From 52f4238326fdf2d74df520d7d8bba7bc365a3620 Mon Sep 17 00:00:00 2001 From: hochlaf Date: Wed, 15 Oct 2025 11:56:34 +0200 Subject: [PATCH] tout est good --- Ex3_Trie_Tableau_Double.py | 64 +++++++++++++++++++++++ README.md | 104 +++++++++++++++++++++++++++++++++++++ image/function_1.png | Bin 0 -> 44488 bytes image/function_2.png | Bin 0 -> 17402 bytes image/function_3.png | Bin 0 -> 21036 bytes 5 files changed, 168 insertions(+) create mode 100644 Ex3_Trie_Tableau_Double.py create mode 100644 README.md create mode 100644 image/function_1.png create mode 100644 image/function_2.png create mode 100644 image/function_3.png diff --git a/Ex3_Trie_Tableau_Double.py b/Ex3_Trie_Tableau_Double.py new file mode 100644 index 0000000..a36c42c --- /dev/null +++ b/Ex3_Trie_Tableau_Double.py @@ -0,0 +1,64 @@ + +def Trie_Tableau_Double(tab) : # complexitée O(n(m²+n)) + sorted_dico = {} + + print(tab[0]) + + # n^(m+m*((m(m+1))/2))+n((m(m+1))/2) + + for sub_tab in tab : # n + val = 0 + sub_tab2 = [] + for elt in sub_tab : # m + val += elt + + for i in range(len(sub_tab)): # m + if i == 0 : + sub_tab2.append(sub_tab[i]) + else : + for j in range(len(sub_tab2)+1): # (m(m+1))/2 + if j >= len(sub_tab2): + sub_tab2.append(sub_tab[i]) + else : + if sub_tab[i] <= sub_tab2[j] : + sub_tab2.insert(j,sub_tab[i]) + break + + sorted_dico[val] = sub_tab2 + + tab = [] + index_tab = [] + + # n*(m(m+1))/2 + + for clef,valeur in sorted_dico.items() : # n + if index_tab == [] : + tab.append(valeur) + index_tab.append(clef) + else : + for j in range(len(index_tab)+1): # (m(m+1))/2 + if j >= len(index_tab): + tab.append(valeur) + index_tab.append(clef) + else : + if clef <= index_tab[j] : + tab.insert(j,valeur) + index_tab.insert(j,clef) + break + + return tab + + +def Trie_Tableau_Double_bySort(tab) : # complexitée O(n*m * log(m)) + + tab.sort() # n log(n) + + for sub_tab in tab : # n + sub_tab.sort() # m log(m) + + return tab + + +Tableau_test = [[0,3,2], [9,4,5], [4,1,3]] + +print(Trie_Tableau_Double(Tableau_test)) \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 0000000..09ad61b --- /dev/null +++ b/README.md @@ -0,0 +1,104 @@ +# TD4 - DEV5.1 Qualité algorithmique +Complexité algorithmique + +## Ex 2 - Calculs de complexité de fonctions +Calculez la complexité des fonctions suivantes : +![alt text](image/function_1.png) + +Ici on prend un tableau 1 contenant **n** valeurs et un tableau 2 contenant **m** valeurs. + +On parcour entièrement les deux pour savoir si une valeur ce trouve dans l'autre tableau. + +On a donc : +> O ( n x m ) + + + +![alt text](image/function_2.png) + +Ici on prend un une variable x de valeur **n**. + +Tant que x est positif, on le décrémente pour arriver a 0 + +On a donc : +> O ( n ) ou O ( x ) + + + +![alt text](image/function_3.png) + +Cette fonction n'a pas de boucle donc elle ne ce répète pas. + +On a donc : +> O ( 1 ) + +## Ex 3 - Algorithme de tri +- Créer un algorithme pour trier un tableau à N dimensions de M valeurs +- Chaque dimension doit être trié par ordre croissant de la somme des valeurs de la +dimension inférieur +- Exemple pour un tableau à 2 dimensions de 3 valeurs +[ [0,3,2], [9,4,5], [4,1,3] ] → [ [0,2,3], [1,3,4], [4,5,9] ] +- Calculer la complexité algorithmique de l’algorithme écrit + * la complecitée de ce programme est de O(n(m²+n)) +```python +def Trie_Tableau_Double(tab) : # complexitée O(n(m²+n)) + sorted_dico = {} + + print(tab[0]) + + # n^(m+m*((m(m+1))/2))+n((m(m+1))/2) + + for sub_tab in tab : # n + val = 0 + sub_tab2 = [] + for elt in sub_tab : # m + val += elt + + for i in range(len(sub_tab)): # m + if i == 0 : + sub_tab2.append(sub_tab[i]) + else : + for j in range(len(sub_tab2)+1): # (m(m+1))/2 + if j >= len(sub_tab2): + sub_tab2.append(sub_tab[i]) + else : + if sub_tab[i] <= sub_tab2[j] : + sub_tab2.insert(j,sub_tab[i]) + break + + sorted_dico[val] = sub_tab2 + + tab = [] + index_tab = [] + + # n*(m(m+1))/2 + + for clef,valeur in sorted_dico.items() : # n + if index_tab == [] : + tab.append(valeur) + index_tab.append(clef) + else : + for j in range(len(index_tab)+1): # (m(m+1))/2 + if j >= len(index_tab): + tab.append(valeur) + index_tab.append(clef) + else : + if clef <= index_tab[j] : + tab.insert(j,valeur) + index_tab.insert(j,clef) + break + + return tab +``` + + * la complecitée de ce programme est de O(n*m * log(m)) + ```python + def Trie_Tableau_Double_bySort(tab) : # complexitée O(n*m * log(m)) + + tab.sort() # n log(n) + + for sub_tab in tab : # n + sub_tab.sort() # m log(m) + + return tab + ``` \ No newline at end of file diff --git a/image/function_1.png b/image/function_1.png new file mode 100644 index 0000000000000000000000000000000000000000..18f5f938c305ba165f2682cd70497016a2168e18 GIT binary patch literal 44488 zcmeAS@N?(olHy`uVBq!ia0y~yVEoU(!0?uXiGhK^?$_(H3=9m+#ZI0f92^|CANoIF zU{GN2ba4!+nDb_Cd4kCCo5$wwzWsXditqQdg_u}6;zSQ5H0K)Zcp!GX@R7yY!b$p_ 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