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Chinese remainder theorem: Difference between revisions

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Chinese remainder theorem (view source)

Revision as of 02:42, 25 May 2021

10,687 bytes added ,  3 years ago
m
→‎{{header|Phix}}: added syntax colouring the hard wa, made runnable
(Added Arturo implementation)
m (→‎{{header|Phix}}: added syntax colouring the hard wa, made runnable)
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=={{header|Phix}}==
{{trans|C}}
Uses the function mul_inv() from [[Modular_inverse#Phix]] (reproduced below)
<!--<lang Phix>function chinese_remainder(sequence n, aphixonline)-->
<span style="color: #008080;">function</span> <span style="color: #000000;">mul_inv</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
integer p, prod = 1, tot = 0;
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">n</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
for i=1 to length(n) do prod *= n[i] end for
<span style="color: #008080;">if</span> <span style="color: #000000;">a</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">-</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">a</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>
for i=1 to length(n) do
<span style="color: #004080;">integer</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
p = prod / n[i];
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">;</span>
object m = mul_inv(p, n[i])
<span style="color: #008080;">while</span> <span style="color: #000000;">nr</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
if string(m) then return "fail" end if
<span style="color: #004080;">integer</span> <span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">/</span><span style="color: #000000;">nr</span><span style="color: #0000FF;">)</span>
tot += a[i] * m * p;
<span style="color: #0000FF;">{</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nt</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">nt</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">-</span><span style="color: #000000;">q</span><span style="color: #0000FF;">*</span><span style="color: #000000;">nt</span><span style="color: #0000FF;">}</span>
end for
<span style="color: #0000FF;">{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nr</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">nr</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">q</span><span style="color: #0000FF;">*</span><span style="color: #000000;">nr</span><span style="color: #0000FF;">}</span>
return mod(tot,prod)
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
end function
<span style="color: #008080;">if</span> <span style="color: #000000;">r</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: #008000;">"a is not invertible"</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">t</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">n</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">t</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">chinese_remainder</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
?chinese_remainder({3,5,7},{2,3,2})
<span style="color: #004080;">integer</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">prod</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tot</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">;</span>
?chinese_remainder({11,12,13},{10,4,12})
<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;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000000;">prod</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">n</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;">for</span>
?chinese_remainder({11,22,19},{10,4,9})
<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;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
?chinese_remainder({100,23},{19,0})</lang>
<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">prod</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">];</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mul_inv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #008000;">"fail"</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">tot</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">a</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;">m</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">;</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tot</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prod</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">chinese_remainder</span><span style="color: #0000FF;">({</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">})</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">chinese_remainder</span><span style="color: #0000FF;">({</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">})</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">chinese_remainder</span><span style="color: #0000FF;">({</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">22</span><span style="color: #0000FF;">,</span><span style="color: #000000;">19</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">})</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">chinese_remainder</span><span style="color: #0000FF;">({</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">23</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">})</span>
<!--</lang>-->
{{out}}
<pre>
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