Add elisp/grains

2019-06-26 21:14:07 +00:00
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+# Grains
+
+Calculate the number of grains of wheat on a chessboard given that the number
+on each square doubles.
+
+There once was a wise servant who saved the life of a prince. The king
+promised to pay whatever the servant could dream up. Knowing that the
+king loved chess, the servant told the king he would like to have grains
+of wheat. One grain on the first square of a chess board. Two grains on
+the next. Four on the third, and so on.
+
+There are 64 squares on a chessboard.
+
+Write code that shows:
+- how many grains were on each square, and
+- the total number of grains
+
+
+## For bonus points
+
+Did you get the tests passing and the code clean? If you want to, these
+are some additional things you could try:
+
+- Optimize for speed.
+- Optimize for readability.
+
+Then please share your thoughts in a comment on the submission. Did this
+experiment make the code better? Worse? Did you learn anything from it?
+## Source
+
+JavaRanch Cattle Drive, exercise 6 [http://www.javaranch.com/grains.jsp](http://www.javaranch.com/grains.jsp)
+
+## Submitting Incomplete Solutions
+It's possible to submit an incomplete solution so you can see how others have completed the exercise.
@@ -0,0 +1,38 @@
+;;; grains-test.el --- Test for Grains (exercism)
+
+;;; Commentary:
+
+;;; Code:
+
+(load-file "grains.el")
+
+(ert-deftest square-1 ()
+  (should (= 1 (square 1))))
+
+(ert-deftest square-2 ()
+  (should (= 2 (square 2))))
+
+(ert-deftest square-3 ()
+  (should (= 4 (square 3))))
+
+(ert-deftest square-4 ()
+  (should (= 8 (square 4))))
+
+(ert-deftest square-16 ()
+  (should (= 32768
+             (square 16))))
+
+(ert-deftest square-32 ()
+  (should (= 2147483648
+             (square 32))))
+
+(ert-deftest square-64 ()
+  (should (= 9223372036854775808
+             (square 64))))
+
+(ert-deftest total-grains ()
+  (should (= 18446744073709551615
+             (total))))
+
+(provide 'grains-test.el)
+;;; grains-test.el ends here.
@@ -0,0 +1,123 @@
+;;; grains.el --- Grains exercise (exercism)
+
+;;; Commentary:
+;;; I solved this problem on the C track. There, the solution was
+;;; simpler: simply shift an unsigned long long to get the number of
+;;; grains at square n.
+;;;
+;;; In Emacs, that approach doesn't seem to work. Only 30 bits are used
+;;; for integers, resulting in overflows above square 60.
+;;;
+;;; The solution, if one wants to calculate it, seems to be to rely on
+;;; the calc package to calculate bigger numbers. The functions
+;;; calculate-square and calculate-total rely on that approach.
+;;;
+;;; However, it also occurred to me that the values here are known,
+;;; limited, and not likely to change anytime soon. By using contants,
+;;; we can get constant time determination of the number of grains for
+;;; a square. The functions used by the tests, square and total, simply
+;;; return constant values, with the number of grains for a square
+;;; relying on a vector that matches the n-th index to the corresponding
+;;; grains.
+;;;
+;;; Emacs itself was useful in effectuating this solution. I used a
+;;; macro to evaluate calculate-square for n, and then insert the
+;;; results in this buffer. There's probably a more elegant way to do
+;;; this in Emacs, but this approach was adequate for the task.
+;;; Sometimes, making the programmer's life easier can lead to more
+;;; efficient code.
+
+;;; Code:
+
+(require 'calc)
+
+(defun calculate-square(n)
+  "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."
+  (cond ((< n 0) 0)
+	((> n 65) 0)
+	((<= n 60) (lsh 1 (- n 1)))
+	(t (string-to-number (calc-eval (format "2^%d" (1- n)))))))
+
+(defun calculate-total()
+  "Return the total number of grains on a chessboard with 64 squares."
+  (1- (square 65)))
+
+(defvar grains [0
+		1
+		2
+		4
+		8
+		16
+		32
+		64
+		128
+		256
+		512
+		1024
+		2048
+		4096
+		8192
+		16384
+		32768
+		65536
+		131072
+		262144
+		524288
+		1048576
+		2097152
+		4194304
+		8388608
+		16777216
+		33554432
+		67108864
+		134217728
+		268435456
+		536870912
+		1073741824
+		2147483648
+		4294967296
+		8589934592
+		17179869184
+		34359738368
+		68719476736
+		137438953472
+		274877906944
+		549755813888
+		1099511627776
+		2199023255552
+		4398046511104
+		8796093022208
+		17592186044416
+		35184372088832
+		70368744177664
+		140737488355328
+		281474976710656
+		562949953421312
+		1125899906842624
+		2251799813685248
+		4503599627370496
+		9007199254740992
+		18014398509481984
+		36028797018963968
+		72057594037927936
+		144115188075855872
+		288230376151711744
+		576460752303423488
+		1152921504606846976
+		2305843009213693952
+		4611686018427387904
+		9223372036854775808]
+  "Vector containing the number of grains for a square with the corresponding index.")
+
+(defun square(n)
+  "Return the number of grans at square n; 0 for negative numbers and numbers above 64."
+  (cond ((< n 0) 0)
+	((> n 64) 0)
+	(t (aref grains n))))
+
+(defun total()
+  "Return the total number of grains on a chessboard with 64 squares."
+  18446744073709551616)
+
+(provide 'grains)
+;;; grains.el ends here