Data update
This commit is contained in:
Ingy döt Net
parent
5150844a7d
commit
4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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@ -1,4 +1,4 @@
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# count the how many numbers up to 100 000 000 have squared digit sums of 89 #
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# count how many numbers up to 100 000 000 have squared digit sums of 89 #
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# compute a table of the sum of the squared digits of the numbers 00 to 99 #
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[ 0 : 99 ]INT digit pair square sum;
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@ -1,40 +0,0 @@
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with Ada.Text_IO;
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procedure Digits_Squaring is
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function Is_89 (Number : in Positive) return Boolean
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is
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Squares : constant array (0 .. 9) of Natural :=
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(0, 1, 4, 9, 16, 25, 36, 49, 64, 81);
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Sum : Natural := Number;
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Acc : Natural;
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begin
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loop
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Acc := Sum;
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Sum := 0;
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while Acc > 0 loop
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Sum := Sum + Squares (Acc mod 10);
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Acc := Acc / 10;
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end loop;
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if Sum = 89 then return True; end if;
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if Sum = 1 then return False; end if;
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end loop;
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end Is_89;
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use Ada.Text_IO;
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Count : Natural := 0;
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begin
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for A in 1 .. 99_999_999 loop
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if Is_89 (A) then
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Count := Count + 1;
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end if;
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if A = 999_999 then
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Put_Line ("In range 1 .. 999_999: " & Count'Image);
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end if;
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end loop;
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Put_Line ("In range 1 .. 99_999_999: " & Count'Image);
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end Digits_Squaring;
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@ -1,7 +1,7 @@
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gen: function [n][
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result: n
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while [not? in? result [1 89]][
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s: new 0
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s: 0
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loop digits result 'd ->
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's + d*d
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result: s
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@ -13,7 +13,7 @@ chainsEndingWith89: function [ndigits][
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[prevCount,currCount]: #[]
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loop 0..9 'i -> prevCount\[i*i]: 1
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res: new 0
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res: 0
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loop 2..ndigits 'x [
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currCount: #[]
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@ -1,2 +1,2 @@
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+´1?1? ?˜?(?2???) ?+?´6?<ט?10
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+´1↓1≠ ⊏˜⍟(⌈2⋆⁼≠) ⥊+⌜´6⥊<ט↕10
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856929
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@ -1,8 +1,8 @@
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DigSq ? {
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d ? ט ?10 # Digit values
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m ? 1+81×2??? # One plus maximum digit sum
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c ? (+´ d ??0?»¨ <)??? m??1 # Count of numbers having each sum
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s ? m ? ? d +??(?10??m) 0 # Sum for each sum
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e ? 1??˜?(?2???)s # Which sums end at 89
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DigSq ← {
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d ← ט ↕10 # Digit values
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m ← 1+81×2⌈𝕩 # One plus maximum digit sum
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c ← (+´ d ⥊⟜0⊸»¨ <)⍟𝕩 m↑⥊1 # Count of numbers having each sum
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s ← m ↑ ⥊ d +⌜⍟(⌈10⋆⁼m) 0 # Sum for each sum
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e ← 1≠⊏˜⍟(⌈2⋆⁼≠)s # Which sums end at 89
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¯1 +´ c×e # Total up; subtract 1 to exclude 0
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}
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@ -1,6 +1,6 @@
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>??DigSq¨ 1+?16
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+-
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? 1 7
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>⋈⟜DigSq¨ 1+↕16
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┌─
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╵ 1 7
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2 80
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3 857
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4 8558
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@ -16,4 +16,4 @@
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14 86229146720315
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15 869339034137667
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16 8754780882739336
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+
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┘
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@ -1,44 +1,42 @@
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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: #008080;">constant</span> <span style="color: #000000;">MAXINT</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</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: #000000;">53</span><span style="color: #0000FF;">:</span><span style="color: #000000;">64</span><span style="color: #0000FF;">))</span>
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with javascript_semantics
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constant MAXINT = power(2,iff(machine_bits()=32?53:64))
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">limit</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">sums</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;">limit</span><span style="color: #0000FF;">*</span><span style="color: #000000;">81</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">sums</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
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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;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">do</span>
