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Project-Euler

1. Problems

1.1. p1

  • https://projecteuler.net/problem=1

  • warming up 

    (defun divides (num divisor)
  (= 0 (mod num divisor)))

(defun sol ()
  (let ((accumulation 0))
    (dotimes (i 1000)
      (when (or (divides i 3) (divides i 5))
        (setf accumulation (+ accumulation i))))
    accumulation))

(sol)

1.2. p2

  • https://projecteuler.net/problem=2

  • basic knuckle popper 

    (defvar *limit* 4000000)

(defun build-fib (accer)
  (cond ((> (car accer) *limit*) accer)
        (t (build-fib (cons (+ (car accer) (cadr accer)) accer)))))

(reduce #'+ (remove-if-not #'evenp (build-fib '(1 0))))

1.3. p3

  • https://projecteuler.net/problem=3

  • alright, let's get going.. 

    (defvar *number* 600851475143)

(defun divides (divisor number) (= 0 (mod number divisor)))

(defun largest-prime-factor (number)
  (defvar limit (sqrt number))
  (defun updater (current last-divisor left-number)
    (cond ((> current limit) last-divisor)
          ((divides current left-number) (updater (+ 1 current) current (/ left-number current)))
          (t (updater (+ 1 current) last-divisor left-number))))
  (updater 1 1 number))

(largest-prime-factor *number*)

1.4. p4

  • https://projecteuler.net/problem=4

  • I know I'm a caveman. 

    (defun range (low high) (loop for i from low to high collect i))

(defvar *limits* (range 100 999))

(defun palindrome-p (number)
  (let ((str (format nil "~a" number)))
    (string= str (reverse str))))

(defun cartesian-product-combine (l1 l2 combinator) 
  (reduce #'append
          (mapcar #'(lambda (l1ele)
                      (mapcar #'(lambda (l2ele)
                                  `(,l1ele ,l2ele ,(funcall combinator l1ele l2ele)))
                              l2))
                  l1)
          :initial-value '()))

(funcall #'max (remove-if-not #'palindrome-p (cartesian-product-combine *limits* *limits* #'*)))

1.5. p5

(defun range (low high)
  (loop for i from low to high collect i))

(defun evenly-divisible (numbers)
  (defun satisfier (curr candidate)
    (/ candidate (gcd curr candidate)))
  (defun iter-subproc (curr left)
    (if left
        (iter-subproc (* curr (satisfier curr (car left)))
                      (cdr left))
        curr))
  (when numbers
    (iter-subproc (car numbers)
                  (cdr numbers))))

(evenly-divisible (range 1 20))

1.6. p6

(defun square (x) (* x x))
(defun sum-upto (n)
  (/ (* n (+ 1 n))
     2 ))
(defun sum-of-squares-upto (n)
  (/ (* n (+ 1 n) (+ (* 2 n) 1))
     6))

(defun sol-upto (n)
  (- (square (sum-upto n))
     (sum-of-squares-upto n)))

(sol-upto 100)

1.7. p7

(defun sieve-of-eratosthenes (n)
  (let ((primes (make-array (1+ n) :initial-element t)))
    (setf (elt primes 0) nil
          (elt primes 1) nil)
    (loop for p from 2 to (isqrt n)
          while p
          do (if (elt primes p)
                 (loop for multiple from (* p p) to n by p
                       do (setf (elt primes multiple) nil))))
    (loop for i from 2 to n
          when (elt primes i)
          collect i)))

(nth 10000 (sieve-of-eratosthenes 1000000))

1.8. p8

(defvar *number* "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450")

(defun duplicate (base-char times)
  (coerce (loop for i from 1 to times collect base-char) 'string ))

(defun range (low high)
  (loop for i from low to high collect i))

(defun generate-shifted (number-string shift)
  (concatenate 'string
             (subseq number-string shift)
             (duplicate #\0 shift)))

(defun char-to-num (ch)
  (- (char-code ch) (char-code #\0)))

(defun max-product (max-characters number-string)
  (let* ((feeders (map 'list
                     #'(lambda (shift)
                         (generate-shifted number-string
                                           shift))
                     (range 0 (- max-characters 1))))
       (prods (eval `(map
                      'list
                      #'(lambda (&rest chars)
                          (apply #'* (map 'list #'char-to-num chars)))
                      ,@feeders))))
    (apply #'max prods)))

(max-product 13 *number*)

1.9. p9

(defun square (x) (* x x))
(loop for i from 1 to 1000
      do (loop for j from (+ 1 i) to 1000
               do (when (= (square (- 1000 i j))
                           (+ (square i)
                              (square j)))
                    (format t "~&found triplet ~s,~s,~s with prod ~s"
                            i j (- 1000 i j) (* i j (- 1000 i j))))))

