# HG changeset patch # User Steve Losh # Date 1486761098 0 # Node ID 829e38d1f82503900dfdc5db071ebe48ff39804d # Parent a66997c0fad34674f1a21bb02e33746ed18be780 Fuck a `LOOP` diff -r a66997c0fad3 -r 829e38d1f825 src/euler.lisp --- 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 -------------------------------------------------------------------- diff -r a66997c0fad3 -r 829e38d1f825 src/primes.lisp --- 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) diff -r a66997c0fad3 -r 829e38d1f825 vendor/make-quickutils.lisp --- 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") diff -r a66997c0fad3 -r 829e38d1f825 vendor/quickutils.lisp --- 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 ;;;;