analyse_tris

tp7/analyse_tris.csv

@@ -2,101 +2,101 @@ taille;"tri séléction";"tri insertion"
   0;    0.00;    0.00
   1;    0.00;    0.00
   2;    1.00;    1.00
-  3;    3.00;    2.62
-  4;    6.00;    4.98
-  5;   10.00;    7.42
-  6;   15.00;   11.32
-  7;   21.00;   14.50
-  8;   28.00;   19.66
-  9;   36.00;   23.54
- 10;   45.00;   29.06
- 11;   55.00;   33.92
- 12;   66.00;   40.18
- 13;   78.00;   46.80
- 14;   91.00;   55.38
- 15;  105.00;   63.56
- 16;  120.00;   68.94
- 17;  136.00;   82.32
- 18;  153.00;   94.00
- 19;  171.00;   97.78
- 20;  190.00;  110.16
- 21;  210.00;  118.80
- 22;  231.00;  132.90
- 23;  253.00;  146.12
- 24;  276.00;  159.76
- 25;  300.00;  171.24
- 26;  325.00;  186.10
- 27;  351.00;  198.52
- 28;  378.00;  217.76
- 29;  406.00;  233.10
- 30;  435.00;  239.36
- 31;  465.00;  263.44
- 32;  496.00;  272.58
- 33;  528.00;  299.42
- 34;  561.00;  311.48
- 35;  595.00;  323.00
- 36;  630.00;  346.86
- 37;  666.00;  360.70
- 38;  703.00;  386.82
- 39;  741.00;  405.70
- 40;  780.00;  430.26
- 41;  820.00;  455.18
- 42;  861.00;  462.10
- 43;  903.00;  495.82
- 44;  946.00;  526.60
- 45;  990.00;  533.54
- 46; 1035.00;  567.98
- 47; 1081.00;  587.28
- 48; 1128.00;  618.48
- 49; 1176.00;  633.90
- 50; 1225.00;  659.22
- 51; 1275.00;  657.48
- 52; 1326.00;  711.12
- 53; 1378.00;  722.72
- 54; 1431.00;  761.36
- 55; 1485.00;  809.52
- 56; 1540.00;  816.98
- 57; 1596.00;  852.90
- 58; 1653.00;  877.80
- 59; 1711.00;  933.96
- 60; 1770.00;  938.76
- 61; 1830.00;  970.32
- 62; 1891.00;  993.92
- 63; 1953.00; 1034.12
- 64; 2016.00; 1038.70
- 65; 2080.00; 1094.32
- 66; 2145.00; 1125.18
- 67; 2211.00; 1155.90
- 68; 2278.00; 1206.86
- 69; 2346.00; 1260.22
- 70; 2415.00; 1262.76
- 71; 2485.00; 1285.74
- 72; 2556.00; 1358.64
- 73; 2628.00; 1381.72
- 74; 2701.00; 1401.52
- 75; 2775.00; 1477.98
- 76; 2850.00; 1493.06
- 77; 2926.00; 1526.38
- 78; 3003.00; 1560.82
- 79; 3081.00; 1617.40
- 80; 3160.00; 1663.76
- 81; 3240.00; 1691.06
- 82; 3321.00; 1744.06
- 83; 3403.00; 1752.94
- 84; 3486.00; 1819.04
- 85; 3570.00; 1868.20
- 86; 3655.00; 1917.44
- 87; 3741.00; 1921.42
- 88; 3828.00; 2030.48
- 89; 3916.00; 2050.78
- 90; 4005.00; 2078.02
- 91; 4095.00; 2152.64
- 92; 4186.00; 2185.64
- 93; 4278.00; 2221.32
- 94; 4371.00; 2304.18
- 95; 4465.00; 2331.54
- 96; 4560.00; 2387.02
