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ada8f303 JB |
1 | #!/usr/bin/env newlisp |
2 | ||
c4cb602c JB |
3 | ;O(N) |
4 | (define (Puissance1 P N) | |
ada8f303 JB |
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 -)) |
dc802a3e | 63 | (setq N '(10 10 5 / +)) |
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64 | (define (calculExp P L) |
65 | (cond | |
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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))) | |
57122701 | 69 | ((= (first L) '-) (calculExp (cons (- (P 1) (first P)) (rest (rest P))) (rest L))) |
25450b84 | 70 | ((= (first L) '*) (calculExp (cons (* (P 1) (first P)) (rest (rest P))) (rest L))) |
c4cb602c | 71 | ;FIXME: test for divide by zero |
57122701 | 72 | ((= (first L) '/) (calculExp (cons (/ (P 1) (first P)) (rest (rest P))) (rest L))) |
a54a070c | 73 | ((number? (first L)) (calculExp (cons (first L) P) (rest L))))) |
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74 | (println "calculExp") |
75 | (println (calculExp '() L)) | |
76 | ;(trace true) | |
77 | (println (calculExp '() M)) | |
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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) '()) | |
a54a070c | 86 | ; I'm having hard time to find a way of escaping the '(' and ')' characters |
dc802a3e | 87 | ((= (first L) ) (rest L)) |
a54a070c | 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. |
0d4022bb | 89 | ;then if it match a known pattern, simplify it by following the matching rule. |
a54a070c | 90 | ;do it again on the upper layer recursively until we only have (op A B) that just match no known simplication rules. |
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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)) | |
a54a070c | 112 | ;this create a LIFO (or stack) of all previous fibonnaci serie result values |
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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))) | |
57122701 | 118 | |
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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 | ||
57122701 | 132 | ;(trace nil) |
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133 | |
134 | (exit) |