EXO 4 - optimisation F7

COMPTE_RENDU.md

@@ -0,0 +1,108 @@
+# Groupe : 
+- Karl FRAMERY
+- Ozvann ABRAHAM
+
+
+
+# 1.Mesurer
+
+```
+gcc -O2 banque.c -o banque && time ./banque
+```
+
+```
+Empreinte           : ff68d260a7a58441
+
+real    0m4,793s
+user    0m4,772s
+sys     0m0,005s
+```
+
+Le temps d'éxecution du programme est de 4.793 seconde et l'emprunte est : [ff68d260a7a58441]
+
+
+# 2.Profiler
+
+
+La fonction F1 : <trier_par_montant> est d'une complexité <span style="color:yellow">[O(n²)]</span> pour une utilisation du temps de 43.77% du temps totale d'exécution pour 1 call.
+
+La fonction F7 : <nb_paires_opposees> est d'une complexité <span style="color:yellow">[O(n²)]</span> pour une utilisation du temps de 15.32% du temps totale d'exécution pour 1 call.
+
+La fonction F8 : <nb_facons_rendre> est d'une complexité <span style="color:red">[O(2^n)]</span> pour une utilisation du temps de 12.84% du temps totale d'exécution pour 1 call.
+
+La fonction F6 : <rechercher_par_id> est d'une complexité <span style="color:blue">[O(n)]</span> pour une utilisation du temps de 12.21% du temps totale d'exécution pour 30000 calls.
+
+
+On peut voir que les fonctions les plus coûteuse ont les plus grande complexité.
+
+
+
+# 3.Calculer
+
+
+### Fonction F1
+
+La complexité de la fonction est de <span style="color:yellow">[O(n²)]</span> pour un M de 6
+
+### Fonction F2
+
+La complexité de la fonction est de <span style="color:yellow">[O(n²)]</span> pour un M de 5
+
+### Fonction F3
+
+La complexité de la fonction est de <span style="color:yellow">[O(n²)]</span> pour un M de 4
+
+### Fonction F4
+
+La complexité de la fonction est de <span style="color:yellow">[O(n²)]</span> pour un M de 4
+
+### Fonction F5
+
+La complexité de la fonction est de <span style="color:yellow">[O(n³)]</span> pour un M de 5
+
+### Fonction F6
+
+La complexité de la fonction est de <span style="color:blue">[O(n)]</span> pour un M de 3
+
+### Fonction F7
+
+La complexité de la fonction est de <span style="color:yellow">[O(n²)]</span> pour un M de 4
+
+### Fonction F8
+
+La complexité de la fonction est de <span style="color:red">[O(2^n)]</span> pour un M de 4
+
+### Fonction F9
+
+La complexité de la fonction est de <span style="color:blue">[O(1)]</span> pour un M de 14
+
+### Fonction F10
+
+La complexité de la fonction est de <span style="color:blue">[O(n)]</span> pour un M de 2
+
+
+
+# 4. Optimisation
+
+- Optimisation de la fonction 1 nom du commit : ""
+
+- Optimisation de la fonction 2 nom du commit : "fonction 2 : O(n + C)". Emprunte : ff68d260a7a58441
+
+- Optimisation de la fonction 3 nom du commit : "". Emprunte : ff68d260a7a58441
+
+- Optimisation de la fonction 4 nom du commit : "fonction 4 : O(n + J)". Emprunte : ff68d260a7a58441
+
+- Optimisation de la fonction 5 nom du commit : "". Emprunte : ff68d260a7a58441
+
+- Optimisation de la fonction 6 nom du commit : "". Emprunte : ff68d260a7a58441
+
+- Optimisation de la fonction 7 nom du commit : "". Emprunte : ff68d260a7a58441
+
+- Optimisation de la fonction 8 nom du commit : "". Emprunte : ff68d260a7a58441
+
+- Optimisation de la fonction 9 nom du commit : "". Emprunte : ff68d260a7a58441
+
+- Optimisation de la fonction 10 nom du commit : "". Emprunte : ff68d260a7a58441
+
+
+

