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1 | #!/usr/bin/env newlisp |
2 | ||
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3 | ;O(N) |
4 | (define (Puissance1 P N) | |
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5 | (cond |
6 | ((= N 0) 1) | |
7 | ((= N 1) P) | |
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8 | ((< N 0) (div 1 (Puissance1 P (- N)))) |
9 | ((* P (Puissance1 P (- N 1)))))) | |
10 | (println "Puissance1") | |
11 | (println (Puissance1 5 5)) | |
7c69bee5 | 12 | (println (Puissance1 2 12)) |
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13 | |
14 | ;(trace true) | |
15 | ||
16 | ;O(log N) | |
17 | (define (Puissance2 P N) | |
18 | (cond | |
c4cb602c | 19 | ((= N 1) P) |
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20 | ((= N 2) (* P P)) |
21 | ((> N 2) | |
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22 | (cond |
23 | ((= (mod N 2) 0) (Puissance2 (Puissance2 P 2) (/ N 2))) | |
7c69bee5 | 24 | ((* P (Puissance2 (Puissance2 P 2) (/ (- N 1) 2)))))))) |
c4cb602c | 25 | (println "Puissance2") |
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26 | (println (Puissance2 5 5)) |
27 | (println (Puissance2 2 12)) | |
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28 | |
29 | ;(trace nil) | |
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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)))) | |
c4cb602c | 38 | (println "PGCD") |
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39 | (println (pgcd 12 4)) |
40 | (println (pgcd 25 5)) | |
41 | (println (pgcd 21 7)) | |
42 | ||
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43 | ;(trace true) |
44 | ||
ada8f303 | 45 | ; https://fr.wikipedia.org/wiki/Coefficient_binomial |
7c69bee5 | 46 | ; relation de pascal commenté |
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47 | (define (comb N P) |
48 | (cond | |
49 | ((= P 0) 1) | |
50 | ((= N P) 1) | |
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51 | ;((+ (comb (- N 1) P) (comb (- N 1) (- P 1)))))) |
52 | ((/ (* N (comb (- N 1) (- P 1))) P)))) | |
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53 | (println "comb") |
54 | (println (comb 5 4)) | |
55 | (println (comb 60 4)) | |
7c69bee5 | 56 | (println "(comb 12 8) = "(comb 12 8)) |
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57 | |
58 | ;(trace nil) | |
57122701 | 59 | ;(trace true) |
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60 | |
61 | (setq L '(3 7 + 4 2 + *)) | |
57122701 | 62 | (setq M '(4 3 7 + * 2 -)) |
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63 | (define (calculExp P L) |
64 | (cond | |
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65 | ((null? L) P) |
66 | ((= (first L) '+) (calculExp (cons (+ (first P) (P 1)) (rest (rest P))) (rest L))) | |
67 | ((= (first L) '-) (calculExp (cons (- (P 1) (first P)) (rest (rest P))) (rest L))) | |
68 | ((= (first L) '*) (calculExp (cons (* (first P) (P 1)) (rest (rest P))) (rest L))) | |
c4cb602c | 69 | ;FIXME: test for divide by zero |
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70 | ((= (first L) '/) (calculExp (cons (/ (P 1) (first P)) (rest (rest P))) (rest L))) |
71 | ((calculExp (cons (first L) P) (rest L))))) | |
72 | (println "calculExp") | |
73 | (println (calculExp '() L)) | |
74 | ;(trace true) | |
75 | (println (calculExp '() M)) | |
76 | ||
77 | ;(trace nil) | |
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78 | |
79 | (exit) |