111 lines
2.5 KiB
Common Lisp
111 lines
2.5 KiB
Common Lisp
(defun binomial (n k)
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(cond
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((= k 0) 1)
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((= n k) 1)
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(t (+ (binomial (- n 1) k) (binomial (- n 1) (- k 1))))))
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(defun next_row (row)
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(mapcar #'+ (append '(0) row) (append row '(0))))
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(defun generate_pascal_row (n current_row)
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(if (= n 0)
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current_row
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(generate_pascal_row (- n 1) (next_row current_row))))
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(defun generate_pascal (n)
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(generate_pascal_row n '(1)))
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(defun binomial2 (n k)
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(nth k (generate_pascal n)))
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(defun empty_or_singleton (list)
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(or (null list) (null (cdr list))))
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(defun right_half (list)
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(last list (ceiling (/ (length list) 2))))
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(defun left_half (list)
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(ldiff list (right_half list)))
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(defun mergelists (list1 list2)
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(merge 'list list1 list2 #'<))
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(defun mergesort (list)
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(if (empty_or_singleton list) list
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(mergelists
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(mergesort (left_half list))
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(mergesort (right_half list)))))
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(defun gcde (a b)
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(if (= a 0)
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(values b 0 1)
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(multiple-value-bind (g x y)
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(gcde (mod b a) a)
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(values g (- y (* (floor b a) x)) x))))
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(defun de (a b)
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(multiple-value-bind (x y g)
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(gcde a b)
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(values x y g)))
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(defun factorize (n factor)
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(cond
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((= 1 n) nil)
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((= 0 (mod n factor)) (cons factor (factorize (/ n factor) factor)))
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(t (factorize n (+ factor 1)))))
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(defun prime_factors (n)
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(factorize n 2))
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(defun _gcd (a b)
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(if (= a 0) b
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(_gcd (mod b a) a)))
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(defun is_coprime (a b)
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(= (_gcd a b) 1))
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(defun totient_helper (n i)
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(cond ((= i n) (if (is_coprime n i) 1 0))
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((is_coprime n i) (1+ (totient_helper n (1+ i))))
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(t (totient_helper n (1+ i)))))
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(defun totient (n)
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(totient_helper n 1))
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(defun totient2 (n)
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(let ((unique_factors (remove-duplicates (prime_factors n))))
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(reduce #'(lambda (acc p) (floor (/ (* acc (- p 1)) p))) unique_factors :initial-value n)))
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(defun prime? (n &optional (divisor 2))
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(cond ((<= n 1) nil)
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((= n 2) t)
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((evenp n) nil)
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((> divisor (isqrt n)) t)
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((zerop (mod n divisor)) nil)
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(t (prime? n (+ divisor 1)))))
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(defun primes_helper (n result)
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(if (zerop n)
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result
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(if (prime? n)
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(primes_helper (- n 1) (cons n result))
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(primes_helper (- n 1) result))))
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(defun primes (n)
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(primes_helper n '()))
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