(require srfi/1)
(define (front lst)
(reverse (cdr (reverse lst))))
(define (sum-row upper lower)
(map (lambda (u l1 l2)
(+ u (if (< l1 l2) l2 l1)))
upper
(cdr lower)
(front lower)))
(define data '((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)))
(define (loop lower rest)
(display lower)
(newline)
(if (null? rest)
lower
(loop (sum-row (car rest) lower) (cdr rest))))
ようこそ DrRacket, バージョン 5.3.3 [3m].
言語: Pretty Big; memory limit: 512 MB.
> (loop (car (reverse data))
(cdr (reverse data)))
(4 62 98 27 23 9 70 98 73 93 38 53 60 4 23)
(125 164 102 95 112 123 165 128 166 109 122 147 100 54)
(255 235 154 150 140 179 256 209 224 172 174 176 148)
(325 246 187 178 256 329 273 302 263 242 193 233)
(378 317 231 321 354 372 393 354 360 293 247)
(419 365 393 387 419 425 430 376 454 322)
(460 434 419 475 508 470 510 524 487)
(559 499 479 536 514 526 594 616)
(647 501 613 609 533 657 683)
(666 614 636 684 660 717)
(686 640 766 731 782)
(704 801 853 792)
(818 900 935)
(995 999)
(1074)
(1074)
>
(require srfi/1)
(define (nbr-to-word n)
(define (loop nbr)
(cond ((= nbr 1) (list "one"))
((= nbr 2) (list "two"))
((= nbr 3) (list "three"))
((= nbr 4) (list "four"))
((= nbr 5) (list "five"))
((= nbr 6) (list "six"))
((= nbr 7) (list "seven"))
((= nbr 8) (list "eight"))
((= nbr 9) (list "nine"))
((= nbr 10) (list "ten"))
((= nbr 11) (list "eleven"))
((= nbr 12) (list "twelve"))
((= nbr 13) (list "thirteen"))
((= nbr 14) (list "fourteen"))
((= nbr 15) (list "fifteen"))
((= nbr 16) (list "sixteen"))
((= nbr 17) (list "seventeen"))
((= nbr 18) (list "eighteen"))
((= nbr 19) (list "nineteen"))
((= nbr 20) (list "twenty"))
((= nbr 30) (list "thirty"))
((= nbr 40) (list "forty"))
((= nbr 50) (list "fifty"))
((= nbr 60) (list "sixty"))
((= nbr 70) (list "seventy"))
((= nbr 80) (list "eighty"))
((= nbr 90) (list "ninety"))
((= nbr 1000) (list "one" "thousand"))
((and (>= nbr 100) (= (remainder nbr 100) 0))
(append (loop (quotient nbr 100)) (list "hundred")))
((>= nbr 100)
(append (loop (quotient nbr 100))
(list "hundred" "and")
(loop (remainder nbr 100))))
((>= nbr 21)
(append (loop (* (quotient nbr 10) 10))
(loop (remainder nbr 10))))))
(loop n))
(define (word-length word)
(length (apply append (map string->list word))))
ようこそ DrRacket, バージョン 5.3.3 [3m].
言語: Pretty Big; memory limit: 512 MB.
> (map nbr-to-word (iota 150 1))
(("one")
("two")
("three")
("four")
("five")
("six")
("seven")
("eight")
("nine")
("ten")
("eleven")
("twelve")
("thirteen")
("fourteen")
("fifteen")
("sixteen")
("seventeen")
("eighteen")
("nineteen")
("twenty")
("twenty" "one")
("twenty" "two")
... 省略 ...
("ninety" "six")
("ninety" "seven")
("ninety" "eight")
("ninety" "nine")
("one" "hundred")
("one" "hundred" "and" "one")
("one" "hundred" "and" "two")
("one" "hundred" "and" "three")
("one" "hundred" "and" "four")
... 省略 ...
