70 lines
2.8 KiB
EmacsLisp
70 lines
2.8 KiB
EmacsLisp
;;; grains.el --- Grains exercise (exercism)
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;;; Commentary:
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;;; I solved this problem on the C track. There, the solution was
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;;; simpler: simply shift an unsigned long long to get the number of
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;;; grains at square n.
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;;;
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;;; In Emacs, that approach doesn't seem to work. Only 61 bits are used
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;;; for integers, resulting in overflows above square 60.
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;;;
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;;; The solution, if one wants to calculate it, seems to be to rely on
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;;; the calc package to calculate bigger numbers. The functions
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;;; calculate-square and calculate-total rely on that approach.
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;;;
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;;; However, it also occurred to me that the values here are known,
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;;; limited, and not likely to change anytime soon. By using contants,
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;;; we can get constant time determination of the number of grains for
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;;; a square. The functions used by the tests, square and total, return
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;;; these constant values.
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;;;
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;;; Emacs itself was useful in effectuating this solution. I used a
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;;; macro to evaluate calculate-square for n, and then insert the
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;;; results in this buffer. There's probably a more elegant way to do
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;;; this, but the approach was adequate for this task.
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;;;
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;;; Sometimes, making the programmer's life easier can lead to more
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;;; efficient code.
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;;; Code:
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(require 'calc)
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(defvar grains
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[0 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072
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262144 524288 1048576 2097152 4194304 8388608 16777216 33554432 67108864
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134217728 268435456 536870912 1073741824 2147483648 4294967296 8589934592
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17179869184 34359738368 68719476736 137438953472 274877906944 549755813888
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1099511627776 2199023255552 4398046511104 8796093022208 17592186044416
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35184372088832 70368744177664 140737488355328 281474976710656
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562949953421312 1125899906842624 2251799813685248 4503599627370496
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9007199254740992 18014398509481984 36028797018963968 72057594037927936
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144115188075855872 288230376151711744 576460752303423488
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1152921504606846976 2305843009213693952 4611686018427387904
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9223372036854775808]
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"Vector containing the number of grains for a square with the corresponding index.")
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(defun square(n)
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"Return the number of grans at square n; 0 for negative numbers and numbers above 64."
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(cond ((< n 0) 0)
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((> n 64) 0)
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(t (aref grains n))))
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(defun total()
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"Return the total number of grains on a chessboard with 64 squares."
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18446744073709551616)
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(defun calculate-square(n) ;; Not used, for reference only.
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"Return the number of grains at square N. Use left shifts when n is equal to or below 60, and calc for numbers up to 65."
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(cond ((< n 0) 0)
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((> n 65) 0)
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((<= n 60) (lsh 1 (- n 1)))
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(t (string-to-number (calc-eval (format "2^%d" (1- n)))))))
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(defun calculate-total() ;; Not used, for reference only.
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"Return the total number of grains on a chessboard with 64 squares."
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(1- (square 65)))
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(provide 'grains)
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;;; grains.el ends here
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