Project Euler Problem 48
(defun problem48 ()
(nth-value 1 (truncate (loop for i from 1 to 1000
sum (expt i i))
(expt 10 10))))
Sunday, April 10, 2016
Project Euler Problem 49 Common Lisp
Project Euler Problem 49
(defun digits-to-list (x &optional (lst nil))
(multiple-value-bind (a b)
(truncate x 10)
(if (zerop a)
(cons b lst)
(digits-to-list a (cons b lst)))))
(defun prime? (num)
(cond ((= 2 num) num)
((= 3 num) num)
((< num 1) nil)
((evenp num) nil)
((zerop (mod num 3)) nil)
(t (loop for i from 5 to (isqrt num) by 6
if (or (zerop (mod num i))
(zerop (mod num (+ i 2)))) return nil
finally (return num)))))
(defun primes (num)
(append '(2 3)
(loop for i from 5 to num by 6
if (prime? i) collect it
if (prime? (+ i 2)) collect it)))
(defun perm? (x y z)
(let ((a (sort (digits-to-list x) #'<))
(b (sort (digits-to-list y) #'<))
(c (sort (digits-to-list z) #'<)))
(and (equal a b) (equal b c))))
(defun four-digit-perms ()
(loop with primes2 = (delete 1000 (primes 9999) :test #'>)
for a in primes2
nconc (loop for b in primes2
nconc (loop for c in primes2
while (> a b c)
when (= (- a b) (- b c))
when (perm? a b c)
collect (list c b a)))))
(defun problem49 ()
(format nil "The answer to Project Euler problem 49 is ~{~a~}"
(remove-if-not #'stringp
(mapcar #'write-to-string
(second (four-digit-perms))))))
(defun digits-to-list (x &optional (lst nil))
(multiple-value-bind (a b)
(truncate x 10)
(if (zerop a)
(cons b lst)
(digits-to-list a (cons b lst)))))
(defun prime? (num)
(cond ((= 2 num) num)
((= 3 num) num)
((< num 1) nil)
((evenp num) nil)
((zerop (mod num 3)) nil)
(t (loop for i from 5 to (isqrt num) by 6
if (or (zerop (mod num i))
(zerop (mod num (+ i 2)))) return nil
finally (return num)))))
(defun primes (num)
(append '(2 3)
(loop for i from 5 to num by 6
if (prime? i) collect it
if (prime? (+ i 2)) collect it)))
(defun perm? (x y z)
(let ((a (sort (digits-to-list x) #'<))
(b (sort (digits-to-list y) #'<))
(c (sort (digits-to-list z) #'<)))
(and (equal a b) (equal b c))))
(defun four-digit-perms ()
(loop with primes2 = (delete 1000 (primes 9999) :test #'>)
for a in primes2
nconc (loop for b in primes2
nconc (loop for c in primes2
while (> a b c)
when (= (- a b) (- b c))
when (perm? a b c)
collect (list c b a)))))
(defun problem49 ()
(format nil "The answer to Project Euler problem 49 is ~{~a~}"
(remove-if-not #'stringp
(mapcar #'write-to-string
(second (four-digit-perms))))))
Project Euler Problem 50 Common Lisp
Project Euler Problem 50
(defun prime? (num)
(cond ((= 2 num) num)
((= 3 num) num)
((< num 1) nil)
((evenp num) nil)
((zerop (mod num 3)) nil)
(t (loop for i from 5 to (isqrt num) by 6
if (or (zerop (mod num i))
(zerop (mod num (+ i 2)))) return nil
finally (return num)))))
(defun primes (num)
(append '(2 3)
(loop for i from 5 to num by 6
if (prime? i) collect it
if (prime? (+ i 2)) collect it)))
(defun prime-sums (num)
(loop for i in (primes num)
sum i into j
unless (< num j)
collect j))
(defun sum-of-consecutive-primes (num)
(loop with sums = (prime-sums num)
for i in sums
collect (member-if #'prime?
(loop for j in (cons 0 sums)
while (> i j)
collect (- i j)))))
(defun longest-sum-of-consecutive-primes (num)
(let ((x (sort (sum-of-consecutive-primes num)
#'>
:key #'length)))
(list (caar x) (length (first x)))))
(defun problem50 ()
(let ((x (longest-sum-of-consecutive-primes 1000000)))
(format t "The answer to Problem 50 is ~A with ~A terms."
(first x) (second x))))
(defun prime? (num)
(cond ((= 2 num) num)
((= 3 num) num)
((< num 1) nil)
((evenp num) nil)
((zerop (mod num 3)) nil)
(t (loop for i from 5 to (isqrt num) by 6
if (or (zerop (mod num i))
(zerop (mod num (+ i 2)))) return nil
finally (return num)))))
(defun primes (num)
(append '(2 3)
(loop for i from 5 to num by 6
if (prime? i) collect it
if (prime? (+ i 2)) collect it)))
(defun prime-sums (num)
(loop for i in (primes num)
sum i into j
unless (< num j)
collect j))
(defun sum-of-consecutive-primes (num)
(loop with sums = (prime-sums num)
for i in sums
collect (member-if #'prime?