("one" "hundred" "and" "forty" "seven")
("one" "hundred" "and" "forty" "eight")
("one" "hundred" "and" "forty" "nine")
("one" "hundred" "and" "fifty"))
> (fold + 0 (map word-length (map nbr-to-word (iota 1000 1))))
21124
>
(require srfi/1)
(define (square x) (* x x))
(define (fast-expt-iter b n p)
(cond ((= n 0) p)
((even? n) (fast-expt-iter (square b) (/ n 2) p))
(else (fast-expt-iter b (- n 1) (* b p)))))
(define (fast-expt b n)
(fast-expt-iter b n 1))
(define (decimal-format nbr)
(define (loop ans n)
(if (= 0 n)
ans
(loop (cons (remainder n 10) ans) (quotient n 10))))
(loop () nbr))
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 512 MB. > (fast-expt 2 1000) 1071508607186267320948425049060001810561404811705 5336074437503883703510511249361224931983788156958 5812759467291755314682518714528569231404359845775 7469857480393456777482423098542107460506237114187 7954182153046474983581941267398767559165543946077 0629145711964776865421676604298316526243868372056 68069376 > (apply + (decimal-format (fast-expt 2 1000))) 1366 >
(require srfi/1)
(define (square n) (* n n))
(define (divides? a b)
(= (remainder b a) 0))
(define (find-divisor n test-divisor)
(cond ((> (square test-divisor) n) n)
((divides? test-divisor n) test-divisor)
(else (find-divisor n (+ test-divisor 1)))))
(define (smallest-divisor n)
(find-divisor n 2))
(define (prime-factorization n)
(let ((a (smallest-divisor n)))
(if (= a n)
(list n)
(cons a (prime-factorization (/ n a))))))
(define (comb i j)
(define (pf items)
(sort (apply append (map prime-factorization items))
<))
(define (remove-one lst obj)
(cond ((null? lst) ())
((equal? (car lst) obj) (cdr lst))
(else (cons (car lst) (remove-one (cdr lst) obj)))))
(define (diff a b)
(cond ((null? b) a)
((member (car b) a) (diff (remove-one a (car b)) (cdr b)))
(else (error "diff"))))
(apply * (diff (pf (iota j i -1))
(pf (iota (- j 1) 2)))))
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 512 MB. > (comb 40 20) 137846528820 >
(define (collatz n)
(define (loop ans i)
(cond ((= i 1) (reverse (cons i ans)))
((even? i) (loop (cons i ans) (quotient i 2)))
(else (loop (cons i ans) (+ (* i 3) 1)))))
(loop '() n))
(define (max-collatz upper)
(define (loop ans i)
(if (< upper i)
ans
(let ((c (collatz i)))
(if (< (length ans) (length c))
(loop c (+ i 1))
(loop ans (+ i 1))))))
(loop '() 1))
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 512 MB. > (collatz 13) (13 40 20 10 5 16 8 4 2 1) > (max-collatz 999999) (837799 2513398 1256699 3770098 1885049 5655148 2827574 1413787 4241362 2120681 6362044 3181022 1590511 4771534 2385767 7157302 3578651 10735954 5367977 16103932 8051966 4025983 12077950 6038975 18116926 9058463 27175390 13587695 40763086 20381543 61144630 30572315 91716946 45858473 137575420 68787710 34393855 103181566 51590783 154772350 77386175 232158526 116079263 348237790 174118895 522356686 261178343 783535030 391767515 1175302546 587651273 1762953820 881476910 440738455 1322215366 661107683 1983323050 991661525 2974984576 1487492288 743746144 371873072 185936536 92968268 46484134 23242067 69726202 34863101 104589304 52294652 26147326 13073663 39220990 19610495 58831486 29415743 88247230 44123615 132370846 66185423 198556270 99278135 297834406 148917203 446751610 223375805 670127416 335063708 167531854 83765927 251297782 125648891 376946674 188473337 565420012 282710006 141355003 424065010 212032505 636097516 318048758 159024379 477073138 238536569 715609708 357804854 178902427 536707282 268353641 805060924 402530462 201265231 603795694 301897847 905693542 452846771 1358540314 679270157 2037810472 1018905236 509452618 254726309 764178928 382089464 191044732 95522366 47761183 143283550 