#!/usr/bin/env newlisp
-(define (Puissance P N)
+;O(N)
+(define (Puissance1 P N)
(cond
((= N 0) 1)
((= N 1) P)
- ((< N 0) (div 1 (Puissance P (- N))))
- ((* P (Puissance P (- N 1))))))
-(println (Puissance 5 5))
+ ((< N 0) (div 1 (Puissance1 P (- N))))
+ ((* P (Puissance1 P (- N 1))))))
+(println "Puissance1")
+(println (Puissance1 5 5))
+(println (Puissance1 2 12))
+
+;(trace true)
+
+;O(log N)
+(define (Puissance2 P N)
+ (cond
+ ((= N 1) P)
+ ((= N 2) (* P P))
+ ((> N 2)
+ (cond
+ ((= (mod N 2) 0) (Puissance2 (Puissance2 P 2) (/ N 2)))
+ ((* P (Puissance2 (Puissance2 P 2) (/ (- N 1) 2))))))))
+(println "Puissance2")
+(println (Puissance2 5 5))
+(println (Puissance2 2 12))
+
+;(trace nil)
; https://fr.wikipedia.org/wiki/Algorithme_d%27Euclide
(define (pgcd N P)
((= N P) N)
((= P 0) N)
((pgcd (- N P) P))))
+(println "PGCD")
(println (pgcd 12 4))
(println (pgcd 25 5))
(println (pgcd 21 7))
+;(trace true)
+
; https://fr.wikipedia.org/wiki/Coefficient_binomial
+; relation de pascal commenté
(define (comb N P)
(cond
((= P 0) 1)
((= N P) 1)
- ((+ (comb (- 1 N) P) (comb (- 1 N) (- 1 P))))))
-;(println (comb 5 4))
+ ;((+ (comb (- N 1) P) (comb (- N 1) (- P 1))))))
+ ((/ (* N (comb (- N 1) (- P 1))) P))))
+(println "comb")
+(println (comb 5 4))
+(println (comb 60 4))
+(println "(comb 12 8) = "(comb 12 8))
+
+;(trace nil)
+;(trace true)
+
+(setq L '(3 7 + 4 2 + *))
+(setq M '(4 3 7 + * 2 -))
+(setq N '(10 10 5 / +))
+(define (calculExp P L)
+ (cond
+ ((null? L) (first P))
+ ; all these conditions could probably be simplified
+ ((= (first L) '+) (calculExp (cons (+ (P 1) (first P)) (rest (rest P))) (rest L)))
+ ((= (first L) '-) (calculExp (cons (- (P 1) (first P)) (rest (rest P))) (rest L)))
+ ((= (first L) '*) (calculExp (cons (* (P 1) (first P)) (rest (rest P))) (rest L)))
+ ;FIXME: test for divide by zero
+ ((= (first L) '/) (calculExp (cons (/ (P 1) (first P)) (rest (rest P))) (rest L)))
+ ((number? (first L)) (calculExp (cons (first L) P) (rest L)))))
+(println "calculExp")
+(println (calculExp '() L))
+;(trace true)
+(println (calculExp '() M))
+(println (calculExp '() N))
+
+;(trace nil)
+
+(setq Q '(+ (* x 0) (* 10 (+ y 0))))
+(define (algsimplificator L)
+ (cond
+ ((null? L) '())
+ ((= (first L) ) (rest L))
+
+ ))
+(println "algsimplificator")
+;(println algsimplificator(Q))
+
+(define (fibonacci N)
+ (cond
+ ((= N 0) 0)
+ ((= N 1) 1)
+ ((> N 1) (+ (fibonacci (- N 1)) (fibonacci (- N 2))))))
+(println "fibonacci")
+;(println (fibonacci 21))
+;(println (fibonacci 14))
+(println (fibonacci 20))
+(println (time (fibonacci 20)))
+
+;(trace true)
+
+(define (fibo:fibo n)
+ (if (not fibo:mem) (set 'fibo:mem '(0 1)))
+ (dotimes (i (- n 1))
+ (push (+ (fibo:mem -1) (fibo:mem -2)) fibo:mem -1))
+ (last fibo:mem))
+(println "fibo")
+(println (fibo 20))
+(println (time (fibo 20)))
+
+;(trace nil)
(exit)