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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;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">81</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
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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;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">*</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i1</span><span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i1ms</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">s</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">></span><span style="color: #000000;">i</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #000000;">sums</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">sums</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i1ms</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: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">count89</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
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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: #0000FF;">*</span><span style="color: #000000;">81</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">digit</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
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<span style="color: #008080;">while</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
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<span style="color: #008080;">while</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">digit</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">r</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">digit</span><span style="color: #0000FF;">*</span><span style="color: #000000;">digit</span>
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<span style="color: #000000;">w</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</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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<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">89</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">count89</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">sums</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i1</span><span style="color: #0000FF;">]</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">count89</span><span style="color: #0000FF;">></span><span style="color: #000000;">MAXINT</span> <span style="color: #008080;">then</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;">"counter overflow for 10^%d\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</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;">exit</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #000000;">w</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</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;">"There are %d numbers from 1 to 10^%d ending with 89\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count89</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</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: #008080;">end</span> <span style="color: #008080;">procedure</span>
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procedure main(integer limit)
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sequence sums = repeat(0,limit*81+1)
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sums[1] = 1
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for n=1 to limit do
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for i=n*81 to 1 by -1 do
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for j=1 to 9 do
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integer s = j*j, i1= i+1, i1ms = i1-s
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if s>i then exit end if
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sums[i1] += sums[i1ms]
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end for
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end for
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atom count89 = 0
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for i=1 to n*81 do
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integer r, digit, w = i, i1 = i+1
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while w!=1 do
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r = 0
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while w!=0 do
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digit = mod(w,10)
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r += digit*digit
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w = floor(w/10)
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end while
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if r=89 then
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count89 += sums[i1]
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if count89>MAXINT then
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printf(1,"counter overflow for 10^%d\n",n)
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return
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end if
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exit
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end if
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w = r
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end while
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end for
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printf(1,"There are %d numbers from 1 to 10^%d ending with 89\n",{count89,n})
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end for
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end procedure
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<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>
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<span style="color: #000000;">main</span><span style="color: #0000FF;">(</span><span style="color: #000000;">20</span><span style="color: #0000FF;">)</span>
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<span style="color: #0000FF;">?</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span>
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<!--
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atom t0 = time()
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main(20)
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?time()-t0
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@ -1,29 +1,27 @@
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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: #008080;">function</span> <span style="color: #000000;">comb</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: #000000;">set</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">at</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">chosen</span><span style="color: #0000FF;">={})</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">n</span> <span style="color: #008080;">then</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">digits</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;">10</span><span style="color: #0000FF;">)</span>
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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;">chosen</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">idx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">chosen</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span>
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<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]+=</span><span style="color: #000000;">1</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</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: #7060A8;">factorial</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">))</span>
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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;">10</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">p</span> <span style="color: #0000FF;">/=</span> <span style="color: #7060A8;">factorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</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;">for</span>
