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Task/Self-referential-sequence/EchoLisp/self-referential-sequence-1.echolisp

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+(lib 'hash)
+(lib 'list) ;; permutations
+
+(define H (make-hash))
+
+;; G R A P H
+;; generate 'normalized' starter vectors  D[i] = number of digits 'i' (0 <=i < 10)
+;; reduce graph size : 9009, 9900 ..  will be generated once : vector #(2 0 0 0 0 0 0 0 0 2)
+
+(define (generate D dstart ndigits (sd 0))
+(when (> ndigits 0)
+	(set! sd (vector-ref D dstart)) ;; save before recurse
+	(for ((i (in-range 0 (1+ ndigits))))
+		#:continue (and ( = i 0) (> dstart 0))
+		(vector-set! D dstart i)
+		(sequence D) ;; sequence length from D
+		(for ((j (in-range (1+ dstart) 10)))
+		(generate D j  (- ndigits i))))
+	(vector-set! D dstart sd))) ;; restore
+	
+
+;; compute follower of D (at most 99 same digits)
+(define (dnext D (dd 0))
+	(define N (make-vector 10))
+	(for ((d D) (i 10))
+		#:continue (zero? d)
+		(vector-set! N i (1+ (vector-ref N i)))
+		(if (< d 10)
+		(vector-set! N d (1+ (vector-ref N d))) ;; d < 9
+		(begin
+		(set! dd (modulo d 10))
+		(vector-set! N dd (1+ (vector-ref N dd)))
+		(set! dd (quotient d 10))
+		(vector-set! N dd (1+ (vector-ref N dd))))))
+		N)
+		
+		
+;; update all nodes in same sequence
+;; seq-length (next D) = 1 - seq-length(D)
+(define (sequence D)
+(define (dists D d)
+	(unless (hash-ref H D)
+		  (hash-set H  D d)
+		  (dists (dnext D ) (1- d))))
+		
+		(unless  (hash-ref H D)
+				 (dists D (sequence-length D))))		
+		
+;; sequence length from D
+;; stops on loop found (node N)
+(define (sequence-length D )
+(define (looper N looplg depth) ;; looper 2 : a b a
+	(when ( > depth 0)
+			(hash-set H N looplg)
+			(looper (dnext N)  looplg (1- depth))))
+			
+		(define followers (make-hash))
+		(define N (dnext D))
+		(define seqlg 0)
+		(define looplg 0)
+		
+		(hash-set followers D 0)
+		
+	(set! seqlg
+		(for ((lg (in-naturals 1 )))
+			 #:break (hash-ref H N) =>  (+ lg (hash-ref H N)) ;; already known
+			 #:break (hash-ref followers N) => lg ;; loop found
+			 (hash-set followers N lg)
+			 (set! N (dnext N))))
+			
+;; update nodes in loop : same seq-length
+		(when (hash-ref followers N) ;; loop found
+			(set! looplg  ( - seqlg  (hash-ref followers N)))
+			(looper N looplg looplg))
+		
+		seqlg )
+		
+;; O U T P U T
+;; backwards from D - normalized vector - to numbers (as strings)
+(define (starters D)
+(define (not-leading-zero list) (!zero? (first list)))
+	(map list->string
+	(filter not-leading-zero (make-set (permutations (for/fold (acc null) ((d D) (i 10))
+		#:continue (zero? d)
+		(append acc   (for/list ((j d)) i))))))))
+	
+		
+;; printing one node
+(define (D-print D)
+	 (set! D (reverse (vector->list D)))
+	 (for/string ( (d D) (i (in-range 9 -1 -1)))
+		#:continue (zero? d)
+		(string-append d i)))
+			
+;; print graph contents
+(define (print-sequence D)
+		(writeln 1 (starters D))
+		(writeln 2 (D-print D ))
+		(for ((i (in-range 1 (hash-ref H D))))
+			(writeln (+ i 2)  (D-print (setv! D (dnext D))))))
+	
+
+;; TA S K
+(define (task (n 6)  (verbose #t))
+	(generate (make-vector 10) 0 n)
+	(define seqmax (apply max (hash-values H)))
+	(when verbose (for ((kv H))
+		#:continue (!= (rest kv ) seqmax)
+		(print-sequence (first kv))))
+
+	(writeln (expt 10 n) '--> 'max-sequence= (1+ seqmax)  'nodes= (length (hash-values H))))
+