71641775 214925326 107462663 322387990 161193995 483581986 241790993 725372980 362686490 181343245 544029736 272014868 136007434 68003717 204011152 102005576 51002788 25501394 12750697 38252092 19126046 9563023 28689070 14344535 43033606 21516803 64550410 32275205 96825616 48412808 24206404 12103202 6051601 18154804 9077402 4538701 13616104 6808052 3404026 1702013 5106040 2553020 1276510 638255 1914766 957383 2872150 1436075 4308226 2154113 6462340 3231170 1615585 4846756 2423378 1211689 3635068 1817534 908767 2726302 1363151 4089454 2044727 6134182 3067091 9201274 4600637 13801912 6900956 3450478 1725239 5175718 2587859 7763578 3881789 11645368 5822684 2911342 1455671 4367014 2183507 6550522 3275261 9825784 4912892 2456446 1228223 3684670 1842335 5527006 2763503 8290510 4145255 12435766 6217883 18653650 9326825 27980476 13990238 6995119 20985358 10492679 31478038 15739019 47217058 23608529 70825588 35412794 17706397 53119192 26559596 13279798 6639899 19919698 9959849 29879548 14939774 7469887 22409662 11204831 33614494 16807247 50421742 25210871 75632614 37816307 113448922 56724461 170173384 85086692 42543346 21271673 63815020 31907510 15953755 47861266 23930633 71791900 35895950 17947975 53843926 26921963 80765890 40382945 121148836 60574418 30287209 90861628 45430814 22715407 68146222 34073111 102219334 51109667 153329002 76664501 229993504 114996752 57498376 28749188 14374594 7187297 21561892 10780946 5390473 16171420 8085710 4042855 12128566 6064283 18192850 9096425 27289276 13644638 6822319 20466958 10233479 30700438 15350219 46050658 23025329 69075988 34537994 17268997 51806992 25903496 12951748 6475874 3237937 9713812 4856906 2428453 7285360 3642680 1821340 910670 455335 1366006 683003 2049010 1024505 3073516 1536758 768379 2305138 1152569 3457708 1728854 864427 2593282 1296641 3889924 1944962 972481 2917444 1458722 729361 2188084 1094042 547021 1641064 820532 410266 205133 615400 307700 153850 76925 230776 115388 57694 28847 86542 43271 129814 64907 194722 97361 292084 146042 73021 219064 109532 54766 27383 82150 41075 123226 61613 184840 92420 46210 23105 69316 34658 17329 51988 25994 12997 38992 19496 9748 4874 2437 7312 3656 1828 914 457 1372 686 343 1030 515 1546 773 2320 1160 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) >
(define sum
(+ 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))
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 512 MB. > sum 5537376230390876637302048746832985971773659831892672 >
| 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: | 1,2,4,7,14,28 |
(require srfi/1)
(define (square n) (* n n))
(define (divides? a b)
(= (remainder b a) 0))
(define (find-divisor n test-divisor)
(cond ((< (square test-divisor) n) n)
((divides? test-divisor n) test-divisor)
(else (find-divisor n (+ test-divisor 1)))))
(define (smallest-divisor n)
(find-divisor n 2))
;; 素因数分解
(define (prime-factorization n)
(let ((a (smallest-divisor n)))
(if (= a n)
(list n)
(cons a (prime-factorization (/ n a))))))
;; sizeの数の変数を持つ真理値表を作る
(define (0-1-table size)
(define (loop ans n)
(if (= n 0)
ans
(loop (append (map (lambda (lst) (cons #f lst)) ans)
(map (lambda (lst) (cons #t lst)) ans))
(- n 1))))
(loop '(()) size))
;; リストから集合を作る. つまり重複する要素を取り除く.
(define (make-set items)
(define (loop ans rest)
(cond ((null? rest) ans)
((find (lambda (a) (= (car rest) a)) ans) (loop ans (cdr rest)))
(else (loop (cons (car rest) ans) (cdr rest)))))
(loop '() items))
;; すべての約数を求める.
(define (all-divisor nbr)
(let* ((pf (prime-factorization nbr))
(tbl (0-1-table (length pf))))
(sort
(make-set (map (lambda (row)
(apply * (map (lambda (a b) (if a 1 b))
row
pf)))
tbl))
<)))
;; 約数の数が500以上になるまでループさせる.
