src/euler.lisp @ 5effe1bc7876

Problem 21
author Steve Losh <steve@stevelosh.com>
date Fri, 17 Feb 2017 13:07:45 +0000
parents 137ba2e799c4
children 7c082c0289d5
(in-package :euler)

;;;; Utils --------------------------------------------------------------------
(defmacro-driver (FOR var IN-DIGITS-OF integer &optional RADIX (radix 10))
  "Iterate `var` through the digits of `integer` in base `radix`, low-order first."
  (let ((kwd (if generate 'generate 'for)))
    (with-gensyms (i r remaining digit)
      `(progn
         (with ,r = ,radix)
         (with ,i = (abs ,integer))
         (,kwd ,var :next (if (zerop ,i)
                            (terminate)
                            (multiple-value-bind (,remaining ,digit)
                                (truncate ,i ,r)
                              (setf ,i ,remaining)
                              ,digit)))))))

(defun digits (n &optional (radix 10))
  "Return a fresh list of the digits of `n` in base `radix`."
  (iterate (for d :in-digits-of n :radix radix)
           (collect d :at :beginning)))

(defun digits-length (n &optional (radix 10))
  "Return how many digits `n` has in base `radix`."
  (if (zerop n)
    1
    (values (1+ (truncate (log (abs n) radix))))))


(defun definitely-palindrome-p (n)
  "Return whether `n` is a palindrome (in base 10), the slow-but-sure way."
  (let ((s (format nil "~D" n)))
    (string= s (reverse s))))

(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
  ;; the awful string comparison. E.g.:
  ;;
  ;;   abccba =
  ;;   100001 * a +
  ;;   010010 * b +
  ;;   001100 * c
  (cond
    ((zerop n) t)
    ((and (evenp (digits-length n))
          (not (dividesp n 11))) nil)
    (t (definitely-palindrome-p n))))


(defun sum (sequence &key key)
  (iterate (for n :in-whatever sequence)
           (sum (if key
                  (funcall key n)
                  n))))


(defun divisors (n)
  (sort (iterate (for i :from 1 :to (sqrt n))
                 (when (dividesp n i)
                   (collect i)
                   (collect (/ n i))))
        #'<))

(defun proper-divisors (n)
  (remove n (divisors n)))

(defun count-divisors (n)
  (* 2 (iterate (for i :from 1 :to (sqrt n))
                (counting (dividesp n i)))))


(defmacro-driver (FOR var IN-COLLATZ n)
  (let ((kwd (if generate 'generate 'for)))
    `(progn
       (,kwd ,var :next (cond ((null ,var) ,n)
                              ((= 1 ,var) (terminate))
                              ((evenp ,var) (/ ,var 2))
                              (t (1+ (* 3 ,var))))))))

(defun collatz (n)
  (iterate (for i :in-collatz n)
           (collect i)))

(defun collatz-length (n)
  (iterate (for i :in-collatz n)
           (counting t)))


(defun binomial-coefficient (n k)
  "Return `n` choose `k`."
  ;; https://en.wikipedia.org/wiki/Binomial_coefficient#Multiplicative_formula
  (iterate (for i :from 1 :to k)
           (multiply (/ (+ n 1 (- i))
                        i))))


(defun factorial (n)
  (iterate (for i :from 1 :to n)
           (multiplying i)))


;;;; Problems -----------------------------------------------------------------
(defun problem-1 ()
  ;; If we list all the natural numbers below 10 that are multiples of 3 or 5,
  ;; 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.
  (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
  ;; two terms. By starting with 1 and 2, the first 10 terms will be:
  ;;
  ;;     1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
  ;;
  ;; By considering the terms in the Fibonacci sequence whose values do not
  ;; exceed four million, find the sum of the even-valued terms.
  (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.
  ;;
  ;; What is the largest prime factor of the number 600851475143 ?
  (apply #'max (prime-factorization 600851475143)))

