> |
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else |
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<span style="color: #7060A8;">mpz_sub_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">num</span><span style="color: #0000FF;">,</span><span style="color: #000000;">num</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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mpz_add_ui(num,num,1) |
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<span style="color: #008080;">else</span> |
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end if |
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<span style="color: #7060A8;">mpz_add_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">num</span><span style="color: #0000FF;">,</span><span style="color: #000000;">num</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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res[i] = mpz_get_str(num) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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-- res[i] = mpz_init_set(num) |
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<span style="color: #000000;">res</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;">num</span><span style="color: #0000FF;">)</span> |
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end for |
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<span style="color: #000080;font-style:italic;">-- res[i] = mpz_init_set(num)</span> |
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return res |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</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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?extract(subfactorial(20),tagset(9)&20)</lang> |
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<span style="color: #0000FF;">?</span><span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">subfactorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">20</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)&</span><span style="color: #000000;">20</span><span style="color: #0000FF;">)</span> |
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<!--</lang>--> |
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{{out}} |
{{out}} |
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<pre>{"0","1","2","9","44","265","1854","14833","133496","895014631192902121"}</pre> |
<pre>{"0","1","2","9","44","265","1854","14833","133496","895014631192902121"}</pre> |
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