1.10. p10

(defun sieve-of-eratosthenes (n)
  (let ((primes (make-array (1+ n) :initial-element t)))
    (setf (elt primes 0) nil
          (elt primes 1) nil)
    (loop for p from 2 to (isqrt n)
          while p
          do (if (elt primes p)
                 (loop for multiple from (* p p) to n by p
                       do (setf (elt primes multiple) nil))))
    (loop for i from 2 to n
          when (elt primes i)
            collect i)))
(reduce #'+ (sieve-of-eratosthenes 2000000)
      :initial-value 0)

1.11. p11

(defvar *array-base* ( list 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))

(defun list-to-2d-array (linear-list rows cols)
  (loop for i below rows
        collect (subseq linear-list (* i cols) (* (1+ i) cols))))

(defvar *rows* 20)
(defvar *cols* 20)

(defvar *array* (make-array `(,*rows* ,*cols*) :initial-contents (list-to-2d-array *array-base* *rows* *cols*)))

(defun ele (i j)
  (aref *array* i j))   

(defun assert-range (x low high) (and (>= x low)
                                      (<= x high)))

(defun check-ele (i j &key (low 0) (high 19))
  (and (assert-range i low high)
       (assert-range j low high)))

(defun get-row (i)
  (loop for col from 0 to (- *cols* 1)
        collect (aref *array* i col)))

(defun get-col (j)
  (loop for row from 0 to (- *rows* 1)
        collect (aref *array* row j)))

(defun range (low high)
  (loop for i from low to high collect i))

(defvar *diag-starts-td*
  (append (list (list 0 0))
          (mapcar #'(lambda (col-index)
                      (list 0 col-index))
                  (range 1 (- *cols* 1)))
          (mapcar #'(lambda (row-index)
                      (list row-index 0))
                  (range 1 (- *rows* 1)))))

(defvar *diag-starts-bu*
  (append (list (list (- *rows* 1) 0))
          (mapcar #'(lambda (col-index)
                      (list (- *rows* 1) col-index))
                  (range 1 (- *cols* 1)))
          (mapcar #'(lambda (row-index)
                      (list row-index 0))
                  (range 1 (- *rows* 1)))))

(defun get-diag-td (i j)
  (if (check-ele i j)
      (cons (aref *array* i j) (get-diag-td (+ 1 i) (+ 1 j)))
      '()))

(defun get-diag-bu (i j)
  (if (check-ele i j)
      (cons (aref *array* i j) (get-diag-bu (- i 1) (+ 1 j)))
      '()))

(defvar *all-lists*
  (append (mapcar #'get-row (range 0 (- *rows* 1)))
          (mapcar #'get-col (range 0 (- *cols* 1)))
          (mapcar #'(lambda (pnt)
                      (get-diag-td (car pnt)
                                   (cadr pnt))) *diag-starts-td*)
          (mapcar #'(lambda (pnt)
                      (get-diag-bu (car pnt)
                                   (cadr pnt))) *diag-starts-bu*)))

(defun fetch-submax-prod (window elements)
  (if (< (length elements) window)
      0
      (apply #'max
             (mapcar #'(lambda (start)
                         (apply #'* (subseq elements start (+ window start))))
                (range 0 (- (length elements) window))) )))

(defun fetch-max-prod (window elements-lists)
  (apply #'max (mapcar #'(lambda (elements) (fetch-submax-prod window elements))
                       elements-lists)))

(fetch-max-prod 4 *all-lists*)

1.12. p12

(defun prime-factorize (n)
  (labels ((iter-accumulate (curr-divisor curr-accumulate curr-count left-n)
             (cond
               ((= left-n 1) (cons (list curr-divisor curr-count)
                                   curr-accumulate))
               ((zerop (mod left-n curr-divisor)) (iter-accumulate curr-divisor
                                                                   curr-accumulate
                                                                   (+ curr-count 1)
                                                                   (/ left-n curr-divisor)))
               (t (iter-accumulate (+ curr-divisor 1)
                                   (cons (list curr-divisor curr-count)
                                         curr-accumulate)
                                   0
                                   left-n)))))
    (cond
      ((< n 2) nil)
      (t (remove-if #'(lambda (count) (zerop (cadr count)))
                    (iter-accumulate 2 '() 0 n) )))))

(defun num-factors (n)
  (apply #'* (mapcar #'(lambda (factor-info)
                         (+ 1 (cadr factor-info)))
                     (prime-factorize n))))

(defun sol-triangle-num (factor-count-thresh)
  (do* ((index 1 (+ 1 index))
        (curr-triang 1 (+ curr-triang index)))
       ((> (num-factors curr-triang) factor-count-thresh) curr-triang)))

(sol-triangle-num 500)

1.13. p13

(defvar *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))

(defun sol ()
  (apply #'+ (mapcar #'(lambda (number) (parse-integer (subseq (format nil "~a" number) 0 13) ))
                   *numbers*)))
(sol)

;9*50 = 450 : max influence of two to three more place values
;series goes as 450 + 45 + 4.5 + ...
;chance of flipping the first 4
;check from 0 to 12
;this being a lisp, I could just add it all
Tags::lisp:programming: