irrational rational
もう時効っぽいから晒してみよう。必殺仕事請負人で適当に作った課題作品。
循環小数(=> 有理数)の計算結果の小数ストリームから循環部分を探すスクリプト。除算の結果を先頭から適当な状態機械に食わせて循環部分とそれ以外の 2 値を返す。
コマンドラインから 2 つの数字が与えられた場合にはその除算結果を、与えられなかった場合には Gauche の (test) フレームワークで適当なテストを実行した結果を返している。
#!/usr/bin/env gosh ;; ;; Display cyclic part of real number and its length ;; ;; % gosh rational.scm 1 3 ;; 0.(3) ;; 1 ;; ;; % gosh rational.scm 5 7 ;; 0.71(428571) ;; 6 ;; (use srfi-1) (use srfi-43) (define *division-limit* 50) ; limitation of divisor places ;; get the quotient of `num' by `dem' inexactly. (define (quotient->list num dem) (cond [(zero? dem) (error "zero division error")] ; euclid [else (let loop ((n (remainder num dem)) ; numerator (d dem) ; denominator (i 0) ; loop counter (r '())) ; result (if (and (not (zero? n)) (< i *division-limit*)) (loop (remainder (* n 10) d) d (+ i 1) (cons (quotient (* n 10) d) r)) (values (quotient num dem) (reverse r))))])) ;; test if the vector `vec' is a multipler of `sub' (define (cyclic-vector? vec sub) (cond [(vector-empty? vec) #t] ; n * 0 ==> 0 [(vector-empty? sub) #f] [(equal? (vector-copy vec 0 (vector-length sub)) sub) ; test from prefix (cyclic-vector? (vector-copy vec (vector-length sub)) sub)] [else #f])) ;; separate list of `lis' into two lists of non-cycled numbers and cycled numbers. (define (find-cycle lis) (if (not (<= 0 (apply min lis) (apply max lis) 9)) (error "no proper list given")) (let ((vec (list->vector lis)) ; convert to vector for easy index accessing (len (length lis))) (let ind_loop ((ind 0)) ; test from first in the vector (if (< ind (- len 1)) ; til one before last one (let loop ((shift (+ ind 1))) (if (< shift len) ; search same value in vec@ind after ind (let* ((eir (vector-index (cut = (vector-ref vec ind) <>) ; relative value from shift (vector-copy vec shift))) (eia (if eir (+ shift eir) eir))) ; absolute value from zero (if (and eia (< eia len) (<= (- (* eia 2) ind) len)) ;; construct subset of the vector starts from `ind' and `eia' ;; the first value of them are the same. (was tested before) (let ((head (vector-copy vec ind eia)) (tail (vector-copy vec eia (- (* eia 2) ind)))) ;; test if head and tail are equal. ;; if they are same, test the rest of vector if the multiple of `head'. ;; the rested vector will be rounded as the multipler of length of `head'. (if (and (equal? head tail) (cyclic-vector? (vector-copy vec eia (- len (remainder (- len eia) (- eia ind)))) head)) (values (vector->list (vector-copy vec 0 ind)) ; return results (vector->list head)) ; head is cycled (loop (+ eia 1)))) ; if head and tail are not proper, try vector-index again (ind_loop (+ ind 1)))) (ind_loop (+ ind 1)))) ; if same value of the first one not found, increment the index (values lis '()))))) ; if no proper result found, return original list as non-cycled. (define (main args) (if (< (length args) 3) ; run tests if arguments not reached to run calculation (begin (use gauche.test) (test-start (car args)) (let test:quotient->list ((lis '( (3 1 (3 ())) (1 6 (0 (1 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6))) (5 7 (0 (7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1))) (1 250 (0 (0 0 4))) ))) (if (pair? lis) (let ((n (caar lis)) (d (cadar lis)) (r (caddar lis))) (test* #`"(quotient->list ,n ,d)" r (receive (div lis) (quotient->list n d) (list div lis))) (test:quotient->list (cdr lis))))) (let test:cyclic-vector? ((lis '( (#(0 0 0 0) #() #f) (#(0 0 0 0) #(0) #t) (#(0 1 0 1) #(0 1) #t) (#(0 1 2 0 1 2) #(0 1 2) #t) ))) (if (pair? lis) (let ((v (caar lis)) (s (cadar lis)) (r (caddar lis))) (test* #`"(cyclic-vector? ,v ,s)" r (cyclic-vector? v s)) (test:cyclic-vector? (cdr lis))))) (let test:find-cycle ((lis '( ((0 0 0 0) (() (0))) ((0 1 0 1) (() (0 1))) ((0 1 0 1 0) (() (0 1))) ((0 1 1 1) ((0) (1))) ((0 1 1 1 1) ((0) (1))) ((0 1 2 0 1 2) (() (0 1 2))) ((0 1 2 0 1 2 0) (() (0 1 2))) ((0 1 2 0 1 2 0 1) (() (0 1 2))) ((1 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6) ((1) (6))) ((7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5 7 1) (() (7 1 4 2 8 5))) ((0 0 4) ((0 0 4) ())) ((0 0 5 0 0) ((0 0 5) (0))) ((0 0 6 0 0 0) ((0 0 6) (0))) ))) (if (pair? lis) (let ((l (caar lis)) (r (cadar lis))) (test* #`"(find-cycle ,l)" r (receive (base cycle) (find-cycle l) (list base cycle))) (test:find-cycle (cdr lis))))) (test-end)) (begin ;; for validation ; (print (/. (string->number (list-ref args 1)) ; (string->number (list-ref args 2)))) (display #`",(list-ref args 1) / ,(list-ref args 2) == ") (receive (div base cycle) (receive (div lis) (quotient->list (string->number (list-ref args 1)) (string->number (list-ref args 2))) (if (null? lis) ; lis is null -> rational (values div '(0) '(0)) (receive (base cycle) (find-cycle lis) (values div base cycle)))) ;; display quotient and cycled value (format #t "~a.~a(~a)\n" div ; (not (null? cycle)) -> rational (list->string (map integer->digit base)) (list->string (map integer->digit cycle))) ;; display length of cycled numbers (format #t "~a\n" (length cycle))))) 0)
作り終わって一通りテストも通ってから、状態機械なんか作らなくても解ける問題だったらしいことを聞いてしまって自分の数学的センスのなさに軽くブルー。
べ、別に状態機械作ってみたくなっただけなんだからねっ…ってのは置いといて、Gauche の UnitTest フレームワークを実際に使ってみる良い機会になった。もっと勉強しないといけない。
Project Euler: Problem 18
By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.
3 7 5 2 4 6 8 5 9 3That is, 3 + 7 + 4 + 9 = 23.
Find the maximum total from top to bottom of the triangle below:
75 95 64 17 47 82 18 35 87 10 20 04 82 47 65 19 01 23 75 03 34 88 02 77 73 07 63 67 99 65 04 28 06 16 70 92 41 41 26 56 83 40 80 70 33 41 48 72 33 47 32 37 16 94 29 53 71 44 65 25 43 91 52 97 51 14 70 11 33 28 77 73 17 78 39 68 17 57 91 71 52 38 17 14 91 43 58 50 27 29 48 63 66 04 68 89 53 67 30 73 16 69 87 40 31 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)
