--- a/src/euler.lisp Fri Feb 10 20:26:42 2017 +0000
+++ b/src/euler.lisp Fri Feb 10 21:11:38 2017 +0000
@@ -10,7 +10,7 @@
(let ((s (format nil "~D" n)))
(string= s (reverse s))))
-(defun palindrome-p (n)
+(defun palindromep (n)
"Return whether `n` is a palindrome (in base 10)."
(assert (>= n 0) (n) "~A must be a non-negative integer" n)
;; All even-length base-10 palindromes are divisible by 11, so we can shortcut
@@ -26,20 +26,9 @@
(not (dividesp n 11))) nil)
(t (definitely-palindrome-p n))))
-(defun range (from below)
- (loop :for i :from from :below below
- :collect i))
-
-(defun square (n)
- (* n n))
-
-
-(defun random-exclusive (min max)
- "Return an integer in the range (`min`, `max`)."
- (+ 1 min (random (- max min 1))))
-(defun dividesp (n divisor)
- "Return whether `n` is evenly divisible by `divisor`."
- (zerop (mod n divisor)))
+(defun sum (sequence)
+ (iterate (for n :in-whatever sequence)
+ (sum n)))
;;;; Problems -----------------------------------------------------------------
@@ -48,10 +37,10 @@
;; we get 3, 5, 6 and 9. The sum of these multiples is 23.
;;
;; Find the sum of all the multiples of 3 or 5 below 1000.
- (loop :for i :from 1 :below 1000
- :when (or (dividesp i 3)
- (dividesp i 5))
- :sum i))
+ (iterate (for i :from 1 :below 1000)
+ (when (or (dividesp i 3)
+ (dividesp i 5))
+ (sum i))))
(defun problem-2 ()
;; Each new term in the Fibonacci sequence is generated by adding the previous
@@ -61,12 +50,13 @@
;;
;; By considering the terms in the Fibonacci sequence whose values do not
;; exceed four million, find the sum of the even-valued terms.
- (loop :with p = 0
- :with n = 1
- :while (<= n 4000000)
- :when (evenp n) :sum n
- :do (psetf p n
- n (+ p n))))
+ (iterate (with a = 0)
+ (with b = 1)
+ (while (<= b 4000000))
+ (when (evenp b)
+ (sum b))
+ (psetf a b
+ b (+ a b))))
(defun problem-3 ()
;; The prime factors of 13195 are 5, 7, 13 and 29.
@@ -79,13 +69,11 @@
;; from the product of two 2-digit numbers is 9009 = 91 × 99.
;;
;; Find the largest palindrome made from the product of two 3-digit numbers.
- (let ((result (list)))
- (loop :for i :from 0 :to 999
- :do (loop :for j :from 0 :to 999
- :for product = (* i j)
- :when (palindrome-p product)
- :do (push product result)))
- (apply #'max result)))
+ (iterate (for-nested ((i :from 0 :to 999)
+ (j :from 0 :to 999)))
+ (for product = (* i j))
+ (when (palindromep product)
+ (maximize product))))
(defun problem-5 ()
;; 2520 is the smallest number that can be divided by each of the numbers from
@@ -93,7 +81,7 @@
;;
;; What is the smallest positive number that is evenly divisible by all of the
;; numbers from 1 to 20?
- (let ((divisors (range 11 21)))
+ (iterate
;; all numbers are divisible by 1 and we can skip checking everything <= 10
;; because:
;;
@@ -106,18 +94,17 @@
;; anything divisible by 16 is automatically divisible by 8
;; anything divisible by 18 is automatically divisible by 9
;; anything divisible by 20 is automatically divisible by 10
- (loop :for i
- :from 20 :by 20 ; it must be divisible by 20
- :when (every (lambda (n) (dividesp i n))
- divisors)
- :return i)))
+ (with divisors = (range 11 21))
+ (for i :from 20 :by 20) ; it must be divisible by 20
+ (finding i :such-that (every (lambda (n) (dividesp i n))
+ divisors))))
(defun problem-6 ()
;; The sum of the squares of the first ten natural numbers is,
- ;; 1^2 + 2^2 + ... + 10^2 = 385
+ ;; 1² + 2² + ... + 10² = 385
;;
;; The square of the sum of the first ten natural numbers is,
- ;; (1 + 2 + ... + 10)^2 = 55^2 = 3025
+ ;; (1 + 2 + ... + 10)² = 55² = 3025
;;
;; Hence the difference between the sum of the squares of the first ten
;; natural numbers and the square of the sum is 3025 − 385 = 2640.