(loop for j in (cons 0 sums)
while (> i j)
collect (- i j)))))
(defun longest-sum-of-consecutive-primes (num)
(let ((x (sort (sum-of-consecutive-primes num)
#'>
:key #'length)))
(list (caar x) (length (first x)))))
(defun problem50 ()
(let ((x (longest-sum-of-consecutive-primes 1000000)))
(format t "The answer to Problem 50 is ~A with ~A terms."
(first x) (second x))))
Project Euler Problem 46 Common Lisp
Project Euler Problem 46
Note that all square integers from 1 to some number can be found by summing all the odd numbers, e.g. 2 *2 = 4 = 1 + 3, 3 * 3 = 9 = 1 + 3 + 5, 4 * 4 = 16 = 1 + 3 + 5 + 7. That's what is happening in function conjecture-false?
(defun prime? (num)
(cond ((= 2 num) num)
((= 3 num) num)
((< num 1) nil)
((evenp num) nil)
((zerop (mod num 3)) nil)
(t (loop for i from 5 to (isqrt num) by 6
if (or (zerop (mod num i))
(zerop (mod num (+ i 2)))) return nil
finally (return num)))))
(defun conjecture-false? (num)
(loop for i from 1 to num by 2
sum i into j
if (prime? (- num (* j 2))) return nil
finally (return t)))
(defun problem46 ()
(loop for i upfrom 1 by 2
unless (prime? i)
when (conjecture-false? i) return i))
Note that all square integers from 1 to some number can be found by summing all the odd numbers, e.g. 2 *2 = 4 = 1 + 3, 3 * 3 = 9 = 1 + 3 + 5, 4 * 4 = 16 = 1 + 3 + 5 + 7. That's what is happening in function conjecture-false?
(defun prime? (num)
(cond ((= 2 num) num)
((= 3 num) num)
((< num 1) nil)
((evenp num) nil)
((zerop (mod num 3)) nil)
(t (loop for i from 5 to (isqrt num) by 6
if (or (zerop (mod num i))
(zerop (mod num (+ i 2)))) return nil
finally (return num)))))
(defun conjecture-false? (num)
(loop for i from 1 to num by 2
sum i into j
if (prime? (- num (* j 2))) return nil
finally (return t)))
(defun problem46 ()
(loop for i upfrom 1 by 2
unless (prime? i)
when (conjecture-false? i) return i))
Monday, February 22, 2016
Project Euler Problem 67 Common Lisp
Project Euler Problem 67
(defparameter *data*
(with-open-file (input "p067_triangle.txt")
(loop for line = (read-line input nil nil)
while line
collect (read-from-string
(concatenate 'string "(" line ")")))))
The above code for converting lines in a text file into a nested list came from here.
(defun bottom-up-max (a b)
(mapcar #'max
(mapcar #'+ a b)
(mapcar #'+ (rest a) b)))
(defun problem67 (lst)
(first (reduce #'bottom-up-max (reverse lst))))
To get the solution, evaluate:
(problem67 *data*)
(defparameter *data*
(with-open-file (input "p067_triangle.txt")
(loop for line = (read-line input nil nil)
while line
collect (read-from-string
(concatenate 'string "(" line ")")))))
The above code for converting lines in a text file into a nested list came from here.
(defun bottom-up-max (a b)
(mapcar #'max
(mapcar #'+ a b)
(mapcar #'+ (rest a) b)))
(defun problem67 (lst)
(first (reduce #'bottom-up-max (reverse lst))))
To get the solution, evaluate:
(problem67 *data*)
Sunday, February 21, 2016
Project Euler Problem 18 Common Lisp
Project Euler Problem 18
The idea for the solution below came from Stackoverflow. Working from "bottom to top", *data* is reversed in function problem18.
(defparameter *data*
'((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)))
(defun bottom-up-max (a b)
(mapcar #'max
(mapcar #'+ a b)
(mapcar #'+ (rest a) b)))
(defun problem18 (lst)
(first (reduce #'bottom-up-max (reverse lst))))
To get the solution, evaluate:
(problem18 *data*)
The idea for the solution below came from Stackoverflow. Working from "bottom to top", *data* is reversed in function problem18.
(defparameter *data*
'((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)))
(defun bottom-up-max (a b)
(mapcar #'max
(mapcar #'+ a b)
(mapcar #'+ (rest a) b)))
(defun problem18 (lst)
(first (reduce #'bottom-up-max (reverse lst))))
To get the solution, evaluate:
(problem18 *data*)
Friday, February 19, 2016
Project Euler Problem 11 Common Lisp
Project Euler Problem 11
(defparameter *data*
'((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 multiply-first-4 (lst)
(if (> 4 (length lst))
0
(reduce #'* (subseq lst 0 4))))
(defun all-multiples (lst)
(maplist #'multiply-first-4 lst))
(defun all-horizontals (lst)
(mapcan #'all-multiples lst))
(defun all-verticals (lst)
(all-horizontals (apply #'mapcar #'list lst)))
(defun %all-left-diagonals (lst &optional (n 0))
(if (< n 4)
(cons (nthcdr n (car lst))
(%all-left-diagonals (cdr lst) (1+ n)))
nil))
(defun all-left-diagonals (lst)
(mapcon #'(lambda (x) (all-verticals (%all-left-diagonals x)))
lst))
(defun all-right-diagonals (lst)
(all-left-diagonals (reverse lst)))
(defun problem11 ()
(reduce #'max (append (all-horizontals *data*)
(all-verticals *data*)
(all-left-diagonals *data*)
(all-right-diagonals *data*))))
Function multiply-first-4 returns the multiplication of the first 4 elements of a list, or it returns 0 if the list has less than 4 elements--otherwise the function will error out. Better to just simply return 0 then the code complexity for handling a list with less than 4 elements.
