X-Git-Url: https://git.piment-noir.org/?p=TD_LISP.git;a=blobdiff_plain;f=exercices%2Farithmetic.lsp;fp=exercices%2Farithmetic.lsp;h=a3f27ce90d7c99e6e7ca71575b0b7a16d336c6b0;hp=85f3f0145e446732be437de2f02cb280541aa8f9;hb=c4cb602cbbf151134a81d95e6d07a016521cbb48;hpb=d4b2508d9663596624e7f44c701147c27c6cceb2

diff --git a/exercices/arithmetic.lsp b/exercices/arithmetic.lsp
index 85f3f01..a3f27ce 100755
--- a/exercices/arithmetic.lsp
+++ b/exercices/arithmetic.lsp
@@ -1,12 +1,30 @@
 #!/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))
+
+;(trace true)
+
+;O(log N)
+(define (Puissance2 P N)
+  (cond
+    ((= N 0) 1)
+    ((= N 1) P)
+    ((> N 1)
+     (cond
+       ((= (mod N 2) 0) (Puissance2 (Puissance2 P 2) (/ N 2)))
+       ((* P (Puissance2 (Puissance2 P 2) (/ (- 1 N) 2))))))))
+(println "Puissance2")
+;(println (Puissance2 5 5))
+
+;(trace nil)
 
 ; https://fr.wikipedia.org/wiki/Algorithme_d%27Euclide
 (define (pgcd N P) 
@@ -15,16 +33,37 @@
     ((= 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
 (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))))))
+(println "comb")
+(println (comb 5 4))
+(println (comb 60 4))
+
+;(trace nil)
+
+(setq L '(3 7 + 4 2 + *))
+(setq P '())
+(define (calculExp P L)
+  (cond
+    ((null? L) 0)
+    ((= (first L) '+) (+ (first P) (calculExp (rest P) (rest L)))) 
+    ((= (first L) '-) (- (first P) (calculExp (rest P) (rest L))))
+    ((= (first L) '*) (* (first P) (calculExp (rest P) (rest L))))
+    ;FIXME: test for divide by zero
+    ((= (first L) '/) (/ (first P) (calculExp (rest P) (rest L))))
+    ((cons (first L) (calculExp P (rest L))))))    
+;(println (calculExp P L))
 
 (exit)