- 97; 4656.00; 2416.54
- 98; 4753.00; 2460.58
- 99; 4851.00; 2562.00
-100; 4950.00; 2549.66
+  3;    3.00;    2.54
+  4;    6.00;    4.94
+  5;   10.00;    7.74
+  6;   15.00;   10.94
+  7;   21.00;   15.12
+  8;   28.00;   18.32
+  9;   36.00;   24.46
+ 10;   45.00;   28.74
+ 11;   55.00;   36.26
+ 12;   66.00;   42.60
+ 13;   78.00;   47.62
+ 14;   91.00;   55.40
+ 15;  105.00;   64.76
+ 16;  120.00;   75.72
+ 17;  136.00;   81.50
+ 18;  153.00;   93.78
+ 19;  171.00;   99.70
+ 20;  190.00;  108.00
+ 21;  210.00;  121.72
+ 22;  231.00;  136.70
+ 23;  253.00;  148.32
+ 24;  276.00;  154.62
+ 25;  300.00;  177.60
+ 26;  325.00;  185.98
+ 27;  351.00;  195.04
+ 28;  378.00;  214.66
+ 29;  406.00;  228.92
+ 30;  435.00;  243.02
+ 31;  465.00;  263.00
+ 32;  496.00;  278.32
+ 33;  528.00;  300.08
+ 34;  561.00;  313.08
+ 35;  595.00;  332.32
+ 36;  630.00;  347.46
+ 37;  666.00;  363.56
+ 38;  703.00;  385.38
+ 39;  741.00;  402.26
+ 40;  780.00;  431.92
+ 41;  820.00;  449.30
+ 42;  861.00;  468.26
+ 43;  903.00;  482.66
+ 44;  946.00;  514.60
+ 45;  990.00;  547.12
+ 46; 1035.00;  558.56
+ 47; 1081.00;  591.68
+ 48; 1128.00;  596.86
+ 49; 1176.00;  638.16
+ 50; 1225.00;  662.70
+ 51; 1275.00;  682.62
+ 52; 1326.00;  707.10
+ 53; 1378.00;  754.44
+ 54; 1431.00;  758.76
+ 55; 1485.00;  804.98
+ 56; 1540.00;  815.14
+ 57; 1596.00;  856.56
+ 58; 1653.00;  857.58
+ 59; 1711.00;  914.12
+ 60; 1770.00;  921.60
+ 61; 1830.00;  983.40
+ 62; 1891.00;  987.16
+ 63; 1953.00; 1037.34
+ 64; 2016.00; 1086.56
+ 65; 2080.00; 1084.88
+ 66; 2145.00; 1158.24
+ 67; 2211.00; 1172.10
+ 68; 2278.00; 1185.94
+ 69; 2346.00; 1220.80
+ 70; 2415.00; 1292.92
+ 71; 2485.00; 1308.74
+ 72; 2556.00; 1343.22
+ 73; 2628.00; 1390.08
+ 74; 2701.00; 1428.48
+ 75; 2775.00; 1445.40
+ 76; 2850.00; 1475.92
+ 77; 2926.00; 1534.34
+ 78; 3003.00; 1604.52
+ 79; 3081.00; 1610.94
+ 80; 3160.00; 1674.74
+ 81; 3240.00; 1693.34
+ 82; 3321.00; 1729.02
+ 83; 3403.00; 1799.78
+ 84; 3486.00; 1800.70
+ 85; 3570.00; 1884.10
+ 86; 3655.00; 1954.98
+ 87; 3741.00; 1964.98
+ 88; 3828.00; 2012.42
+ 89; 3916.00; 2011.72
+ 90; 4005.00; 2080.66
+ 91; 4095.00; 2147.18
+ 92; 4186.00; 2161.90
+ 93; 4278.00; 2216.44
+ 94; 4371.00; 2290.34
+ 95; 4465.00; 2347.26
+ 96; 4560.00; 2389.54
+ 97; 4656.00; 2413.08
+ 98; 4753.00; 2483.92
+ 99; 4851.00; 2523.12
+100; 4950.00; 2608.62