http://projecteuler.net/index.php?section=problems&id=18
数字でできたピラミッドを上から下まで巡って、通った数字の合計値のうち最大のものを求めよ。
Gauche で書いてみた。木を作って上から下に総当たり。あたまわるい。
#!/usr/bin/env gosh (use srfi-1) (use util.queue) (define-class <node> () [(value :init-keyword :value :init-value #f) (nodes :init-keyword :nodes :init-value '())]) (define-method insert! ((self <node>) (other <node>)) (slot-set! self 'nodes (cons other (slot-ref self 'nodes)))) (define-method child-ref ((self <node>) id) (let ((nl (length (slot-ref self 'nodes)))) (if (or (< id 0) (<= nl id)) (error "index out of range") (list-ref (slot-ref self 'nodes) (- nl id 1))))) (define-method children-of ((self <node>)) (reverse (slot-ref self 'nodes))) (define-method children-count ((self <node>)) (length (slot-ref self 'nodes))) (define-method length ((self <node>)) (let loop ((node self) (nlen 1)) (if (and (equal? (class-of node) <node>) (< 0 (children-count node))) (loop (child-ref node 0) (+ 1 nlen)) nlen))) (define-method traverse ((self <node>)) (let ((zero (make <node> :value 0)) (depth (length self))) (let loop ((que (list->queue `((,self)))) (res '())) (if (not (queue-empty? que)) (let1 line (dequeue! que) (if (zero? (children-count (car line))) (loop que (cons line res)) (begin (for-each (cut enqueue! que <>) (let1 next (map (cut cons <> line) (children-of (car line))) next ; TODO: フィルタかまして枝を刈る )) (loop que res)))) res)))) (define (main args) (define pyramid (map (lambda (str) (map string->number (string-split str char-whitespace?))) (list "75" "95 64" "17 47 82" "18 35 87 10" "20 04 82 47 65" "19 01 23 75 03 34" "88 02 77 73 07 63 67" "99 65 04 28 06 16 70 92" "41 41 26 56 83 40 80 70 33" "41 48 72 33 47 32 37 16 94 29" "53 71 44 65 25 43 91 52 97 51 14" "70 11 33 28 77 73 17 78 39 68 17 57" "91 71 52 38 17 14 91 43 58 50 27 29 48" "63 66 04 68 89 53 67 30 73 16 69 87 40 31" "04 62 98 27 23 09 70 98 73 93 38 53 60 04 23" ))) (let ((root (make <node> :value (caar pyramid)))) (let loop ((plis (list root)) (rest (cdr pyramid))) (if (pair? rest) (let ((clis (map (cut make <node> :value <>) (car rest)))) (for-each (lambda (p clis) (for-each (cut insert! p <>) clis)) ; 子ノードの追加 plis (zip clis (cdr clis))) ; 子ノードを 2 つ取り出す (loop clis (cdr rest)) ) (print (apply max (map (lambda (line) (fold + 0 (map (cut slot-ref <> 'value) line))) (traverse root))))))) 0)
どうやら Problem 67 も入力値は違えども同様の問題らしいので気合いを入れようかと思ったけど、結局のところ普通に総当たりで解いたところで終わってしまっている。
途中で良い感じに枝を刈っていけばもっと速くなることが見込めると思うけど実装できてない。Gauche のクラスを使ってみたけど、オブジェクトの定義は Problem 67 までに見直したほうが良いかも知れない。
dumb
あたまがはたらいてるきがしない。
マンガばっか読んでるのもアレなので、気分転換に Project Euler。
Project Euler: Problem 17
If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.
If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?
NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of "and" when writing out numbers is in compliance with British usage.
