Data update
This commit is contained in:
Ingy döt Net
parent
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4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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@ -1,33 +0,0 @@
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with Ada.Text_IO;
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procedure Pythagorean_Triples is
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type Large_Natural is range 0 .. 2**63-1;
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-- this is the maximum for gnat
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procedure New_Triangle(A, B, C: Large_Natural;
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Max_Perimeter: Large_Natural;
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Total_Cnt, Primitive_Cnt: in out Large_Natural) is
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Perimeter: constant Large_Natural := A + B + C;
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begin
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if Perimeter <= Max_Perimeter then
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Primitive_Cnt := Primitive_Cnt + 1;
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Total_Cnt := Total_Cnt + Max_Perimeter / Perimeter;
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New_Triangle(A-2*B+2*C, 2*A-B+2*C, 2*A-2*B+3*C, Max_Perimeter, Total_Cnt, Primitive_Cnt);
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New_Triangle(A+2*B+2*C, 2*A+B+2*C, 2*A+2*B+3*C, Max_Perimeter, Total_Cnt, Primitive_Cnt);
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New_Triangle(2*B+2*C-A, B+2*C-2*A, 2*B+3*C-2*A, Max_Perimeter, Total_Cnt, Primitive_Cnt);
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end if;
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end New_Triangle;
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T_Cnt, P_Cnt: Large_Natural;
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begin
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for I in 1 .. 9 loop
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T_Cnt := 0;
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P_Cnt := 0;
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New_Triangle(3,4,5, 10**I, Total_Cnt => T_Cnt, Primitive_Cnt => P_Cnt);
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Ada.Text_IO.Put_Line("Up to 10 **" & Integer'Image(I) & " :" &
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Large_Natural'Image(T_Cnt) & " Triples," &
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Large_Natural'Image(P_Cnt) & " Primitives");
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end loop;
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end Pythagorean_Triples;
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@ -1,4 +1,4 @@
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triples: new []
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triples: []
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loop 1..50 'x [
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loop 1..50 'y [
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loop (max @[x y])..100 'z [
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@ -14,7 +14,7 @@ unique 'triples
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print ["Found" size triples "pythagorean triples with a perimeter no larger than 100:"]
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print triples
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primitive: select triples => [1 = gcd]
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primitive: select triples => [1 = gcd &]
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print ""
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print [size primitive "of them are primitive:"]
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@ -1,21 +0,0 @@
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function tri(atom lim, sequence in)
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sequence r
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atom p
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p = in[1] + in[2] + in[3]
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if p > lim then
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return {0, 0}
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end if
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r = {1, floor(lim / p)}
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r += tri(lim, { in[1]-2*in[2]+2*in[3], 2*in[1]-in[2]+2*in[3], 2*in[1]-2*in[2]+3*in[3]})
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r += tri(lim, { in[1]+2*in[2]+2*in[3], 2*in[1]+in[2]+2*in[3], 2*in[1]+2*in[2]+3*in[3]})
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r += tri(lim, {-in[1]+2*in[2]+2*in[3], -2*in[1]+in[2]+2*in[3], -2*in[1]+2*in[2]+3*in[3]})
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return r
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end function
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atom max_peri
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max_peri = 10
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while max_peri <= 100000000 do
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printf(1,"%d: ", max_peri)
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? tri(max_peri, {3, 4, 5})
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max_peri *= 10
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end while
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@ -1,23 +1,44 @@
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(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: #004080;">atom</span> <span style="color: #000000;">total</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">prim</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">maxPeri</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10</span>
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with javascript_semantics
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function count_triplets(atom max_perimeter)
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integer limit = floor(sqrt(max_perimeter/2))+1
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atom total = 0, primitive = 0, t0 = time(), t1 = t0+1
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// The formulas below generate primitive triples if:
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// 0 < n < m
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// m and n are relatively prime (gcd == 1)
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// m + n is odd
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for m=2 to limit do
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for n=1+odd(m) to m-1 by 2 do
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-- if gcd(m,n)=1 then
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-- inlined for a 5-fold speedup:
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integer u = m, v = n, t
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do
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t = u
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u = v
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v = rmdr(t,v)
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until v=0
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if u=1 then
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-- a = m*m - n*n
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-- b = 2*m*n
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-- c = m*m + n*n
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-- perimeter = a + b + c
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atom perimeter = 2*m*(m+n)
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if perimeter <= max_perimeter then
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primitive += 1
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total += floor(max_perimeter/perimeter)
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end if
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end if
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end for
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if time()>t1 then
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progress("m:%d/%d (%d%%)\r",{m,limit,m/limit*100})
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t1 = time()+1
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end if
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end for
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string e = elapsed_short(time()-t0,1," (%s)")
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return {max_perimeter, total, primitive, e}
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end function
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">tri</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">s0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s2</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s0</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">s1</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">s2</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">maxPeri</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">prim</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<span style="color: #000000;">total</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">maxPeri</span><span style="color: #0000FF;">/</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">tri</span><span style="color: #0000FF;">(</span> <span style="color: #000000;">s0</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*(-</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*(</span> <span style="color: #000000;">s0</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*(</span> <span style="color: #000000;">s0</span><span style="color: #0000FF;">-</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">);</span>
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<span style="color: #000000;">tri</span><span style="color: #0000FF;">(</span> <span style="color: #000000;">s0</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*(</span> <span style="color: #000000;">s1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*(</span> <span style="color: #000000;">s0</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*(</span> <span style="color: #000000;">s0</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">);</span>