(define (triangular-number)
(define (loop tri n)
(let ((ad (all-divisor (+ tri n))))
(if (<= 500 (length ad))
(list (+ tri n) ad)
(loop (+ tri n) (+ n 1)))))
(loop 0 1))
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 512 MB. > (all-divisor 28) (1 2 4 7 14 28) > (triangular-number) (76576500 (1 2 3 4 5 6 7 9 10 11 12 13 14 15 17 18 20 21 22 25 26 28 30 33 34 35 36 39 42 44 45 50 51 52 55 60 63 65 66 68 70 75 77 78 84 85 90 91 99 100 102 105 110 117 119 125 126 130 132 140 143 150 153 154 156 165 170 175 180 182 187 195 198 204 210 220 221 225 231 234 238 250 252 255 260 273 275 286 300 306 308 315 325 330 340 350 357 364 374 375 385 390 396 420 425 429 442 450 455 462 468 476 495 500 510 525 546 550 561 572 585 595 612 630 650 660 663 693 700 714 715 748 750 765 770 780 819 825 850 858 875 884 900 910 924 935 975 990 1001 1020 1050 1071 1092 1100 1105 1122 1125 1155 1170 1190 1260 1275 1287 1300 1309 1326 1365 1375 1386 1428 1430 1500 1530 1540 1547 1575 1625 1638 1650 1683 1700 1716 1750 1785 1820 1870 1925 1950 1980 1989 2002 2100 2125 2142 2145 2210 2244 2250 2275 2310 2340 2380 2431 2475 2550 2574 2618 2625 2652 2730 2750 2772 2805 2860 2925 2975 3003 3060 3094 3150 3250 3276 3300 3315 3366 3465 3500 3570 3575 3740 3825 3850 3900 3927 3978 4004 4095 4125 4250 4284 4290 4420 4500 4550 4620 4641 4675 4862 4875 4950 5005 5100 5148 5236 5250 5355 5460 5500 5525 5610 5775 5850 5950 6006 6188 6300 6375 6435 6500 6545 6630 6732 6825 6930 7140 7150 7293 7650 7700 7735 7854 7875 7956 8190 8250 8415 8500 8580 8925 9009 9100 9282 9350 9625 9724 9750 9900 9945 10010 10500 10710 10725 11050 11220 11375 11550 11700 11781 11900 12012 12155 12375 12750 12870 13090 13260 13650 13860 13923 14025 14300 14586 14625 14875 15015 15300 15470 15708 15750 16380 16500 16575 16830 17017 17325 17850 17875 18018 18564 18700 19125 19250 19500 19635 19890 20020 20475 21420 21450 21879 22100 22750 23100 23205 23375 23562 24310 24750 25025 25500 25740 26180 26775 27300 27625 27846 28050 28875 29172 29250 29750 30030 30940 31500 32175 32725 33150 33660 34034 34125 34650 35700 35750 36036 36465 38250 38500 38675 39270 39780 40950 42075 42900 43758 44625 45045 45500 46410 46750 47124 48620 49500 49725 50050 51051 53550 53625 55250 55692 56100 57750 58500 58905 59500 60060 60775 64350 65450 66300 68068 68250 69300 69615 70125 71500 72930 75075 76500 77350 78540 81900 82875 84150 85085 86625 87516 89250 90090 92820 93500 98175 99450 100100 102102 102375 107100 107250 109395 110500 115500 116025 117810 121550 125125 128700 130900 133875 136500 139230 140250 145860 150150 153153 154700 160875 163625 165750 168300 170170 173250 178500 180180 182325 193375 196350 198900 204204 204750 210375 214500 218790 225225 232050 235620 243100 248625 250250 255255 267750 278460 280500 294525 300300 303875 306306 321750 327250 331500 340340 346500 348075 364650 375375 386750 392700 409500 420750 425425 437580 450450 464100 490875 497250 500500 510510 535500 546975 580125 589050 607750 612612 643500 654500 696150 729300 750750 765765 773500 841500 850850 900900 911625 981750 994500 1021020 1093950 1126125 1160250 1178100 1215500 1276275 1392300 1472625 1501500 1531530 1701700 1740375 1823250 1963500 2127125 2187900 2252250 2320500 2552550 2734875 2945250 3063060 3480750 3646500 3828825 4254250 4504500 5105100 5469750 5890500 6381375 6961500 7657650 8508500 10939500 12762750 15315300 19144125 25525500 38288250 76576500)) >
(require srfi/1)
(define data
'((08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08)
(49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00)
(81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65)
(52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91)
(22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80)
(24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50)
(32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70)
(67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21)
(24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72)
(21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95)
(78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92)
(16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57)
(86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58)
(19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40)
(04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66)
(88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69)
(04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36)
(20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16)
(20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54)
(01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48)))
(define (value-of x-y)
(let ((x (list-ref x-y 0))
(y (list-ref x-y 1)))
(list-ref (list-ref data y) x)))
(define (diagonal-r x-y)
(let ((x (list-ref x-y 0))
(y (list-ref x-y 1)))
(map (lambda (n) (list (+ x n) (+ y n)))
(iota 4))))
(define (diagonal-l x-y)
(let ((x (list-ref x-y 0))
(y (list-ref x-y 1)))
(map (lambda (n) (list (- x n) (+ y n)))
(iota 4))))
(define (product list-a list-b)
(apply append
(map (lambda (a)
(map (lambda (b) (list a b))
list-b))
list-a)))
ようこそ DrRacket, バージョン 5.3.3 [3m].