tp7/analyse_tris2.py

@@ -41,7 +41,7 @@ def analyser_tri(tri: Callable[[list[T], Callable[[T, T], int]], NoneType],
         res += compare.counter
     return res / nbre_essais
 
-def comp_sort(l:list[T], comp: Callable[[T, T], int] = compare):
+def tri_comp(l:list[T], comp: Callable[[T, T], int] = compare):
     """à_remplacer_par_ce_que_fait_la_fonction
 
     Précondition : 
@@ -49,8 +49,7 @@ def comp_sort(l:list[T], comp: Callable[[T, T], int] = compare):
     $$$ 
 
     """
-    sorted_l = sorted(l, key= lambda x: comp(x,x))
-    return sorted_l
+    sorted(l, key= lambda x: comp(x,x))
 
 
 if (__name__ == '__main__'):
@@ -70,7 +69,7 @@ if (__name__ == '__main__'):
         # inutile de moyenner pour le tri par sélection
         c_insert[t] = analyser_tri(tri_insert, NB_ESSAIS, t)
         # for sorting
-        c_sort[t] = analyser_tri(comp_sort, NB_ESSAIS, t)
+        c_sort[t] = analyser_tri(tri_comp, NB_ESSAIS, t)
 
     # Sauvegarde des données calculées dans un fichier au format CSV
     prem_ligne = 'taille;"tri séléction";"tri insertion"\n'
@@ -80,8 +79,7 @@ if (__name__ == '__main__'):
         for t in range(TAILLE_MAX + 1):
             sortie.write(ligne.format(t,
                                       c_select[t],
-                                      c_insert[t],
-                                      c_sort[t]))
+                                      c_insert[t]))
 
     # Représentation graphique
     plt.plot(list(range(TAILLE_MAX + 1)), c_select, 'b.', label='Tri sélection')

tp7/timethis.py

+import timeit
+import matplotlib.pyplot as plt
\ No newline at end of file

tp7/tp_tris.py

 from random import shuffle
+import timeit
 import matplotlib.pyplot as plt
-from ap_decorators import count
-from compare import compare
+from analyse_tris import tri_select
+from math import sqrt
+from analyse_tris import analyser_tri
 
+
+# Préliminaires
 def liste_alea(n: int) -> list[int]:
     """construit une liste de longueur n contenant les entiers 0 à n-1 mélangés
 
@@ -15,5 +19,69 @@ def liste_alea(n: int) -> list[int]:
     shuffle(l)
     return l
 
+# Évaluation expérimentale de la complexité en temps
+TAILLE_MAX = 100
+L = []
+T = []
+
+for t in range(1, TAILLE_MAX + 1):
+    rlist = liste_alea(t)
+    time = timeit.timeit(stmt='tri_select(l)', setup='from __main__ import tri_select, l', globals={'l': rlist}, number=5000)
+    L.append(t)
+    times.append(time)
+    
+plt.plot(lengths, times, label='Selection Sort')
+plt.xlabel('Length of List')
+plt.ylabel('Time (s)')
+plt.title('Selection Sort Execution Time')
+plt.legend()
+plt.grid(True)
+plt.show()
+
+#3
+import timeit
+import matplotlib.pyplot as plt
+import random
+from analyse_tris import tri_insert
+
+Nmax = 100
+number = 5000
+
+best_case = []
+average_case = []
+worst_case = []
+
+for t in range(1, Nmax + 1):
+    # Best Case: Sorted List
+    sorted_list = list(range(t))
+    best_time = timeit.timeit(stmt='tri_insert(liste)', setup='from __main__ import tri_insert, liste', globals={'liste': sorted_list}, number=number)
+    best_case.append(best_time)
+
+    # Average Case: Random List
+    random_list = random.sample(range(t), t)
+    average_time = timeit.timeit(stmt='tri_insert(liste)', setup='from __main__ import tri_insert, liste; import random', globals={'liste': random_list}, number=number)
+    shuffle_time = timeit.timeit(stmt='random.shuffle(liste)', setup='import random; liste = list(range(t))', globals={'t': t, 'random': random}, number=number)
+    average_case.append(average_time - shuffle_time)
+
+    # Worst Case: Reverse Sorted List
+    reverse_sorted_list = list(range(t - 1, -1, -1))
+    worst_time = timeit.timeit(stmt='tri_insert(liste[::-1])', setup='from __main__ import tri_insert, liste', globals={'liste': reverse_sorted_list}, number=number)
+    reverse_time = timeit.timeit(stmt='liste.reverse()', setup='liste = list(range(t))', globals={'t': t}, number=number)
+    worst_case.append(worst_time - reverse_time)
+
+# Plotting
+plt.plot(range(1, Nmax + 1), best_case, label='Best Case')
+plt.plot(range(1, Nmax + 1), average_case, label='Average Case')
+plt.plot(range(1, Nmax + 1), worst_case, label='Worst Case')
+plt.xlabel('Length of List')
+plt.ylabel('Time (s)')
+plt.title('Insertion Sort Time Complexity')
+plt.legend()
+plt.grid(True)
+plt.show()
+
+
+
+