(defun problem-4 ()
  ;; A palindromic number reads the same both ways. The largest palindrome made
  ;; 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.
  (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
  ;; 1 to 10 without any remainder.
  ;;
  ;; What is the smallest positive number that is evenly divisible by all of the
  ;; numbers from 1 to 20?
  (iterate
    ;; all numbers are divisible by 1 and we can skip checking everything <= 10
    ;; because:
    ;;
    ;; anything divisible by 12 is automatically divisible by 2
    ;; anything divisible by 12 is automatically divisible by 3
    ;; anything divisible by 12 is automatically divisible by 4
    ;; anything divisible by 15 is automatically divisible by 5
    ;; anything divisible by 12 is automatically divisible by 6
    ;; anything divisible by 14 is automatically divisible by 7
    ;; 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
    (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,
  ;;   1² + 2² + ... + 10² = 385
  ;;
  ;; The square of the sum of the first ten natural numbers is,
  ;;   (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.
  ;;
  ;; 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)
           (sum (range 1 (1+ to) :key #'square)))
         (square-of-sum (to)
           (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 ()
  ;; 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))))
    ;; 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 ()
  ;; 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)))

(defun problem-11 ()
  ;; In the 20×20 grid below, four numbers along a diagonal line have been marked
  ;; in red.
  ;;
  ;; The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
  ;;
  ;; What is the greatest product of four adjacent numbers in the same direction
  ;; (up, down, left, right, or diagonally) in the 20×20 grid?
  (let ((grid
          #2A((08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08)
              (49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00)
              (81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65)
              (52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91)
              (22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80)
              (24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50)
              (32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70)
              (67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21)
              (24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72)
              (21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95)
              (78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92)
              (16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57)
              (86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58)
              (19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40)
              (04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66)
              (88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69)
              (04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36)
              (20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16)
              (20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54)
              (01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48))))
    (max
      ;; horizontal
      (iterate (for-nested ((row :from 0 :below 20)
                            (col :from 0 :below 16)))
               (maximize (* (aref grid row (+ 0 col))
                            (aref grid row (+ 1 col))
                            (aref grid row (+ 2 col))
                            (aref grid row (+ 3 col)))))
      ;; vertical
      (iterate (for-nested ((row :from 0 :below 16)
                            (col :from 0 :below 20)))
               (maximize (* (aref grid (+ 0 row) col)
                            (aref grid (+ 1 row) col)
                            (aref grid (+ 2 row) col)
                            (aref grid (+ 3 row) col))))
      ;; backslash \
      (iterate (for-nested ((row :from 0 :below 16)
                            (col :from 0 :below 16)))
               (maximize (* (aref grid (+ 0 row) (+ 0 col))
                            (aref grid (+ 1 row) (+ 1 col))
                            (aref grid (+ 2 row) (+ 2 col))
                            (aref grid (+ 3 row) (+ 3 col)))))
      ;; slash /
      (iterate (for-nested ((row :from 3 :below 20)
                            (col :from 0 :below 16)))
               (maximize (* (aref grid (- row 0) (+ 0 col))
                            (aref grid (- row 1) (+ 1 col))
                            (aref grid (- row 2) (+ 2 col))
                            (aref grid (- row 3) (+ 3 col))))))))

(defun problem-12 ()
  ;; The sequence of triangle numbers is generated by adding the natural
  ;; numbers. So the 7th triangle number would be
  ;; 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
  ;;
  ;; 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
  ;;
  ;; Let us list the factors of the first seven triangle numbers:
  ;;
  ;;  1: 1
  ;;  3: 1,3
  ;;  6: 1,2,3,6
  ;; 10: 1,2,5,10
  ;; 15: 1,3,5,15
  ;; 21: 1,3,7,21
  ;; 28: 1,2,4,7,14,28
  ;;
  ;; We can see that 28 is the first triangle number to have over five divisors.
  ;;
  ;; What is the value of the first triangle number to have over five hundred
  ;; divisors?
  (iterate (for n :from 1)
           (for tri :first n :then (+ tri n))
           (finding tri :such-that (> (count-divisors tri) 500))))