banque.c

@@ -73,15 +73,15 @@ Transaction *generer_transactions(int n)
 /* F1 : trie les transactions par montant croissant, puis par id */
 void trier_par_montant(Transaction *t, int n)
 {
-    for (int i = 0; i < n - 1; i++) {
-        for (int j = 0; j < n - 1 - i; j++) {
-            if (t[j].montant > t[j + 1].montant ||
-                (t[j].montant == t[j + 1].montant && t[j].id > t[j + 1].id)) {
-                Transaction tmp = t[j];
-                t[j] = t[j + 1];
-                t[j + 1] = tmp;
-            }
+    for (int i = 1; i < n; i++) {
+        Transaction cle = t[i];
+        int j = i - 1;
+        while (j >= 0 && (t[j].montant > cle.montant ||
+                         (t[j].montant == cle.montant && t[j].id > cle.id))) {
+            t[j + 1] = t[j];
+            j--;
         }
+        t[j + 1] = cle;
     }
 }
 
@@ -103,14 +103,14 @@ int nb_clients_distincts(const Transaction *t, int n)
     return nb;
 }
 
-/* F3 : solde total de chaque client */
+/* F3 : solde total de chaque client en O(n + c) */
 void total_par_client(const Transaction *t, int n, long *totaux)
 {
     for (int c = 0; c < NB_CLIENTS; c++) {
         totaux[c] = 0;
-        for (int i = 0; i < n; i++)
-            if (t[i].client == c)
-                totaux[c] += t[i].montant;
+    }
+    for (int i = 0; i < n; i++) {
+        totaux[t[i].client] += t[i].montant;
     }
 }
 
@@ -125,24 +125,30 @@ void total_par_jour(const Transaction *t, int n, long *totaux)
     }
 }
 
-/* F5 : période de jours consécutifs dont la somme des soldes est maximale */
+/* F5 : période de jours consécutifs dont la somme des soldes est maximale en O(J) */
 long meilleure_periode(const long *totaux, int nb_jours, int *debut, int *fin)
 {
     long meilleur = totaux[0];
     *debut = 0;
     *fin = 0;
-    for (int i = 0; i < nb_jours; i++) {
-        for (int j = i; j < nb_jours; j++) {
-            long somme = 0;
-            for (int k = i; k <= j; k++)
-                somme += totaux[k];
-            if (somme > meilleur) {
-                meilleur = somme;
-                *debut = i;
-                *fin = j;
-            }
+
+    long somme_courante = totaux[0];
+    int debut_courant = 0;
+
+    for (int j = 1; j < nb_jours; j++) {
+        if (somme_courante < 0) {
+            somme_courante = totaux[j];
+            debut_courant = j;
+        } else {
+            somme_courante += totaux[j];
+        }
+        if (somme_courante > meilleur) {
+            meilleur = somme_courante;
+            *debut = debut_courant;
+            *fin = j;
         }
     }
+
     return meilleur;
 }
 
@@ -156,13 +162,45 @@ const Transaction *rechercher_par_id(const Transaction *t, int n, int id)
 }
 
 /* F7 : nombre de paires de transactions de montants opposés (a + b = 0) */
+
+
+static int cmp_long(const void *a, const void *b)
+{
+    long x = *(const long *)a;
+    long y = *(const long *)b;
+    return (x > y) - (x < y);
+}
+
 long nb_paires_opposees(const Transaction *t, int n)
 {
+    /* 1. Copier et trier les montants : O(n log n) */
+    long *m = malloc(n * sizeof(long));
+    for (int i = 0; i < n; i++) {
+        m[i] = t[i].montant;
+    }
+    qsort(m, n, sizeof(long), cmp_long);
+
+    /* 2. Deux pointeurs : O(n) au lieu de O(n²) */
     long nb = 0;
-    for (int i = 0; i < n; i++)
-        for (int j = i + 1; j < n; j++)
-            if (t[i].montant + t[j].montant == 0)
+    int g = 0, d = n - 1;
+
+    while (g < d) {
+        long somme = m[g] + m[d];
+
+        if (somme < 0) {
+            g++;
+        } else if (somme > 0) {
+            d--;
+        } else {
+            /* somme == 0 : on compte tous les m[d] identiques en face de m[g] */
+            for (int k = d; k > g && m[k] == m[d]; k--) {
                 nb++;
+            }
+            g++; /* Puis on passe simplement au m[g] suivant ! */
+        }
+    }
+
+    free(m);
     return nb;
 }
 