言語: Pretty Big; memory limit: 512 MB.
> (sort
(map (lambda (d)
(let ((vals (map value-of d)))
(list (apply * vals) vals d)))
(map diagonal-r (product (iota 17) (iota 17))))
(lambda (a b) (< (car a) (car b))))
((0 (78 39 0 68) ((0 10) (1 11) (2 12) (3 13)))
(0 (39 0 68 97) ((1 11) (2 12) (3 13) (4 14)))
(0 (81 68 66 0) ((2 6) (3 7) (4 8) (5 9)))
(0 (0 68 97 62) ((2 12) (3 13) (4 14) (5 15)))
(0 (68 66 0 31) ((3 7) (4 8) (5 9) (6 10)))
(0 (66 0 31 47) ((4 8) (5 9) (6 10) (7 11)))
..... 省略 .....
(23569920 (60 64 62 99) ((3 5) (4 6) (5 7) (6 8)))
(26321504 (94 88 37 86) ((9 10) (10 11) (11 12) (12 13)))
(30692718 (51 89 98 69) ((16 12) (17 13) (18 14) (19 15)))
(32565456 (84 66 66 89) ((14 5) (15 6) (16 7) (17 8)))
(32719995 (49 95 71 99) ((1 2) (2 3) (3 4) (4 5)))
(40304286 (94 99 71 61) ((9 16) (10 17) (11 18) (12 19))))
> (sort
(map (lambda (d)
(let ((vals (map value-of d)))
(list (apply * vals) vals d)))
(map diagonal-l (product (iota 17 3) (iota 17))))
(lambda (a b) (< (car a) (car b))))
((0 (42 0 80 4) ((3 11) (2 12) (1 13) (0 14)))
(0 (22 42 0 80) ((4 10) (3 11) (2 12) (1 13)))
(0 (0 22 42 0) ((5 9) (4 10) (3 11) (2 12)))
(0 (0 81 55 23) ((6 0) (5 1) (4 2) (3 3)))
(0 (99 0 22 42) ((6 8) (5 9) (4 10) (3 11)))
(0 (20 99 0 22) ((7 7) (6 8) (5 9) (4 10)))
..... 省略 .....
(27993600 (75 96 48 81) ((5 10) (4 11) (3 12) (2 13)))
(30987600 (98 93 40 85) ((18 14) (17 15) (16 16) (15 17)))
(34826064 (78 98 67 68) ((13 0) (12 1) (11 2) (10 3)))
(38140594 (47 89 94 97) ((7 11) (6 12) (5 13) (4 14)))
(41076896 (98 67 68 92) ((12 1) (11 2) (10 3) (9 4)))
(70600674 (89 94 97 87) ((6 12) (5 13) (4 14) (3 15))))
>
(require srfi/1)
(define (sieve pv n)
(define (loop i)
(when (< i (vector-length pv))
(vector-set! pv i #f)
(loop (+ i n))))
(loop (+ n n)))
(define (find-prime pv start)
(cond ((<= (vector-length pv) start) #f)
((vector-ref pv start) start)
(else (find-prime pv (+ start 1)))))
(define (eratosthenes pv)
(define (loop n)
(when (and n (< n (sqrt (vector-length pv))))
(sieve pv n)
(loop (find-prime pv (+ n 1)))))
(loop 2))
(define (prime-vector n)
(let ((pv (make-vector (+ n 1) #t)))
(eratosthenes pv)
pv))
(define (prime-vect-to-list pv)
(define (loop ans n)
(if (< n (vector-length pv))
(let ((p (find-prime pv n)))
(if p
(loop (cons p ans) (+ p 1))
(reverse ans)))
(reverse ans)))
(loop () 2))
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 512 MB. > (fold + 0 (prime-vect-to-list (prime-vector 10))) 17 > (fold + 0 (prime-vect-to-list (prime-vector 2000000))) 142913828922 >
(require srfi/1)
(define (range lower upper)
(if (<= lower upper)
(iota (+ 1 (- upper lower)) lower)
()))
(define (pythagorean? a b c)
(= (+ (* a a)
(* b b))
(* c c)))
(define (pythagorean-list upper)
(apply append
(map (lambda (a)
(apply append
(map (lambda (b)
(filter-map (lambda (c)
(and (pythagorean? a b c)
(list a b c)))
(range b (- upper (+ a b)))))
(range a (- upper a)))))
(range 1 upper))))
ようこそ DrRacket, バージョン 5.3.3 [3m].