@@ -125,37 +112,55 @@
;; Find the difference between the sum of the squares of the first one hundred
;; natural numbers and the square of the sum.
(flet ((sum-of-squares (to)
- (loop :for i :from 1 :to to
- :sum (square i)))
+ (sum (range 1 (1+ to) :key #'square)))
(square-of-sum (to)
- (square (loop :for i :from 1 :to to
- :sum i))))
+ (square (sum (range 1 (1+ to))))))
(abs (- (sum-of-squares 100) ; apparently it wants the absolute value
(square-of-sum 100)))))
(defun problem-7 ()
+ ;; By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see
+ ;; that the 6th prime is 13.
+ ;;
+ ;; What is the 10 001st prime number?
(nth-prime 10001))
(defun problem-8 ()
- (let ((digits (map 'list #'digit-char-p
- "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450")))
- (loop :for window :in (n-grams 13 digits)
- :maximize (apply #'* window))))
+ ;; The four adjacent digits in the 1000-digit number that have the greatest
+ ;; product are 9 × 9 × 8 × 9 = 5832.
+ ;;
+ ;; Find the thirteen adjacent digits in the 1000-digit number that have the
+ ;; greatest product. What is the value of this product?
+ (let ((digits (map 'list #'digit-char-p
+ "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450")))
+ (iterate (for window :in (n-grams 13 digits))
+ (maximize (apply #'* window)))))
(defun problem-9 ()
+ ;; A Pythagorean triplet is a set of three natural numbers, a < b < c, for
+ ;; which:
+ ;;
+ ;; a² + b² = c²
+ ;;
+ ;; For example, 3² + 4² = 9 + 16 = 25 = 5².
+ ;;
+ ;; There exists exactly one Pythagorean triplet for which a + b + c = 1000.
+ ;; Find the product abc.
(flet ((pythagorean-triplet-p (a b c)
(= (+ (square a) (square b))
(square c))))
- (block search
- (loop :for c :from 998 :downto 1 ; they must add up to 1000, so C can be at most 998
- :do (loop :for a :from (- 999 c) :downto 1 ; A can be at most 999 - C (to leave 1 for B)
- :for b = (- 1000 c a)
- :when (pythagorean-triplet-p a b c)
- :do (return-from search (* a b c)))))))
+ ;; They must add up to 1000, so C can be at most 998.
+ ;; A can be at most 999 - C (to leave 1 for B).
+ (iterate (for c :from 998 :downto 1)
+ (iterate (for a :from (- 999 c) :downto 1)
+ (for b = (- 1000 c a))
+ (when (pythagorean-triplet-p a b c)
+ (return-from problem-9 (* a b c)))))))
(defun problem-10 ()
- (loop :for p :in (primes-below 2000000)
- :sum p))
+ ;; The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
+ ;; Find the sum of all the primes below two million.
+ (sum (primes-below 2000000)))
;;;; Tests --------------------------------------------------------------------
--- a/src/primes.lisp Fri Feb 10 20:26:42 2017 +0000
+++ b/src/primes.lisp Fri Feb 10 21:11:38 2017 +0000
@@ -71,7 +71,7 @@
(flet ((fermat-check (a)
(= (expmod a n n) a)))
(loop :repeat tests
- :when (not (fermat-check (random-exclusive 0 n)))
+ :when (not (fermat-check (random-range-exclusive 0 n)))
:do (return nil)
:finally (return t))))
@@ -112,7 +112,7 @@
:when (= y (1- n))
:do (return t))))))
(loop :repeat k
- :for a = (random-exclusive 1 (1- n))
+ :for a = (random-range-exclusive 1 (1- n))
:always (strong-liar-p a)))))))
(defun brute-force-prime-p (n)
--- a/vendor/make-quickutils.lisp Fri Feb 10 20:26:42 2017 +0000
+++ b/vendor/make-quickutils.lisp Fri Feb 10 21:11:38 2017 +0000
@@ -5,10 +5,11 @@
:utilities '(
:define-constant
+ :ensure-boolean
+ :n-grams
+ :range
:switch
- :ensure-boolean
:with-gensyms
- :n-grams
)
:package "EULER.QUICKUTILS")
--- a/vendor/quickutils.lisp Fri Feb 10 20:26:42 2017 +0000
+++ b/vendor/quickutils.lisp Fri Feb 10 21:11:38 2017 +0000
@@ -2,7 +2,7 @@
;;;; See http://quickutil.org for details.