http://projecteuler.net/index.php?section=problems&id=17
1 から 1000 までの自然数列をその英単語で置き換えたうえ "two"、みたいな。">*1、その文字列の合計長を求めよ (※ただしアルファベットに限る) とのこと。
Gauche で書いてみた。
#!/usr/bin/env gosh (use srfi-1) (define *number-table* (let [(tab (make-hash-table))] (let loop [(lis '((0 . "zero") (1 . "one") (2 . "two") (3 . "three") (4 . "four") (5 . "five") (6 . "six") (7 . "seven") (8 . "eight") (9 . "nine") (10 . "ten") (11 . "eleven") (12 . "twelve") (13 . "thirteen") (14 . "fourteen") (15 . "fifteen") (16 . "sixteen") (17 . "seventeen") (18 . "eighteen") (19 . "nineteen") (20 . "twenty") (30 . "thirty") (40 . "forty") (50 . "fifty") (60 . "sixty") (70 . "seventy") (80 . "eighty") (90 . "ninety")))] (if (pair? lis) [begin (hash-table-put! tab (car (car lis)) (cdr (car lis))) (loop (cdr lis))] tab)))) (define (number->english n) (if (hash-table-exists? *number-table* n) (hash-table-get *number-table* n) (cond [(< n 100) (string-append (number->english (* (quotient n 10) 10)) (if (zero? (remainder n 10)) "" (string-append "-" (number->english (remainder n 10)))))] [(< n 1000) (string-append (number->english (quotient n 100)) (if (zero? (remainder n 100)) " hundred" (string-append " hundred and " (number->english (remainder n 100)))))] [(< n 10000) (cond [(<= 11 (quotient n 100) 12) ; ==> 1192 as "eleven hundred and ninety-two" (string-append (number->english (quotient n 100)) (if (zero? (remainder n 100)) " hundred" (string-append " hundred and " (number->english (remainder n 100)))))] [(<= (remainder n 100) 12) ; ==> 1001 as "one thousand and one" (string-append (number->english (quotient n 1000)) (if (zero? (remainder n 1000)) " thousand" (string-append " thousand and " (number->english (remainder n 1000)))))] [else ; ==> 1969 as "nineteen sixty-nine" (let* [(d (remainder n 100)) (a (quotient n 100))] (string-append (number->english a) " " (number->english d)))])] [else (error "number too big")]))) (define (main args) (let loop [(num 1) (lis '())] (if (<= num 1000) (let [(eng (number->english num))] ; (format #t "~4@a:~a\n" num eng) (loop (+ num 1) (cons eng lis))) (print (fold + 0 (map (lambda (s) (length (filter char-alphabetic? (string->list s)))) (reverse lis)))))) 0)
自然数を受け取って英語の文字列表現を返す number->english を定義して、あとはそのまんま長さを求めている。
ちょっとだけ気を利かせて 1000 < n < 10000 の範囲でも英語っぽく返せるように number->english を作ってみたけど、よく考えたら英語にあんまり強くないので正しい表現かどうかは分かりません。"twenty" みたいな単語は普通にハッシュテーブルな定数にぶち込んでいるので問題ないんだけど、"hundred" や "thousand" を number->english の中に埋め込んでしまったのが気持ち悪い。
*1:e.g. 1 -> "one", 2 -> "two"、みたいな。
Project Euler: Problem 16
すぐ解ける問題から飛ばし飛ばしに解いてしまうのはあまり良くないかな…。
2^(15) = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.
What is the sum of the digits of the number 2^(1000)?
http://projecteuler.net/index.php?section=problems&id=16
2 の 1000 乗の各桁の数を合計したものを求めよとのこと。
Gauche で書いてみた。
#!/usr/bin/env gosh (define (main args) (let* [(a 2) (b 1000) (c (expt a b))] (let loop [(num c) (lis '())] (if (<= 10 num) (loop (quotient num 10) (cons (remainder num 10) lis)) (print (fold + 0 (cons num lis)))))) 0)
特に難しいことは考えず、そのまんま。
Project Euler: Problem 13
Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.
