124 lines
3.0 KiB
EmacsLisp
124 lines
3.0 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 30 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, simply
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;;; return constant values, with the number of grains for a square
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;;; relying on a vector that matches the n-th index to the corresponding
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;;; grains.
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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 in Emacs, but this approach was adequate for the task.
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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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(defun calculate-square(n)
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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()
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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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(defvar grains [0
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1
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2
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4
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8
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16
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32
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64
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128
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256
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512
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1024
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2048
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4096
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8192
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16384
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32768
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65536
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131072
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262144
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524288
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1048576
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2097152
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4194304
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8388608
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16777216
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33554432
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67108864
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134217728
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268435456
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536870912
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1073741824
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2147483648
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4294967296
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8589934592
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17179869184
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34359738368
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68719476736
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137438953472
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274877906944
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549755813888
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1099511627776
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2199023255552
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4398046511104
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8796093022208
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17592186044416
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35184372088832
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70368744177664
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140737488355328
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281474976710656
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562949953421312
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1125899906842624
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2251799813685248
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4503599627370496
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9007199254740992
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18014398509481984
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36028797018963968
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72057594037927936
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144115188075855872
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288230376151711744
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576460752303423488
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1152921504606846976
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2305843009213693952
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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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(provide 'grains)
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;;; grains.el ends here
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