Function all-multiples takes a list of say (1 2 3 4 5 6 7) turning it into ((1 2 3 4 5 6 7) (2 3 4 5 67) (3 4 5 6 7) (4 5 6 7) (5 6 7) (6 7) (7)). It then takes that and applies multiply-first-4 to each of the lists within, resulting in (24 120 360 840 0 0 0).
Function all-horizontals applies all-multiples to a list of list, like *data* above, returning a flat list of all multiplications of 4 elements from left to right (and right to left simultaneously).
Function all-verticals takes a list of list and transposes it. For example ((1 2 3) (4 5 6) ( 7 8 9)) becomes ((1 4 7) (2 5 8) (3 6 9)). all-verticals applies that transposed list to all-horizontals. The result is a flat list of all multiplications of 4 elements going up and down. Transposing the list is a trick taken from Stackoverflow.
Function all-left-diagonals uses %all-left-diagonals to turn a list like ((1 2 3) (4 5 6) (7 8 9)) into ((1 2 3) (5 6) (9)) and applies it to all-verticals. The result is a flat list of all multiplications of 4 elements going diagonal, from upper left to lower right.
Function all-right-diagonals reverses a list of lists, ((1 2 3) (4 5 6) (7 8 9)) becoming ((7 8 9) (4 5 6) (1 2 3)), and applies it to all-left-diagonals. Thus resulting in a flat list of all multiplications of 4 elements going diagonal, from lower left to upper right.
Function problem11 takes all of these flat lists, appends them, and then finds the maximum.
(defparameter *data*
'((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 multiply-first-4 (lst)
(if (> 4 (length lst))
0
(reduce #'* (subseq lst 0 4))))
(defun all-multiples (lst)
(maplist #'multiply-first-4 lst))
(defun all-horizontals (lst)
(mapcan #'all-multiples lst))
(defun all-verticals (lst)
(all-horizontals (apply #'mapcar #'list lst)))
(defun %all-left-diagonals (lst &optional (n 0))
(if (< n 4)
(cons (nthcdr n (car lst))
(%all-left-diagonals (cdr lst) (1+ n)))
nil))
(defun all-left-diagonals (lst)
(mapcon #'(lambda (x) (all-verticals (%all-left-diagonals x)))
lst))
(defun all-right-diagonals (lst)
(all-left-diagonals (reverse lst)))
(defun problem11 ()
(reduce #'max (append (all-horizontals *data*)
(all-verticals *data*)
(all-left-diagonals *data*)
(all-right-diagonals *data*))))
Function multiply-first-4 returns the multiplication of the first 4 elements of a list, or it returns 0 if the list has less than 4 elements--otherwise the function will error out. Better to just simply return 0 then the code complexity for handling a list with less than 4 elements.
Function all-multiples takes a list of say (1 2 3 4 5 6 7) turning it into ((1 2 3 4 5 6 7) (2 3 4 5 67) (3 4 5 6 7) (4 5 6 7) (5 6 7) (6 7) (7)). It then takes that and applies multiply-first-4 to each of the lists within, resulting in (24 120 360 840 0 0 0).
Function all-horizontals applies all-multiples to a list of list, like *data* above, returning a flat list of all multiplications of 4 elements from left to right (and right to left simultaneously).
Function all-verticals takes a list of list and transposes it. For example ((1 2 3) (4 5 6) ( 7 8 9)) becomes ((1 4 7) (2 5 8) (3 6 9)). all-verticals applies that transposed list to all-horizontals. The result is a flat list of all multiplications of 4 elements going up and down. Transposing the list is a trick taken from Stackoverflow.
Function all-left-diagonals uses %all-left-diagonals to turn a list like ((1 2 3) (4 5 6) (7 8 9)) into ((1 2 3) (5 6) (9)) and applies it to all-verticals. The result is a flat list of all multiplications of 4 elements going diagonal, from upper left to lower right.
Function all-right-diagonals reverses a list of lists, ((1 2 3) (4 5 6) (7 8 9)) becoming ((7 8 9) (4 5 6) (1 2 3)), and applies it to all-left-diagonals. Thus resulting in a flat list of all multiplications of 4 elements going diagonal, from lower left to upper right.
Function problem11 takes all of these flat lists, appends them, and then finds the maximum.
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