37107287533902102798797998220837590246510135740250
http://projecteuler.net/index.php?section=problems&id=13
46376937677490009712648124896970078050417018260538
74324986199524741059474233309513058123726617309629
91942213363574161572522430563301811072406154908250
23067588207539346171171980310421047513778063246676
89261670696623633820136378418383684178734361726757
28112879812849979408065481931592621691275889832738
44274228917432520321923589422876796487670272189318
47451445736001306439091167216856844588711603153276
70386486105843025439939619828917593665686757934951
62176457141856560629502157223196586755079324193331
64906352462741904929101432445813822663347944758178
92575867718337217661963751590579239728245598838407
58203565325359399008402633568948830189458628227828
80181199384826282014278194139940567587151170094390
35398664372827112653829987240784473053190104293586
86515506006295864861532075273371959191420517255829
71693888707715466499115593487603532921714970056938
54370070576826684624621495650076471787294438377604
53282654108756828443191190634694037855217779295145
36123272525000296071075082563815656710885258350721
45876576172410976447339110607218265236877223636045
17423706905851860660448207621209813287860733969412
81142660418086830619328460811191061556940512689692
51934325451728388641918047049293215058642563049483
62467221648435076201727918039944693004732956340691
15732444386908125794514089057706229429197107928209
55037687525678773091862540744969844508330393682126
18336384825330154686196124348767681297534375946515
80386287592878490201521685554828717201219257766954
78182833757993103614740356856449095527097864797581
16726320100436897842553539920931837441497806860984
48403098129077791799088218795327364475675590848030
87086987551392711854517078544161852424320693150332
59959406895756536782107074926966537676326235447210
69793950679652694742597709739166693763042633987085
41052684708299085211399427365734116182760315001271
65378607361501080857009149939512557028198746004375
35829035317434717326932123578154982629742552737307
94953759765105305946966067683156574377167401875275
88902802571733229619176668713819931811048770190271
25267680276078003013678680992525463401061632866526
36270218540497705585629946580636237993140746255962
24074486908231174977792365466257246923322810917141
91430288197103288597806669760892938638285025333403
34413065578016127815921815005561868836468420090470
23053081172816430487623791969842487255036638784583
11487696932154902810424020138335124462181441773470
63783299490636259666498587618221225225512486764533
67720186971698544312419572409913959008952310058822
95548255300263520781532296796249481641953868218774
76085327132285723110424803456124867697064507995236
37774242535411291684276865538926205024910326572967
23701913275725675285653248258265463092207058596522
29798860272258331913126375147341994889534765745501
18495701454879288984856827726077713721403798879715
38298203783031473527721580348144513491373226651381
34829543829199918180278916522431027392251122869539
40957953066405232632538044100059654939159879593635
29746152185502371307642255121183693803580388584903
41698116222072977186158236678424689157993532961922
62467957194401269043877107275048102390895523597457
23189706772547915061505504953922979530901129967519
86188088225875314529584099251203829009407770775672
11306739708304724483816533873502340845647058077308
82959174767140363198008187129011875491310547126581
97623331044818386269515456334926366572897563400500
42846280183517070527831839425882145521227251250327
55121603546981200581762165212827652751691296897789
32238195734329339946437501907836945765883352399886
75506164965184775180738168837861091527357929701337
62177842752192623401942399639168044983993173312731
32924185707147349566916674687634660915035914677504
99518671430235219628894890102423325116913619626622
73267460800591547471830798392868535206946944540724
76841822524674417161514036427982273348055556214818
97142617910342598647204516893989422179826088076852
87783646182799346313767754307809363333018982642090
10848802521674670883215120185883543223812876952786
71329612474782464538636993009049310363619763878039
62184073572399794223406235393808339651327408011116
66627891981488087797941876876144230030984490851411
60661826293682836764744779239180335110989069790714
85786944089552990653640447425576083659976645795096