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<span style="color: #000000;">tri</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">s0</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*(</span> <span style="color: #000000;">s1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*(-</span><span style="color: #000000;">s0</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*(-</span><span style="color: #000000;">s0</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">);</span>
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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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<span style="color: #008080;">while</span> <span style="color: #000000;">maxPeri</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">1e8</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">prim</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">;</span>
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<span style="color: #000000;">total</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">;</span>
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<span style="color: #000000;">tri</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</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;">"Up to %d: %d triples, %d primitives.\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">maxPeri</span><span style="color: #0000FF;">,</span><span style="color: #000000;">total</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prim</span><span style="color: #0000FF;">})</span>
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<span style="color: #000000;">maxPeri</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;">while</span>
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<!--
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integer limit = iff(platform()=JS?9:10)
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for max_perimeter in sq_power(10,tagset(limit)) do
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printf(1,"Up to %,d: %,d triples, %,d primitives%s.\n",
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count_triplets(max_perimeter))
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end for
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@ -1,50 +0,0 @@
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function triples($p) {
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if($p -gt 4) {
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# ai + bi + ci = pi <= p
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# ai < bi < ci --> 3ai < pi <= p and ai + 2bi < pi <= p
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$pa = [Math]::Floor($p/3)
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1..$pa | foreach {
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$ai = $_
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$pb = [Math]::Floor(($p-$ai)/2)
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($ai+1)..$pb | foreach {
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$bi = $_
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$pc = $p-$ai-$bi
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($bi+1)..$pc | where {
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$ci = $_
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$pi = $ai + $bi + $ci
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$ci*$ci -eq $ai*$ai + $bi*$bi
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} |
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foreach {
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[pscustomobject]@{
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a = "$ai"
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b = "$bi"
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c = "$ci"
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p = "$pi"
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}
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}
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}
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}
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}
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else {
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Write-Error "$p is not greater than 4"
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}
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}
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function gcd ($a, $b) {
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function pgcd ($n, $m) {
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if($n -le $m) {
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if($n -eq 0) {$m}
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else{pgcd $n ($m%$n)}
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}
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else {pgcd $m $n}
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}
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$n = [Math]::Abs($a)
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$m = [Math]::Abs($b)
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(pgcd $n $m)
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}
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$triples = (triples 100)
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$coprime = $triples |
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where {((gcd $_.a $_.b) -eq 1) -and ((gcd $_.a $_.c) -eq 1) -and ((gcd $_.b $_.c) -eq 1)}
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"There are $(($triples).Count) Pythagorean triples with perimeter no larger than 100
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and $(($coprime).Count) of them are coprime."
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@ -1,5 +1,4 @@
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from fractions import gcd
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from math import gcd
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def pt1(maxperimeter=100):
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'''
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@ -1,14 +1,16 @@
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from sys import setrecursionlimit
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from functools import reduce
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setrecursionlimit(2000) # 2000 ought to be big enough for everybody
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def triples(lim, a = 3, b = 4, c = 5):
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l = a + b + c
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if l > lim: return (0, 0)
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return reduce(lambda x, y: (x[0] + y[0], x[1] + y[1]), [
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(1, lim / l),
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(1, lim // l),
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triples(lim, a - 2*b + 2*c, 2*a - b + 2*c, 2*a - 2*b + 3*c),
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triples(lim, a + 2*b + 2*c, 2*a + b + 2*c, 2*a + 2*b + 3*c),
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triples(lim, -a + 2*b + 2*c, -2*a + b + 2*c, -2*a + 2*b + 3*c) ])
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for peri in [10 ** e for e in range(1, 8)]:
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print peri, triples(peri)
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print(peri, triples(peri))
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@ -1,7 +0,0 @@
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10 (0, 0)
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100 (7, 17)
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1000 (70, 325)
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10000 (703, 4858)
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100000 (7026, 64741)
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1000000 (70229, 808950)
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10000000 (702309, 9706567)
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@ -1,36 +0,0 @@
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For i=1 To 8
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WScript.StdOut.WriteLine triples(10^i)
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Next
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Function triples(pmax)
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prim=0 : count=0 : nmax=Sqr(pmax)/2 : n=1
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Do While n <= nmax
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m=n+1 : p=2*m*(m+n)
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Do While p <= pmax
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If gcd(m,n)=1 Then
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prim=prim+1
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count=count+Int(pmax/p)
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End If
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m=m+2
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p=2*m*(m+n)
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Loop
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n=n+1
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Loop
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triples = "Max Perimeter: " & pmax &_
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", Total: " & count &_
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", Primitive: " & prim
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End Function
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Function gcd(a,b)
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c = a : d = b
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Do
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If c Mod d > 0 Then
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e = c Mod d
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c = d
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d = e
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Else
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gcd = d
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Exit Do
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End If
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Loop
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End Function
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