言語: Pretty Big; memory limit: 2048 MB.
> (pythagorean-list 20)
((3 4 5))
> (sort (map (lambda (x) (list (fold + 0 x) x))
(pythagorean-list 1000))
(lambda (a b) (< (car a) (car b))))
((12 (3 4 5))
(24 (6 8 10))
(30 (5 12 13))
(36 (9 12 15))
(40 (8 15 17))
(48 (12 16 20))
(56 (7 24 25))
(60 (10 24 26))
... 省略 ...
(988 (266 312 410))
(990 (99 440 451))
(990 (165 396 429))
(990 (180 385 425))
(990 (264 315 411))
(992 (31 480 481))
(996 (249 332 415))
(1000 (200 375 425)))
> (+ 200 375 425)
1000
>
(require srfi/1)
(define prob-8
(list 7 3 1 6 7 1 7 6 5 3 1 3 3 0 6 2 4 9 1 9 2 2 5 1 1 9 6 7 4 4 2 6 5 7 4 7 4 2 3 5 5 3 4 9 1 9 4 9 3 4
9 6 9 8 3 5 2 0 3 1 2 7 7 4 5 0 6 3 2 6 2 3 9 5 7 8 3 1 8 0 1 6 9 8 4 8 0 1 8 6 9 4 7 8 8 5 1 8 4 3
8 5 8 6 1 5 6 0 7 8 9 1 1 2 9 4 9 4 9 5 4 5 9 5 0 1 7 3 7 9 5 8 3 3 1 9 5 2 8 5 3 2 0 8 8 0 5 5 1 1
1 2 5 4 0 6 9 8 7 4 7 1 5 8 5 2 3 8 6 3 0 5 0 7 1 5 6 9 3 2 9 0 9 6 3 2 9 5 2 2 7 4 4 3 0 4 3 5 5 7
6 6 8 9 6 6 4 8 9 5 0 4 4 5 2 4 4 5 2 3 1 6 1 7 3 1 8 5 6 4 0 3 0 9 8 7 1 1 1 2 1 7 2 2 3 8 3 1 1 3
6 2 2 2 9 8 9 3 4 2 3 3 8 0 3 0 8 1 3 5 3 3 6 2 7 6 6 1 4 2 8 2 8 0 6 4 4 4 4 8 6 6 4 5 2 3 8 7 4 9
3 0 3 5 8 9 0 7 2 9 6 2 9 0 4 9 1 5 6 0 4 4 0 7 7 2 3 9 0 7 1 3 8 1 0 5 1 5 8 5 9 3 0 7 9 6 0 8 6 6
7 0 1 7 2 4 2 7 1 2 1 8 8 3 9 9 8 7 9 7 9 0 8 7 9 2 2 7 4 9 2 1 9 0 1 6 9 9 7 2 0 8 8 8 0 9 3 7 7 6
6 5 7 2 7 3 3 3 0 0 1 0 5 3 3 6 7 8 8 1 2 2 0 2 3 5 4 2 1 8 0 9 7 5 1 2 5 4 5 4 0 5 9 4 7 5 2 2 4 3
5 2 5 8 4 9 0 7 7 1 1 6 7 0 5 5 6 0 1 3 6 0 4 8 3 9 5 8 6 4 4 6 7 0 6 3 2 4 4 1 5 7 2 2 1 5 5 3 9 7
5 3 6 9 7 8 1 7 9 7 7 8 4 6 1 7 4 0 6 4 9 5 5 1 4 9 2 9 0 8 6 2 5 6 9 3 2 1 9 7 8 4 6 8 6 2 2 4 8 2
8 3 9 7 2 2 4 1 3 7 5 6 5 7 0 5 6 0 5 7 4 9 0 2 6 1 4 0 7 9 7 2 9 6 8 6 5 2 4 1 4 5 3 5 1 0 0 4 7 4
8 2 1 6 6 3 7 0 4 8 4 4 0 3 1 9 9 8 9 0 0 0 8 8 9 5 2 4 3 4 5 0 6 5 8 5 4 1 2 2 7 5 8 8 6 6 6 8 8 1
1 6 4 2 7 1 7 1 4 7 9 9 2 4 4 4 2 9 2 8 2 3 0 8 6 3 4 6 5 6 7 4 8 1 3 9 1 9 1 2 3 1 6 2 8 2 4 5 8 6
1 7 8 6 6 4 5 8 3 5 9 1 2 4 5 6 6 5 2 9 4 7 6 5 4 5 6 8 2 8 4 8 9 1 2 8 8 3 1 4 2 6 0 7 6 9 0 0 4 2
2 4 2 1 9 0 2 2 6 7 1 0 5 5 6 2 6 3 2 1 1 1 1 1 0 9 3 7 0 5 4 4 2 1 7 5 0 6 9 4 1 6 5 8 9 6 0 4 0 8