66024396409905389607120198219976047599490197230297
64913982680032973156037120041377903785566085089252
16730939319872750275468906903707539413042652315011
94809377245048795150954100921645863754710598436791
78639167021187492431995700641917969777599028300699
15368713711936614952811305876380278410754449733078
40789923115535562561142322423255033685442488917353
44889911501440648020369068063960672322193204149535
41503128880339536053299340368006977710650566631954
81234880673210146739058568557934581403627822703280
82616570773948327592232845941706525094512325230608
22918802058777319719839450180888072429661980811197
77158542502016545090413245809786882778948721859617
72107838435069186155435662884062257473692284509516
20849603980134001723930671666823555245252804609722
53503534226472524250874054075591789781264330331690
50 桁の数字 100 個の合計を求めて、そのうち頭から 10 桁を答えよとのこと。
例のごとく Gauche で書いてみた。
#!/usr/bin/env gosh (use srfi-1) ;; string->number があるのに気づかず自分で実装してた ;(define (string->integer s) ; (fold + 0 (map * ; (map (cut expt 10 <>) ; (iota 50 0)) ; acceptable places ; (reverse ; (map digit->integer ; (string->list s)))))) (define (main args) (define blob (list "37107287533902102798797998220837590246510135740250" "46376937677490009712648124896970078050417018260538" "74324986199524741059474233309513058123726617309629" "91942213363574161572522430563301811072406154908250" "23067588207539346171171980310421047513778063246676" "89261670696623633820136378418383684178734361726757" "28112879812849979408065481931592621691275889832738" "44274228917432520321923589422876796487670272189318" "47451445736001306439091167216856844588711603153276" "70386486105843025439939619828917593665686757934951" "62176457141856560629502157223196586755079324193331" "64906352462741904929101432445813822663347944758178" "92575867718337217661963751590579239728245598838407" "58203565325359399008402633568948830189458628227828" "80181199384826282014278194139940567587151170094390" "35398664372827112653829987240784473053190104293586" "86515506006295864861532075273371959191420517255829" "71693888707715466499115593487603532921714970056938" "54370070576826684624621495650076471787294438377604" "53282654108756828443191190634694037855217779295145" "36123272525000296071075082563815656710885258350721" "45876576172410976447339110607218265236877223636045" "17423706905851860660448207621209813287860733969412" "81142660418086830619328460811191061556940512689692" "51934325451728388641918047049293215058642563049483" "62467221648435076201727918039944693004732956340691" "15732444386908125794514089057706229429197107928209" "55037687525678773091862540744969844508330393682126" "18336384825330154686196124348767681297534375946515" "80386287592878490201521685554828717201219257766954" "78182833757993103614740356856449095527097864797581" "16726320100436897842553539920931837441497806860984" "48403098129077791799088218795327364475675590848030" "87086987551392711854517078544161852424320693150332" "59959406895756536782107074926966537676326235447210" "69793950679652694742597709739166693763042633987085" "41052684708299085211399427365734116182760315001271" "65378607361501080857009149939512557028198746004375" "35829035317434717326932123578154982629742552737307" "94953759765105305946966067683156574377167401875275" "88902802571733229619176668713819931811048770190271" "25267680276078003013678680992525463401061632866526" "36270218540497705585629946580636237993140746255962" "24074486908231174977792365466257246923322810917141" "91430288197103288597806669760892938638285025333403" "34413065578016127815921815005561868836468420090470" "23053081172816430487623791969842487255036638784583" "11487696932154902810424020138335124462181441773470" "63783299490636259666498587618221225225512486764533" "67720186971698544312419572409913959008952310058822" "95548255300263520781532296796249481641953868218774" "76085327132285723110424803456124867697064507995236" "37774242535411291684276865538926205024910326572967" "23701913275725675285653248258265463092207058596522" "29798860272258331913126375147341994889534765745501" "18495701454879288984856827726077713721403798879715" "38298203783031473527721580348144513491373226651381" "34829543829199918180278916522431027392251122869539" "40957953066405232632538044100059654939159879593635" "29746152185502371307642255121183693803580388584903" "41698116222072977186158236678