;;;; To regenerate:
-;;;; (qtlc:save-utils-as "quickutils.lisp" :utilities '(:DEFINE-CONSTANT :SWITCH :ENSURE-BOOLEAN :WITH-GENSYMS :N-GRAMS) :ensure-package T :package "EULER.QUICKUTILS")
+;;;; (qtlc:save-utils-as "quickutils.lisp" :utilities '(:DEFINE-CONSTANT :ENSURE-BOOLEAN :N-GRAMS :RANGE :SWITCH :WITH-GENSYMS) :ensure-package T :package "EULER.QUICKUTILS")
(eval-when (:compile-toplevel :load-toplevel :execute)
(unless (find-package "EULER.QUICKUTILS")
@@ -13,9 +13,10 @@
(in-package "EULER.QUICKUTILS")
(when (boundp '*utilities*)
- (setf *utilities* (union *utilities* '(:DEFINE-CONSTANT :STRING-DESIGNATOR
+ (setf *utilities* (union *utilities* '(:DEFINE-CONSTANT :ENSURE-BOOLEAN :TAKE
+ :N-GRAMS :RANGE :STRING-DESIGNATOR
:WITH-GENSYMS :EXTRACT-FUNCTION-NAME
- :SWITCH :ENSURE-BOOLEAN :TAKE :N-GRAMS))))
+ :SWITCH))))
(defun %reevaluate-constant (name value test)
(if (not (boundp name))
@@ -54,6 +55,40 @@
,@(when documentation `(,documentation))))
+ (defun ensure-boolean (x)
+ "Convert `x` into a Boolean value."
+ (and x t))
+
+
+ (defun take (n sequence)
+ "Take the first `n` elements from `sequence`."
+ (subseq sequence 0 n))
+
+
+ (defun n-grams (n sequence)
+ "Find all `n`-grams of the sequence `sequence`."
+ (assert (and (plusp n)
+ (<= n (length sequence))))
+
+ (etypecase sequence
+ ;; Lists
+ (list (loop :repeat (1+ (- (length sequence) n))
+ :for seq :on sequence
+ :collect (take n seq)))
+
+ ;; General sequences
+ (sequence (loop :for i :to (- (length sequence) n)
+ :collect (subseq sequence i (+ i n))))))
+
+
+ (defun range (start end &key (step 1) (key 'identity))
+ "Return the list of numbers `n` such that `start <= n < end` and
+`n = start + k*step` for suitable integers `k`. If a function `key` is
+provided, then apply it to each number."
+ (assert (<= start end))
+ (loop :for i :from start :below end :by step :collecting (funcall key i)))
+
+
(deftype string-designator ()
"A string designator type. A string designator is either a string, a symbol,
or a character."
@@ -147,34 +182,8 @@
"Like `switch`, but signals a continuable error if no key matches."
(generate-switch-body whole object clauses test key '(cerror "Return NIL from CSWITCH.")))
-
- (defun ensure-boolean (x)
- "Convert `x` into a Boolean value."
- (and x t))
-
-
- (defun take (n sequence)
- "Take the first `n` elements from `sequence`."
- (subseq sequence 0 n))
-
-
- (defun n-grams (n sequence)
- "Find all `n`-grams of the sequence `sequence`."
- (assert (and (plusp n)
- (<= n (length sequence))))
-
- (etypecase sequence
- ;; Lists
- (list (loop :repeat (1+ (- (length sequence) n))
- :for seq :on sequence
- :collect (take n seq)))
-
- ;; General sequences
- (sequence (loop :for i :to (- (length sequence) n)
- :collect (subseq sequence i (+ i n))))))
-
(eval-when (:compile-toplevel :load-toplevel :execute)
- (export '(define-constant switch eswitch cswitch ensure-boolean with-gensyms
- with-unique-names n-grams)))
+ (export '(define-constant ensure-boolean n-grams range switch eswitch cswitch
+ with-gensyms with-unique-names)))
;;;; END OF quickutils.lisp ;;;;