(defun problem-13 ()
  ;; Work out the first ten digits of the sum of the following one-hundred
  ;; 50-digit numbers.
  (-<> (+ 37107287533902102798797998220837590246510135740250
          46376937677490009712648124896970078050417018260538
          74324986199524741059474233309513058123726617309629
          91942213363574161572522430563301811072406154908250
          23067588207539346171171980310421047513778063246676
          89261670696623633820136378418383684178734361726757
          28112879812849979408065481931592621691275889832738
          44274228917432520321923589422876796487670272189318
          47451445736001306439091167216856844588711603153276
          70386486105843025439939619828917593665686757934951
          62176457141856560629502157223196586755079324193331
          64906352462741904929101432445813822663347944758178
          92575867718337217661963751590579239728245598838407
          58203565325359399008402633568948830189458628227828
          80181199384826282014278194139940567587151170094390
          35398664372827112653829987240784473053190104293586
          86515506006295864861532075273371959191420517255829
          71693888707715466499115593487603532921714970056938
          54370070576826684624621495650076471787294438377604
          53282654108756828443191190634694037855217779295145
          36123272525000296071075082563815656710885258350721
          45876576172410976447339110607218265236877223636045
          17423706905851860660448207621209813287860733969412
          81142660418086830619328460811191061556940512689692
          51934325451728388641918047049293215058642563049483
          62467221648435076201727918039944693004732956340691
          15732444386908125794514089057706229429197107928209
          55037687525678773091862540744969844508330393682126
          18336384825330154686196124348767681297534375946515
          80386287592878490201521685554828717201219257766954
          78182833757993103614740356856449095527097864797581
          16726320100436897842553539920931837441497806860984
          48403098129077791799088218795327364475675590848030
          87086987551392711854517078544161852424320693150332
          59959406895756536782107074926966537676326235447210
          69793950679652694742597709739166693763042633987085
          41052684708299085211399427365734116182760315001271
          65378607361501080857009149939512557028198746004375
          35829035317434717326932123578154982629742552737307
          94953759765105305946966067683156574377167401875275
          88902802571733229619176668713819931811048770190271
          25267680276078003013678680992525463401061632866526
          36270218540497705585629946580636237993140746255962
          24074486908231174977792365466257246923322810917141
          91430288197103288597806669760892938638285025333403
          34413065578016127815921815005561868836468420090470
          23053081172816430487623791969842487255036638784583
          11487696932154902810424020138335124462181441773470
          63783299490636259666498587618221225225512486764533
          67720186971698544312419572409913959008952310058822
          95548255300263520781532296796249481641953868218774
          76085327132285723110424803456124867697064507995236
          37774242535411291684276865538926205024910326572967
          23701913275725675285653248258265463092207058596522
          29798860272258331913126375147341994889534765745501
          18495701454879288984856827726077713721403798879715
          38298203783031473527721580348144513491373226651381
          34829543829199918180278916522431027392251122869539
          40957953066405232632538044100059654939159879593635
          29746152185502371307642255121183693803580388584903
          41698116222072977186158236678424689157993532961922
          62467957194401269043877107275048102390895523597457
          23189706772547915061505504953922979530901129967519
          86188088225875314529584099251203829009407770775672
          11306739708304724483816533873502340845647058077308
          82959174767140363198008187129011875491310547126581
          97623331044818386269515456334926366572897563400500
          42846280183517070527831839425882145521227251250327
          55121603546981200581762165212827652751691296897789
          32238195734329339946437501907836945765883352399886
          75506164965184775180738168837861091527357929701337
          62177842752192623401942399639168044983993173312731
          32924185707147349566916674687634660915035914677504
          99518671430235219628894890102423325116913619626622
          73267460800591547471830798392868535206946944540724
          76841822524674417161514036427982273348055556214818
          97142617910342598647204516893989422179826088076852
          87783646182799346313767754307809363333018982642090
          10848802521674670883215120185883543223812876952786
          71329612474782464538636993009049310363619763878039
          62184073572399794223406235393808339651327408011116
          66627891981488087797941876876144230030984490851411
          60661826293682836764744779239180335110989069790714
          85786944089552990653640447425576083659976645795096
          66024396409905389607120198219976047599490197230297
          64913982680032973156037120041377903785566085089252
          16730939319872750275468906903707539413042652315011
          94809377245048795150954100921645863754710598436791
          78639167021187492431995700641917969777599028300699
          15368713711936614952811305876380278410754449733078
          40789923115535562561142322423255033685442488917353
          44889911501440648020369068063960672322193204149535
          41503128880339536053299340368006977710650566631954
          81234880673210146739058568557934581403627822703280
          82616570773948327592232845941706525094512325230608
          22918802058777319719839450180888072429661980811197
          77158542502016545090413245809786882778948721859617
          72107838435069186155435662884062257473692284509516
          20849603980134001723930671666823555245252804609722
          53503534226472524250874054075591789781264330331690)
    aesthetic-string
    (subseq <> 0 10)
    parse-integer
    (nth-value 0 <>)))