0 7 1 9 8 4 0 3 8 5 0 9 6 2 4 5 5 4 4 4 3 6 2 9 8 1 2 3 0 9 8 7 8 7 9 9 2 7 2 4 4 2 8 4 9 0 9 1 8 8
8 4 5 8 0 1 5 6 1 6 6 0 9 7 9 1 9 1 3 3 8 7 5 4 9 9 2 0 0 5 2 4 0 6 3 6 8 9 9 1 2 5 6 0 7 1 7 6 0 6
0 5 8 8 6 1 1 6 4 6 7 1 0 9 4 0 5 0 7 7 5 4 1 0 0 2 2 5 6 9 8 3 1 5 5 2 0 0 0 5 5 9 3 5 7 2 9 7 2 5
7 1 6 3 6 2 6 9 5 6 1 8 8 2 6 7 0 4 2 8 2 5 2 4 8 3 6 0 0 8 2 3 2 5 7 5 3 0 4 2 0 7 5 2 9 6 3 4 5 0))
(define (take-5 lst)
(if (< (length lst) 5)
()
(cons (take lst 5) (take-5 (cdr lst)))))
ようこそ DrRacket, バージョン 5.3.3 [3m].
言語: Pretty Big; memory limit: 512 MB.
> (sort
(map (lambda (lst) (list (fold * 1 lst) lst))
(take-5 prob-8))
(lambda (a b) (< (car a) (car b))))
((0 (3 1 3 3 0))
(0 (1 3 3 0 6))
(0 (3 3 0 6 2))
(0 (3 0 6 2 4))
(0 (0 6 2 4 9))
..... 省略 .....
(15552 (8 3 9 9 8))
(16128 (9 4 7 8 8))
(18144 (7 6 6 8 9))
(24696 (7 9 7 7 8))
(28224 (9 8 7 8 7))
(28224 (8 7 8 7 9))
(31752 (9 8 7 9 7))
(31752 (8 7 9 7 9))
(31752 (7 8 7 9 9))
(40824 (9 9 8 7 9)))
>
(require srfi/1)
(define (sieve pv n)
(define (loop i)
(when (< i (vector-length pv))
(vector-set! pv i #f)
(loop (+ i n))))
(loop (+ n n)))
(define (find-prime pv start)
(cond ((<= (vector-length pv) start) #f)
((vector-ref pv start) start)
(else (find-prime pv (+ start 1)))))
(define (eratosthenes pv)
(define (loop n)
(when (and n (< n (sqrt (vector-length pv))))
(sieve pv n)
(loop (find-prime pv (+ n 1)))))
(loop 2))
(define (prime-vector n)
(let ((pv (make-vector (+ n 1) #t)))
(eratosthenes pv)
pv))
(define (prime-vect-to-list pv)
(define (loop ans n)
(if (< n (vector-length pv))
(let ((p (find-prime pv n)))
(if p
(loop (cons p ans) (+ p 1))
(reverse ans)))
(reverse ans)))
(loop () 2))
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 512 MB. > (prime-vect-to-list (prime-vector 100)) (2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97) > (define pl (prime-vect-to-list (prime-vector 1000000))) > (length pl) 78498 > (list-ref pl 10000) 104743 >
(require srfi/1) (define (square n) (* n n))
ようこそ DrRacket, バージョン 5.3.3 [3m].
言語: Pretty Big; memory limit: 512 MB.
