| 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 | |
| 60 | (setq L '(3 7 + 4 2 + *)) |
| 61 | (setq P '()) |
| 62 | (define (calculExp P L) |
| 63 | (cond |
| 64 | ((null? L) 0) |
| 65 | ((= (first L) '+) (+ (first P) (calculExp (rest P) (rest L)))) |
| 66 | ((= (first L) '-) (- (first P) (calculExp (rest P) (rest L)))) |
| 67 | ((= (first L) '*) (* (first P) (calculExp (rest P) (rest L)))) |
| 68 | ;FIXME: test for divide by zero |
| 69 | ((= (first L) '/) (/ (first P) (calculExp (rest P) (rest L)))) |
| 70 | ((cons (first L) (calculExp P (rest L)))))) |
| 71 | ;(println (calculExp P L)) |
| 72 | |
| 73 | (exit) |