Problem 28 » 履歴 » リビジョン 2
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# [[Problem 28]]
## Number Spiral Diagonals
Starting with the number $1$ and moving to the right in a clockwise direction a $5$ by $5$ spiral is formed as follows:
| | | | | |
|--|--|--|--|--|
| <span style="color:red"> **21** </span> | 22 | 23 | 24 | <span style="color:red"> **25** </span> |
| 20 | <span style="color:red"> **7** </span> | 8 | <span style="color:red"> **9** </span> | 10 |
| 19 | 6 | <span style="color:red"> **1** </span> | 2 | 11 |
| 18 | <span style="color:red"> **5** </span> | 4 | <span style="color:red"> **3** </span> | 12 |
| <span style="color:red"> **17** </span> | 16 | 15 | 14 | <span style="color:red"> **13** </span> |
It can be verified that the sum of the numbers on the diagonals is $101$.
What is the sum of the numbers on the diagonals in a $1001$ by $1001$ spiral formed in the same way?
## 螺旋状に並んだ数の対角線
1から初めて右方向に進み時計回りに数字を増やしていき, 5×5の螺旋が以下のように生成される:
| | | | | |
|--|--|--|--|--|
| <span style="color:red"> **21** </span> | 22 | 23 | 24 | <span style="color:red"> **25** </span> |
| 20 | <span style="color:red"> **7** </span> | 8 | <span style="color:red"> **9** </span> | 10 |
| 19 | 6 | <span style="color:red"> **1** </span> | 2 | 11 |
| 18 | <span style="color:red"> **5** </span> | 4 | <span style="color:red"> **3** </span> | 12 |
| <span style="color:red"> **17** </span> | 16 | 15 | 14 | <span style="color:red"> **13** </span> |
両対角線上の数字の合計は101であることが確かめられる.
1001×1001の螺旋を同じ方法で生成したとき, 対角線上の数字の和はいくつか?
```scheme
;;;
;;; 未完成！！！
;;;
(import (scheme base)
(gauche base)
(gauche array))
(define (make-table xynums)
(let ([table (make-array (shape 0 xynums 0 xynums) #f)])
(letrec ([walk-right (^[n y x]
(cond
[(and (< (+ x 1) xynums)
(not (array-ref table y (+ x 1))))
(array-set! table y (+ x 1) n)
(walk-down (+ n 1) y (+ x 1))]
[(and (<= 0 (- y 1))
(not (array-ref table (- y 1) x)))
(array-set! table (- y 1) x n)
(walk-right (+ n 1) (- y 1) x)]
[else table]))]
[walk-down (^[n y x]
(cond
[(and (< (+ y 1) xynums)
(not (array-ref table (+ y 1) x)))
(array-set! table (+ y 1) x n)
(walk-left (+ n 1) (+ y 1) x)]
[(and (< (+ x 1) xynums)
(not (array-ref table y (+ x 1))))
(array-set! table y (+ x 1) n)
(walk-down (+ n 1) y (+ x 1))]
[else table]))]
[walk-left (^[n y x]
(cond
[(and (<= 0 (- x 1))
(not (array-ref table y (- x 1))))
(array-set! table y (- x 1) n)
(walk-up (+ n 1) y (- x 1))]
[(and (< (+ y 1) xynums)
(not (array-ref table (+ y 1) x)))
(array-set! table (+ y 1) x n)
(walk-left (+ n 1) (+ y 1) x)]
[else table]))]
[walk-up (^[n y x]
(cond
[(and (<= 0 (- y 1))
(not (array-ref table (- y 1) x)))
(array-set! table (- y 1) x n)
(walk-right (+ n 1) (- y 1) x)]
[(and (<= 0 (- x 1))
(not (array-ref table y (- x 1))))
(array-set! table y (- x 1) n)
(walk-up (+ n 1) y (- x 1))]
[else table]))])
(array-set! table (div xynums 2) (div xynums 2) 1)
(walk-right 2 (div xynums 2) (div xynums 2)))))
;(define answer-28
;(format #t "28: ~d~%" answer-28)
```