> (- (square (fold + 0 (iota 100 1)))
(fold + 0 (map square (iota 100 1))))
25164150
>
(require srfi/1)
(define (square n) (* n n))
(define (divides? a b)
(= (remainder b a) 0))
(define (find-divisor n test-divisor)
(cond ((> (square test-divisor) n) n)
((divides? test-divisor n) test-divisor)
(else (find-divisor n (+ test-divisor 1)))))
(define (smallest-divisor n)
(find-divisor n 2))
;; 素因数分解
(define (prime-factorization n)
(let ((a (smallest-divisor n)))
(if (= a n)
(list n)
(cons a (prime-factorization (/ n a))))))
;; リストから要素を一つ取り除く
(define (remove-one lst obj)
(cond ((null? lst) ())
((equal? (car lst) obj) (cdr lst))
(else (cons (car lst) (remove-one (cdr lst) obj)))))
;; bの要素がaに含まれてない場合にaに追加する.
(define (merge a b)
(cond ((null? a) b)
((null? b) a)
((member (car b) a)
(cons (car b)
(merge (remove-one a (car b)) (cdr b))))
(else (cons (car b) (merge a (cdr b))))))
(define (my-lcm n)
(fold *
1
(fold merge
()
(map prime-factorization (iota n 1)))))
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 512 MB. > (my-lcm 10) 2520 > (my-lcm 20) 232792560 >
(require srfi/1)
(define (decimal-format nbr)
(define (loop ans n)
(if (= 0 n)
ans
(loop (cons (remainder n 10) ans) (quotient n 10))))
(loop () nbr))
(define (palindromic? nbr)
(let ((dec (decimal-format nbr)))
(equal? dec (reverse dec))))
ようこそ DrRacket, バージョン 5.3.3 [3m].
言語: Pretty Big; memory limit: 512 MB.
> (sort (apply append
(filter (lambda (lst) (not (equal? lst ())))
(map (lambda (n)
(filter (lambda (a) (palindromic? (car a)))
(map (lambda (i) (list (* i n) i n))
(iota 900 100))))
(iota 900 100))))
(lambda (a b) (< (car a) (car b))))
((10201 101 101)
(11211 111 101)
(11211 101 111)
(12221 121 101)
(12221 101 121)
(12321 111 111)
(13231 131 101)
(13231 101 131)
..... 省略 .....
(886688 968 916)
(886688 916 968)
(888888 962 924)
(888888 924 962)
(906609 993 913)
(906609 913 993))
>
(require srfi/1)
(define (square n) (* n n))
(define (divides? a b)
(= (remainder b a) 0))
(define (find-divisor n test-divisor)
(cond ((> (square test-divisor) n) n)
((divides? test-divisor n) test-divisor)
(else (find-divisor n (+ test-divisor 1)))))
(define (smallest-divisor n)
(find-divisor n 2))
(define (prime-factorization n)
(let ((a (smallest-divisor n)))
(if (= a n)
(list n)
(cons a (prime-factorization (/ n a))))))
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 512 MB. > (prime-factorization 600851475143) (71 839 1471 6857) > (* 71 839 1471 6857) 600851475143 >
(define (fib-list n)
(define (loop r a b)
(if (< n a)
(reverse r)
(loop (cons a r) b (+ a b))))
(loop () 1 2))
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 128 MB. > (fib-list 100) (1 2 3 5 8 13 21 34 55 89) > (filter even? (fib-list 100)) (2 8 34) > (apply + (filter even? (fib-list 100))) 44 > (apply + (filter even? (fib-list 4000000))) 4613732
> (fib-list 4000000) (1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 1346269 2178309 3524578)
(require srfi/1)
(define (div-3-or-5? n)
(or (= 0 (remainder n 3))
(= 0 (remainder n 5))))
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 128 MB. > (iota 9 1) (1 2 3 4 5 6 7 8 9) > (filter div-3-or-5? (iota 9 1)) (3 5 6 9) > (apply + (filter div-3-or-5? (iota 9 1))) 23 >
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 128 MB. > (apply + (filter div-3-or-5? (iota 999 1))) 233168 >
ようこそ DrRacket, バージョン 5.3.3 [3m]. 言語: Pretty Big; memory limit: 512 MB. > (require srfi/1) > (apply + (iota 333 3 3)) 166833 > (apply + (iota 199 5 5)) 99500 > (apply + (iota 66 15 15)) 33165 > (- (+ 166833 99500) 33165) 233168 >