| 1 | #!/usr/bin/env newlisp |
| 2 | |
| 3 | ;O(N) |
| 4 | (define (Puissance1 P N) |
| 5 | (cond |
| 6 | ((= N 0) 1) |
| 7 | ((= N 1) P) |
| 8 | ((< N 0) (div 1 (Puissance1 P (- N)))) |
| 9 | ((* P (Puissance1 P (- N 1)))))) |
| 10 | (println "Puissance1") |
| 11 | (println (Puissance1 5 5)) |
| 12 | (println (Puissance1 2 12)) |
| 13 | |
| 14 | ;(trace true) |
| 15 | |
| 16 | ;O(log N) |
| 17 | (define (Puissance2 P N) |
| 18 | (cond |
| 19 | ((= N 1) P) |
| 20 | ((= N 2) (* P P)) |
| 21 | ((> N 2) |
| 22 | (cond |
| 23 | ((= (mod N 2) 0) (Puissance2 (Puissance2 P 2) (/ N 2))) |
| 24 | ((* P (Puissance2 (Puissance2 P 2) (/ (- N 1) 2)))))))) |
| 25 | (println "Puissance2") |
| 26 | (println (Puissance2 5 5)) |
| 27 | (println (Puissance2 2 12)) |
| 28 | |
| 29 | ;(trace nil) |
| 30 | |
| 31 | ; https://fr.wikipedia.org/wiki/Algorithme_d%27Euclide |
| 32 | (define (pgcd N P) |
| 33 | (cond |
| 34 | ((< N P) (pgcd P N)) |
| 35 | ((= N P) N) |
| 36 | ((= P 0) N) |
| 37 | ((pgcd (- N P) P)))) |
| 38 | (println "PGCD") |
| 39 | (println (pgcd 12 4)) |
| 40 | (println (pgcd 25 5)) |
| 41 | (println (pgcd 21 7)) |
| 42 | |
| 43 | ;(trace true) |
| 44 | |
| 45 | ; https://fr.wikipedia.org/wiki/Coefficient_binomial |
| 46 | ; relation de pascal commenté |
| 47 | (define (comb N P) |
| 48 | (cond |
| 49 | ((= P 0) 1) |
| 50 | ((= N P) 1) |
| 51 | ;((+ (comb (- N 1) P) (comb (- N 1) (- P 1)))))) |
| 52 | ((/ (* N (comb (- N 1) (- P 1))) P)))) |
| 53 | (println "comb") |
| 54 | (println (comb 5 4)) |
| 55 | (println (comb 60 4)) |
| 56 | (println "(comb 12 8) = "(comb 12 8)) |
| 57 | |
| 58 | ;(trace nil) |
| 59 | ;(trace true) |
| 60 | |
| 61 | (setq L '(3 7 + 4 2 + *)) |
| 62 | (setq M '(4 3 7 + * 2 -)) |
| 63 | (setq N '(10 10 5 / +)) |
| 64 | (define (calculExp P L) |
| 65 | (cond |
| 66 | ((null? L) (first P)) |
| 67 | ; all these conditions could probably be simplified |
| 68 | ((= (first L) '+) (calculExp (cons (+ (P 1) (first P)) (rest (rest P))) (rest L))) |
| 69 | ((= (first L) '-) (calculExp (cons (- (P 1) (first P)) (rest (rest P))) (rest L))) |
| 70 | ((= (first L) '*) (calculExp (cons (* (P 1) (first P)) (rest (rest P))) (rest L))) |
| 71 | ;FIXME: test for divide by zero |
| 72 | ((= (first L) '/) (calculExp (cons (/ (P 1) (first P)) (rest (rest P))) (rest L))) |
| 73 | ((number? (first L)) (calculExp (cons (first L) P) (rest L))))) |
| 74 | (println "calculExp") |
| 75 | (println (calculExp '() L)) |
| 76 | ;(trace true) |
| 77 | (println (calculExp '() M)) |
| 78 | (println (calculExp '() N)) |
| 79 | |
| 80 | ;(trace nil) |
| 81 | |
| 82 | (setq Q '(+ (* x 0) (* 10 (+ y 0)))) |
| 83 | (define (algsimplificator L) |
| 84 | (cond |
| 85 | ((null? L) '()) |
| 86 | ; I'm having hard time to find a way of escaping the '(' and ')' characters |
| 87 | ((= (first L) ) (rest L)) |
| 88 | ;here is the idea: detect the lower well formed expression: begin with (op and finish with ) where op = + - * / and have only two parameters that are atoms. |
| 89 | ;then if it match a known pattern, simplify it by following the matching rule. |
| 90 | ;do it again on the upper layer recursively until we only have (op A B) that just match no known simplication rules. |
| 91 | |
| 92 | )) |
| 93 | (println "algsimplificator") |
| 94 | ;(println algsimplificator(Q)) |
| 95 | |
| 96 | (define (fibonacci N) |
| 97 | (cond |
| 98 | ((= N 0) 0) |
| 99 | ((= N 1) 1) |
| 100 | ((> N 1) (+ (fibonacci (- N 1)) (fibonacci (- N 2)))))) |
| 101 | (println "fibonacci") |
| 102 | ;(println (fibonacci 21)) |
| 103 | ;(println (fibonacci 14)) |
| 104 | (println (fibonacci 20)) |
| 105 | (println (time (fibonacci 20))) |
| 106 | |
| 107 | ;(trace true) |
| 108 | |
| 109 | (define (fibo:fibo n) |
| 110 | (if (not fibo:mem) (set 'fibo:mem '(0 1))) |
| 111 | (dotimes (i (- n 1)) |
| 112 | ;this create a LIFO (or stack) of all previous fibonnaci serie result values |
| 113 | (push (+ (fibo:mem -1) (fibo:mem -2)) fibo:mem -1)) |
| 114 | (last fibo:mem)) |
| 115 | (println "fibo") |
| 116 | (println (fibo 20)) |
| 117 | (println (time (fibo 20))) |
| 118 | |
| 119 | ;(trace nil) |
| 120 | ;(trace true) |
| 121 | |
| 122 | (setq S '()) |
| 123 | (define (Somme3ou5 N) |
| 124 | (dolist (i (sequence 0 N)) |
| 125 | (cond |
| 126 | ((= (mod i 3) 0) (setq S (cons i S))) |
| 127 | ((= (mod i 5) 0) (setq S (cons i S))))) |
| 128 | (apply + S)) |
| 129 | (println "Somme3ou5") |
| 130 | (println (Somme3ou5 100)) |
| 131 | |
| 132 | ;(trace nil) |
| 133 | |
| 134 | (exit) |