Add tasks for all the new languages
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Tina Müller
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(lib 'hash)
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(lib 'list) ;; permutations
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(define H (make-hash))
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;; G R A P H
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;; generate 'normalized' starter vectors D[i] = number of digits 'i' (0 <=i < 10)
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;; reduce graph size : 9009, 9900 .. will be generated once : vector #(2 0 0 0 0 0 0 0 0 2)
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(define (generate D dstart ndigits (sd 0))
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(when (> ndigits 0)
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(set! sd (vector-ref D dstart)) ;; save before recurse
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(for ((i (in-range 0 (1+ ndigits))))
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#:continue (and ( = i 0) (> dstart 0))
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(vector-set! D dstart i)
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(sequence D) ;; sequence length from D
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(for ((j (in-range (1+ dstart) 10)))
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(generate D j (- ndigits i))))
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(vector-set! D dstart sd))) ;; restore
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;; compute follower of D (at most 99 same digits)
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(define (dnext D (dd 0))
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(define N (make-vector 10))
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(for ((d D) (i 10))
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#:continue (zero? d)
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(vector-set! N i (1+ (vector-ref N i)))
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(if (< d 10)
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(vector-set! N d (1+ (vector-ref N d))) ;; d < 9
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(begin
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(set! dd (modulo d 10))
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(vector-set! N dd (1+ (vector-ref N dd)))
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(set! dd (quotient d 10))
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(vector-set! N dd (1+ (vector-ref N dd))))))
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N)
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;; update all nodes in same sequence
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;; seq-length (next D) = 1 - seq-length(D)
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(define (sequence D)
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(define (dists D d)
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(unless (hash-ref H D)
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(hash-set H D d)
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(dists (dnext D ) (1- d))))
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(unless (hash-ref H D)
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(dists D (sequence-length D))))
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;; sequence length from D
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;; stops on loop found (node N)
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(define (sequence-length D )
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(define (looper N looplg depth) ;; looper 2 : a b a
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(when ( > depth 0)
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(hash-set H N looplg)
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(looper (dnext N) looplg (1- depth))))
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(define followers (make-hash))
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(define N (dnext D))
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(define seqlg 0)
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(define looplg 0)
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(hash-set followers D 0)
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(set! seqlg
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(for ((lg (in-naturals 1 )))
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#:break (hash-ref H N) => (+ lg (hash-ref H N)) ;; already known
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#:break (hash-ref followers N) => lg ;; loop found
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(hash-set followers N lg)
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(set! N (dnext N))))
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;; update nodes in loop : same seq-length
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(when (hash-ref followers N) ;; loop found
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(set! looplg ( - seqlg (hash-ref followers N)))
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(looper N looplg looplg))
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seqlg )
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;; O U T P U T
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;; backwards from D - normalized vector - to numbers (as strings)
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(define (starters D)
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(define (not-leading-zero list) (!zero? (first list)))
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(map list->string
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(filter not-leading-zero (make-set (permutations (for/fold (acc null) ((d D) (i 10))
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#:continue (zero? d)
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(append acc (for/list ((j d)) i))))))))
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;; printing one node
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(define (D-print D)
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(set! D (reverse (vector->list D)))
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(for/string ( (d D) (i (in-range 9 -1 -1)))
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#:continue (zero? d)
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(string-append d i)))
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;; print graph contents
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(define (print-sequence D)
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(writeln 1 (starters D))
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(writeln 2 (D-print D ))
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(for ((i (in-range 1 (hash-ref H D))))
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(writeln (+ i 2) (D-print (setv! D (dnext D))))))
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;; TA S K
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(define (task (n 6) (verbose #t))
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(generate (make-vector 10) 0 n)
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(define seqmax (apply max (hash-values H)))
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(when verbose (for ((kv H))
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#:continue (!= (rest kv ) seqmax)
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(print-sequence (first kv))))
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(writeln (expt 10 n) '--> 'max-sequence= (1+ seqmax) 'nodes= (length (hash-values H))))
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@ -0,0 +1,32 @@
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(task 6)
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1 (9009 9090 9900)
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2 2920
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3 192210
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4 19222110
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5 19323110
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6 1923123110
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7 1923224110
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8 191413323110
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9 191433125110
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10 19151423125110
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11 19251413226110
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12 1916151413325110
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13 1916251423127110
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14 191716151413326110
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15 191726151423128110
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16 19181716151413327110
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17 19182716151423129110
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18 29181716151413328110
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19 19281716151423228110
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20 19281716151413427110
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21 19182716152413228110
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1000000 --> max-sequence= 21 nodes= 10926
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(task 7 #f)
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10000000 --> max-sequence= 21 nodes= 23432
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(task 8 #f)
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100000000 --> max-sequence= 21 nodes= 47359
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(task 9 #f)
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1000000000 --> max-sequence= 21 nodes= 97455
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(task 10 #f)
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10000000000 --> max-sequence= 21 nodes= 188493
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@ -0,0 +1,61 @@
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# Given any array, produce an array of [item, count] pairs for each run.
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def runs:
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reduce .[] as $item
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( [];
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if . == [] then [ [ $item, 1] ]
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else .[length-1] as $last
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| if $last[0] == $item
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then (.[0:length-1] + [ [$item, $last[1] + 1] ] )
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else . + [[$item, 1]]
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end
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end ) ;
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# string to string
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def next_self_referential:
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def runs2integer: # input is an array as produced by runs,
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# i.e. an array of [count, n] pairs, where count is an int,
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# and n is an "exploded" digit
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reduce .[] as $pair
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(""; . + ($pair[1] | tostring) + ([$pair[0]]|implode) ) ;
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explode | sort | reverse | runs | runs2integer;
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# Given an integer as a string,
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# compute the entire sequence (of strings) to convergence:
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def sequence_of_self_referentials:
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def seq:
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. as $ary
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| (.[length-1] | next_self_referential) as $next
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| if ($ary|index($next)) then $ary
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else $ary + [$next] | seq
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end;
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[.] | seq;
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def maximals(n):
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def interesting:
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tostring | (. == (explode | sort | reverse | implode));
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reduce range(0;n) as $i
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([[], 0]; # maximalseeds, length
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if ($i | interesting) then
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($i|tostring|sequence_of_self_referentials|length) as $length
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| if .[1] == $length then [ .[0] + [$i], $length]
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elif .[1] < $length then [ [$i], $length]
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else .
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end
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else .
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end );
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def task(n):
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maximals(n) as $answer
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| "The maximal length to convergence for seeds up to \(n) is \($answer[1]).",
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"The corresponding seeds are the allowed permutations",
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"of the representative number(s): \($answer[0][])",
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"For each representative seed, the self-referential sequence is as follows:",
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($answer[0][] | tostring
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| ("Representative: \(.)",
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"Self-referential sequence:",
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(sequence_of_self_referentials | map(tonumber))))
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;
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task(1000000)
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@ -0,0 +1,30 @@
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$ jq -n -r -f Self_referential_sequence.jq
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The maximal length to convergence for seeds up to 1000000 is 21.
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The corresponding seeds are the allowed permutations
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of the representative number(s): 9900
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For each representative seed, the self-referential sequence is as follows:
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Representative: 9900
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Self-referential sequence:
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[
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9900,
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2920,
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192210,
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19222110,
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19323110,
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1923123110,
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1923224110,
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191413323110,
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191433125110,
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19151423125110,
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19251413226110,
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1916151413325110,
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1916251423127110,
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191716151413326100,
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191726151423128100,
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19181716151413326000,
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19182716151423128000,
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29181716151413330000,
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19281716151423230000,
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19281716151413430000,
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19182716152413230000
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]
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