(defun problem-14 ()
  ;; The following iterative sequence is defined for the set of positive
  ;; integers:
  ;;
  ;;   n → n/2 (n is even)
  ;;   n → 3n + 1 (n is odd)
  ;;
  ;; Using the rule above and starting with 13, we generate the following
  ;; sequence:
  ;;
  ;;   13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
  ;;
  ;; It can be seen that this sequence (starting at 13 and finishing at 1)
  ;; contains 10 terms. Although it has not been proved yet (Collatz Problem),
  ;; it is thought that all starting numbers finish at 1.
  ;;
  ;; Which starting number, under one million, produces the longest chain?
  ;;
  ;; NOTE: Once the chain starts the terms are allowed to go above one million.

  (iterate (for i :from 1 :below 1000000)
           (finding i :maximizing #'collatz-length)))

(defun problem-15 ()
  ;; Starting in the top left corner of a 2×2 grid, and only being able to move
  ;; to the right and down, there are exactly 6 routes to the bottom right
  ;; corner.
  ;;
  ;; How many such routes are there through a 20×20 grid?
  (binomial-coefficient 40 20))

(defun problem-16 ()
  ;; 2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.
  ;;
  ;; What is the sum of the digits of the number 2^1000?
  (sum (digits (expt 2 1000))))

(defun problem-17 ()
  ;; If the numbers 1 to 5 are written out in words: one, two, three, four,
  ;; five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.
  ;;
  ;; If all the numbers from 1 to 1000 (one thousand) inclusive were written out
  ;; in words, how many letters would be used?
  ;;
  ;; NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and
  ;; forty-two) contains 23 letters and 115 (one hundred and fifteen) contains
  ;; 20 letters. The use of "and" when writing out numbers is in compliance with
  ;; British usage, which is awful.
  (labels ((letters (n)
             (-<> n
               (format nil "~R" <>)
               (count-if #'alpha-char-p <>)))
           (has-british-and (n)
             (or (< n 100)
                 (zerop (mod n 100))))
           (silly-british-letters (n)
             (+ (letters n)
                (if (has-british-and n) 0 3))))
    (sum (range 1 (1+ 1000))
         :key #'silly-british-letters)))