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<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</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: #008080;">else</span>
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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;">at</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">comb</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">set</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: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">),</span><span style="color: #000000;">set</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>
|
||||
<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>
|
||||
with javascript_semantics
|
||||
function comb(sequence res, set, integer n, at=1, sequence chosen={})
|
||||
if length(chosen)=n then
|
||||
sequence digits = repeat(0,10)
|
||||
for i=1 to length(chosen) do
|
||||
integer idx = chosen[i]+1
|
||||
digits[idx]+=1
|
||||
end for
|
||||
atom p = factorial(length(chosen))
|
||||
for i=1 to 10 do
|
||||
if digits[i] then
|
||||
p /= factorial(digits[i])
|
||||
end if
|
||||
end for
|
||||
res = sq_add(res,{p,1})
|
||||
else
|
||||
for i=at to length(set) do
|
||||
res = comb(res,set,n,i,append(deep_copy(chosen),set[i]))
|
||||
end for
|
||||
end if
|
||||
return res
|
||||
end function
|
||||
|
||||
<span style="color: #008080;">constant</span> <span style="color: #000000;">nums</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</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;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">8</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">comb</span><span style="color: #0000FF;">({</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},</span><span style="color: #000000;">nums</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>
|
||||
<!--
|
||||
constant nums = {0,1,2,3,4,5,6,7,8,9}
|
||||
for i=1 to 8 do
|
||||
printf(1,"%V\n",{comb({0,0},nums,i)})
|
||||
end for
|
||||
|
|
|
|||
|
|
@ -1,63 +1,61 @@
|
|||
(phixonline)-->
|
||||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">is1</span>
|
||||
with javascript_semantics
|
||||
sequence is1
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">comb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">at</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">chosen</span><span style="color: #0000FF;">={})</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">n</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">digits</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;">10</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">sumsq</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">ci</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">chosen</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">sumsq</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ci</span><span style="color: #0000FF;">*</span><span style="color: #000000;">ci</span>
|
||||
<span style="color: #000000;">ci</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ci</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">sumsq</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">is1</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sumsq</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">perms</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">factorial</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">digits</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: #000000;">perms</span> <span style="color: #0000FF;">/=</span> <span style="color: #7060A8;">factorial</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">perms</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #000000;">chosen</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">)&</span><span style="color: #000000;">0</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">at</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">chosen</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">comb</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">set</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">chosen</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
function comb(atom res, sequence set, integer n, at=1, sequence chosen={})
|
||||
if length(chosen)=n then
|
||||
sequence digits = repeat(0,10)
|
||||
atom sumsq = 0
|
||||
for i=1 to length(chosen) do
|
||||
integer ci = chosen[i]
|
||||
sumsq += ci*ci
|
||||
ci += 1
|
||||
digits[ci] += 1
|
||||
end for
|
||||
if sumsq=0 or is1[sumsq] then
|
||||
atom perms = factorial(length(chosen))
|
||||
for i=1 to 10 do
|
||||
if digits[i] then
|
||||
perms /= factorial(digits[i])
|
||||
end if
|
||||
end for
|
||||
res += perms
|
||||
end if
|
||||
else
|
||||
chosen = deep_copy(chosen)&0
|
||||
for i=at to length(set) do
|
||||
chosen[$] = set[i]
|
||||
res = comb(res,set,n,i,chosen)
|
||||
end for
|
||||
end if
|
||||
return res
|
||||
end function
|
||||
|
||||
<span style="color: #008080;">procedure</span> <span style="color: #000000;">setis1</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">is1</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><span style="color: #000000;">81</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">is1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">digit</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">digit</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">r</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">digit</span><span style="color: #0000FF;">*</span><span style="color: #000000;">digit</span>
|
||||
<span style="color: #000000;">w</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">89</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<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: #000000;">is1</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">exit</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">w</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
|
||||
procedure setis1(integer n)
|
||||
is1 = repeat(0,n*81)
|
||||
for i=1 to length(is1) do
|
||||
integer r, digit, w = i
|
||||
while 1 do
|
||||
r = 0
|
||||
while w!=0 do
|
||||
digit = mod(w,10)
|
||||
r += digit*digit
|
||||
w = floor(w/10)
|
||||
end while
|
||||
if r=89 then exit end if
|
||||
if r=1 then
|
||||
is1[i] = 1
|
||||
exit
|
||||
end if
|
||||
w = r
|
||||
end while
|
||||
end for
|
||||
end procedure
|
||||
|
||||
<span style="color: #008080;">constant</span> <span style="color: #000000;">nums</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</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;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">t00</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">16</span> <span style="color: #008080;">do</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: #000000;">setis1</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"There are %d numbers from 1 to 10^%d ending with 89 (%3.2fs)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">comb</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nums</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">),</span><span style="color: #000000;">i</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>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<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;">t00</span><span style="color: #0000FF;">)</span>
|
||||
<!--
|
||||
constant nums = {0,1,2,3,4,5,6,7,8,9}
|
||||
atom t00 = time()
|
||||
for i=1 to 16 do
|
||||
atom t0 = time()
|
||||
setis1(i)
|
||||
printf(1,"There are %d numbers from 1 to 10^%d ending with 89 (%3.2fs)\n",{power(10,i)-comb(0,nums,i),i,time()-t0})
|
||||
end for
|
||||
?elapsed(time()-t00)
|
||||
|
|
|
|||
|
|
@ -1,20 +0,0 @@
|
|||
start_time = Now
|
||||
cnt = 0
|
||||
For i = 1 To 100000000
|
||||
n = i
|
||||
sum = 0
|
||||
Do Until n = 1 Or n = 89
|
||||
For j = 1 To Len(n)
|
||||
sum = sum + (CLng(Mid(n,j,1))^2)
|
||||
Next
|
||||
n = sum
|
||||
sum = 0
|
||||
Loop
|
||||
If n = 89 Then
|
||||
cnt = cnt + 1
|
||||
End If
|
||||
Next
|
||||
end_time = Now
|
||||
|
||||
WScript.Echo "Elapse Time: " & DateDiff("s",start_time,end_time) &_
|
||||
vbCrLf & "Count: " & cnt
|
||||
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Reference in a new issue