Problem 8 » 履歴 » バージョン 4
Noppi, 2023/12/27 13:26
| 1 | 1 | Noppi | [ホーム](https://redmine.noppi.jp) - [[Wiki|Project Euler]] |
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| 2 | # [[Problem 8]] |
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| 3 | |||
| 4 | 4 | Noppi | ## Largest Product in a Series |
| 5 | The four adjacent digits in the $1000$-digit number that have the greatest product are $9 \times 9 \times 8 \times 9 = 5832$. |
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| 6 | ``` |
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| 7 | 73167176531330624919225119674426574742355349194934 |
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| 8 | 96983520312774506326239578318016984801869478851843 |
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| 9 | 85861560789112949495459501737958331952853208805511 |
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| 10 | 12540698747158523863050715693290963295227443043557 |
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| 11 | 66896648950445244523161731856403098711121722383113 |
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| 12 | 62229893423380308135336276614282806444486645238749 |
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| 13 | 30358907296290491560440772390713810515859307960866 |
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| 14 | 70172427121883998797908792274921901699720888093776 |
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| 15 | 65727333001053367881220235421809751254540594752243 |
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| 16 | 52584907711670556013604839586446706324415722155397 |
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| 17 | 53697817977846174064955149290862569321978468622482 |
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| 18 | 83972241375657056057490261407972968652414535100474 |
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| 19 | 82166370484403199890008895243450658541227588666881 |
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| 20 | 16427171479924442928230863465674813919123162824586 |
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| 21 | 17866458359124566529476545682848912883142607690042 |
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| 22 | 24219022671055626321111109370544217506941658960408 |
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| 23 | 07198403850962455444362981230987879927244284909188 |
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| 24 | 84580156166097919133875499200524063689912560717606 |
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| 25 | 05886116467109405077541002256983155200055935729725 |
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| 26 | 71636269561882670428252483600823257530420752963450 |
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| 27 | ``` |
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| 28 | Find the thirteen adjacent digits in the $1000$-digit number that have the greatest product. What is the value of this product? |
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| 29 | |||
| 30 | ## 数字列中の最大の積 |
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| 31 | 次の1000桁の数字のうち, 隣接する4つの数字の総乗の中で, 最大となる値は, 9 × 9 × 8 × 9 = 5832である. |
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| 32 | ``` |
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| 33 | 73167176531330624919225119674426574742355349194934 |
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| 34 | 96983520312774506326239578318016984801869478851843 |
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| 35 | 85861560789112949495459501737958331952853208805511 |
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| 36 | 12540698747158523863050715693290963295227443043557 |
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| 37 | 66896648950445244523161731856403098711121722383113 |
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| 38 | 62229893423380308135336276614282806444486645238749 |
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| 39 | 30358907296290491560440772390713810515859307960866 |
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| 40 | 70172427121883998797908792274921901699720888093776 |
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| 41 | 65727333001053367881220235421809751254540594752243 |
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| 42 | 52584907711670556013604839586446706324415722155397 |
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| 43 | 53697817977846174064955149290862569321978468622482 |
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| 44 | 83972241375657056057490261407972968652414535100474 |
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| 45 | 82166370484403199890008895243450658541227588666881 |
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| 46 | 16427171479924442928230863465674813919123162824586 |
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| 47 | 17866458359124566529476545682848912883142607690042 |
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| 48 | 24219022671055626321111109370544217506941658960408 |
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| 49 | 07198403850962455444362981230987879927244284909188 |
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| 50 | 84580156166097919133875499200524063689912560717606 |
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| 51 | 05886116467109405077541002256983155200055935729725 |
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| 52 | 71636269561882670428252483600823257530420752963450 |
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| 53 | ``` |
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| 54 | この1000桁の数字から13個の連続する数字を取り出して, それらの総乗を計算する. では、それら総乗のうち、最大となる値はいくらか. |
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| 55 | EX 6桁の数123789から5個の連続する数字を取り出す場合, 1*2*3*7*8と2*3*7*8*9の二通りとなり, 後者の2*3*7*8*9=3024が最大の総乗となる. |
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| 56 | |||
| 57 | 1 | Noppi | ```scheme |
| 58 | #!r6rs |
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| 59 | #!chezscheme |
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| 60 | |||
| 61 | (import (chezscheme)) |
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| 62 | |||
| 63 | (define Problem8-number-string |
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| 64 | (string-append "73167176531330624919225119674426574742355349194934" |
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| 65 | "96983520312774506326239578318016984801869478851843" |
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| 66 | "85861560789112949495459501737958331952853208805511" |
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| 67 | "12540698747158523863050715693290963295227443043557" |
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| 68 | "66896648950445244523161731856403098711121722383113" |
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| 69 | "62229893423380308135336276614282806444486645238749" |
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| 70 | "30358907296290491560440772390713810515859307960866" |
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| 71 | "70172427121883998797908792274921901699720888093776" |
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| 72 | "65727333001053367881220235421809751254540594752243" |
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| 73 | "52584907711670556013604839586446706324415722155397" |
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| 74 | "53697817977846174064955149290862569321978468622482" |
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| 75 | "83972241375657056057490261407972968652414535100474" |
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| 76 | "82166370484403199890008895243450658541227588666881" |
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| 77 | "16427171479924442928230863465674813919123162824586" |
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| 78 | "17866458359124566529476545682848912883142607690042" |
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| 79 | "24219022671055626321111109370544217506941658960408" |
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| 80 | "07198403850962455444362981230987879927244284909188" |
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| 81 | "84580156166097919133875499200524063689912560717606" |
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| 82 | "05886116467109405077541002256983155200055935729725" |
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| 83 | "71636269561882670428252483600823257530420752963450")) |
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| 84 | |||
| 85 | (define answer-8 |
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| 86 | 3 | Noppi | (let* ([count (- (string-length Problem8-number-string) |
| 87 | 13)]) |
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| 88 | (let loop ([index 0] [max-num 0]) |
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| 89 | 1 | Noppi | (if (< count index) |
| 90 | max-num |
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| 91 | 3 | Noppi | (let* ([sub-num (substring Problem8-number-string index (+ index 13))] |
| 92 | [char-lis (string->list sub-num)] |
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| 93 | [num-lis (map |
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| 94 | 1 | Noppi | (lambda (char) |
| 95 | (- (char->integer char) |
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| 96 | (char->integer #\0))) |
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| 97 | 3 | Noppi | char-lis)] |
| 98 | [product-num (fold-left * 1 num-lis)]) |
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| 99 | 1 | Noppi | (loop (add1 index) (max max-num product-num))))))) |
| 100 | |||
| 101 | (printf "8: ~D~%" answer-8) |
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| 102 | ``` |