424689157993532961922" "62467957194401269043877107275048102390895523597457" "23189706772547915061505504953922979530901129967519" "86188088225875314529584099251203829009407770775672" "11306739708304724483816533873502340845647058077308" "82959174767140363198008187129011875491310547126581" "97623331044818386269515456334926366572897563400500" "42846280183517070527831839425882145521227251250327" "55121603546981200581762165212827652751691296897789" "32238195734329339946437501907836945765883352399886" "75506164965184775180738168837861091527357929701337" "62177842752192623401942399639168044983993173312731" "32924185707147349566916674687634660915035914677504" "99518671430235219628894890102423325116913619626622" "73267460800591547471830798392868535206946944540724" "76841822524674417161514036427982273348055556214818" "97142617910342598647204516893989422179826088076852" "87783646182799346313767754307809363333018982642090" "10848802521674670883215120185883543223812876952786" "71329612474782464538636993009049310363619763878039" "62184073572399794223406235393808339651327408011116" "66627891981488087797941876876144230030984490851411" "60661826293682836764744779239180335110989069790714" "85786944089552990653640447425576083659976645795096" "66024396409905389607120198219976047599490197230297" "64913982680032973156037120041377903785566085089252" "16730939319872750275468906903707539413042652315011" "94809377245048795150954100921645863754710598436791" "78639167021187492431995700641917969777599028300699" "15368713711936614952811305876380278410754449733078" "40789923115535562561142322423255033685442488917353" "44889911501440648020369068063960672322193204149535" "41503128880339536053299340368006977710650566631954" "81234880673210146739058568557934581403627822703280" "82616570773948327592232845941706525094512325230608" "22918802058777319719839450180888072429661980811197" "77158542502016545090413245809786882778948721859617" "72107838435069186155435662884062257473692284509516" "20849603980134001723930671666823555245252804609722" "53503534226472524250874054075591789781264330331690")) (let loop [(lis blob) (sum 0)] (if (pair? lis) (loop (cdr lis) (+ sum (string->number (car lis)))) (let answer [(num sum)] (if (<= num 9999999999) (print num) (answer (quotient num 10)))))) 0)
普通に足し算して普通に頭から 10 桁を求めた。無限多倍長整数ってすてきだ。
Project Euler: Problem 12 #1
The sequence of triangle numbers is generated by adding the natural numbers. So the 7^(th) triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
Let us list the factors of the first seven triangle numbers:
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28We can see that 28 is the first triangle number to have over five divisors.
hat is the value of the first triangle number to have over five hundred divisors?
http://projecteuler.net/index.php?section=problem&id=12
自然数 n に対して、1 から n までの合計を求めたものを三角数と呼ぶ。三角数の数列の中から 500 個の因数に分解できる最初の三角数を求めよとのこと。
とりあえず、Gauche で書いてみたけど実行が終わらない。現状は三角数を順番に求めて因数に分解しているけど、そんな方法で答えを求めようにも時間ばっかりかかってどうしようもないのだろう。ちょっくらアルゴリズムを練り直す必要があるが…どうすりゃいいかなぁ。
#!/usr/bin/env gosh (use srfi-1) (use util.combinations) ;; n 以下の素数のリストを返す (define (primes n) ; sieve of eratosthenes (list version) (case n [(1) '()] [else (let loop [(i 0) (m (floor->exact (sqrt n))) (p (iota (- n 1) 2))] (if (< i m) (let* [(e (list-ref p i)) (p (filter (lambda (x) (or (= x e) (not (= (remainder x e) 0)))) p))] (loop (+ i 1) m p)) p))])) ;; n 番目の三角数を求める (define (triangle-number n) (let loop [(n n) (r 0)] (case n [(1) (+ r 1)] [else (loop (- n 1) (+ r n))]))) ;; n を素因数分解した結果のリストを返す (define (prime-factors n) (case n [(1) '()] [(2) '(2)] [else (let loop [(num n) (plis (primes n)) (flis '())] ; factors (if (< 1 num) (if (pair? plis) (if (zero? (remainder num (car plis))) (loop (quotient num (car plis)) plis (cons (car plis) flis)) (loop num (cdr plis) flis)) (error "no prime left for dividing")) flis))])) ;; n の全ての因数のリストを返す (define (factors n) (case n [(1) '(1)] [else (let* [(f (cons '(1) (cons (list n) (power-set (prime-factors n))))) (g (map (cut fold * 1 <>) f)) (h (delete-duplicates (sort g)))] h)])) (define (main args) (let loop [(n 1)] (let* [(tr (triangle-number n)) (rf (factors tr))] (if (< 500 (length rf)) [begin (newline) (newline) (print #`"the answer is ,tr ,rf.")] [begin (format #t "~16@a: ~a\n" tr (string-join (map number->string rf) ", ")) (loop (+ n 1))]))))
つづく。