(defun problem-18 ()
  ;; By starting at the top of the triangle below and moving to adjacent numbers
  ;; on the row below, the maximum total from top to bottom is 23.
  ;;
  ;;        3
  ;;       7 4
  ;;      2 4 6
  ;;     8 5 9 3
  ;;
  ;; That is, 3 + 7 + 4 + 9 = 23.
  ;;
  ;; Find the maximum total from top to bottom of the triangle below.
  ;;
  ;; NOTE: As there are only 16384 routes, it is possible to solve this problem
  ;; by trying every route. However, Problem 67, is the same challenge with
  ;; a triangle containing one-hundred rows; it cannot be solved by brute force,
  ;; and requires a clever method! ;o)
  (let ((triangle '((75)
                    (95 64)
                    (17 47 82)
                    (18 35 87 10)
                    (20 04 82 47 65)
                    (19 01 23 75 03 34)
                    (88 02 77 73 07 63 67)
                    (99 65 04 28 06 16 70 92)
                    (41 41 26 56 83 40 80 70 33)
                    (41 48 72 33 47 32 37 16 94 29)
                    (53 71 44 65 25 43 91 52 97 51 14)
                    (70 11 33 28 77 73 17 78 39 68 17 57)
                    (91 71 52 38 17 14 91 43 58 50 27 29 48)
                    (63 66 04 68 89 53 67 30 73 16 69 87 40 31)
                    (04 62 98 27 23 09 70 98 73 93 38 53 60 04 23))))
    (car (reduce (lambda (prev last)
                   (mapcar #'+
                           prev
                           (mapcar #'max last (rest last))))
                 triangle
                 :from-end t))))

(defun problem-19 ()
  ;; You are given the following information, but you may prefer to do some
  ;; research for yourself.
  ;;
  ;; 1 Jan 1900 was a Monday.
  ;; Thirty days has September,
  ;; April, June and November.
  ;; All the rest have thirty-one,
  ;; Saving February alone,
  ;; Which has twenty-eight, rain or shine.
  ;; And on leap years, twenty-nine.
  ;; A leap year occurs on any year evenly divisible by 4, but not on a century
  ;; unless it is divisible by 400.
  ;;
  ;; How many Sundays fell on the first of the month during the twentieth
  ;; century (1 Jan 1901 to 31 Dec 2000)?
  (iterate
    (for-nested ((year :from 1901 :to 2000)
                 (month :from 1 :to 12)))
    (counting (-<> (local-time:encode-timestamp 0 0 0 0 1 month year)
                local-time:timestamp-day-of-week
                zerop))))

(defun problem-20 ()
  ;; n! means n × (n − 1) × ... × 3 × 2 × 1
  ;;
  ;; For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,
  ;; and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.
  ;;
  ;; Find the sum of the digits in the number 100!
  (sum (digits (factorial 100))))

(defun problem-21 ()
  ;; Let d(n) be defined as the sum of proper divisors of n (numbers less than
  ;; n which divide evenly into n).
  ;;
  ;; If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair
  ;; and each of a and b are called amicable numbers.
  ;;
  ;; For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44,
  ;; 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4,
  ;; 71 and 142; so d(284) = 220.
  ;;
  ;; Evaluate the sum of all the amicable numbers under 10000.
  (labels ((sum-of-divisors (n)
             (sum (proper-divisors n)))
           (amicablep (n)
             (let ((other (sum-of-divisors n)))
               (and (not= n other)
                    (= n (sum-of-divisors other))))))
    (sum (remove-if-not #'amicablep (range 1 10000)))))


;;;; Tests --------------------------------------------------------------------
(def-suite :euler)
(in-suite :euler)

(test p1 (is (= 233168 (problem-1))))
(test p2 (is (= 4613732 (problem-2))))
(test p3 (is (= 6857 (problem-3))))
(test p4 (is (= 906609 (problem-4))))
(test p5 (is (= 232792560 (problem-5))))
(test p6 (is (= 25164150 (problem-6))))
(test p7 (is (= 104743 (problem-7))))
(test p8 (is (= 23514624000 (problem-8))))
(test p9 (is (= 31875000 (problem-9))))
(test p10 (is (= 142913828922 (problem-10))))
(test p11 (is (= 70600674 (problem-11))))
(test p12 (is (= 76576500 (problem-12))))
(test p13 (is (= 5537376230 (problem-13))))
(test p14 (is (= 837799 (problem-14))))
(test p15 (is (= 137846528820 (problem-15))))
(test p16 (is (= 1366 (problem-16))))
(test p17 (is (= 21124 (problem-17))))
(test p18 (is (= 1074 (problem-18))))
(test p19 (is (= 171 (problem-19))))
(test p20 (is (= 648 (problem-20))))
(test p21 (is (= 31626 (problem-21))))


;; (run! :euler)