profil_avant.txt

@@ -0,0 +1,220 @@
+Flat profile:
+
+Each sample counts as 0.01 seconds.
+  %   cumulative   self              self     total           
+ time   seconds   seconds    calls   s/call   s/call  name    
+ 43.77      5.20     5.20        1     5.20     5.20  trier_par_montant
+ 15.32      7.02     1.82        1     1.82     1.82  nb_paires_opposees
+ 12.84      8.54     1.52        1     1.52     1.52  nb_facons_rendre
+ 12.21      9.99     1.45    30000     0.00     0.00  rechercher_par_id
+  6.06     10.71     0.72     6017     0.00     0.00  longueur
+  4.04     11.20     0.48        1     0.48     0.48  meilleure_periode
+  1.94     11.43     0.23        1     0.23     0.23  nb_clients_distincts
+  1.60     11.62     0.19        1     0.19     0.19  total_par_client
+  1.01     11.73     0.12                             _init
+  0.84     11.84     0.10        1     0.10     0.10  total_par_jour
+  0.38     11.88     0.04    30000     0.00     0.00  categorie
+  0.00     11.88     0.00   149998     0.00     0.00  alea
+  0.00     11.88     0.00     6017     0.00     0.00  ajouter_ligne
+  0.00     11.88     0.00        1     0.00     0.00  empreinte
+  0.00     11.88     0.00        1     0.00     0.00  generer_transactions
+
+ %         the percentage of the total running time of the
+time       program used by this function.
+
+cumulative a running sum of the number of seconds accounted
+ seconds   for by this function and those listed above it.
+
+ self      the number of seconds accounted for by this
+seconds    function alone.  This is the major sort for this
+           listing.
+
+calls      the number of times this function was invoked, if
+           this function is profiled, else blank.
+
+ self      the average number of milliseconds spent in this
+ms/call    function per call, if this function is profiled,
+	   else blank.
+
+ total     the average number of milliseconds spent in this
+ms/call    function and its descendents per call, if this
+	   function is profiled, else blank.
+
+name       the name of the function.  This is the minor sort
+           for this listing. The index shows the location of
+	   the function in the gprof listing. If the index is
+	   in parenthesis it shows where it would appear in
+	   the gprof listing if it were to be printed.
+
+Copyright (C) 2012-2026 Free Software Foundation, Inc.
+
+Copying and distribution of this file, with or without modification,
+are permitted in any medium without royalty provided the copyright
+notice and this notice are preserved.
+
+		     Call graph (explanation follows)
+
+
+granularity: each sample hit covers 4 byte(s) for 0.08% of 11.88 seconds
+
+index % time    self  children    called     name
+                                                 <spontaneous>
+[1]     99.0    0.00   11.76                 main [1]
+                5.20    0.00       1/1           trier_par_montant [2]
+                1.82    0.00       1/1           nb_paires_opposees [3]
+                1.52    0.00       1/1           nb_facons_rendre [4]
+                1.45    0.00   30000/30000       rechercher_par_id [5]
+                0.00    0.72    6017/6017        ajouter_ligne [6]
+                0.48    0.00       1/1           meilleure_periode [8]
+                0.23    0.00       1/1           nb_clients_distincts [9]
+                0.19    0.00       1/1           total_par_client [10]
+                0.10    0.00       1/1           total_par_jour [12]
+                0.04    0.00   30000/30000       categorie [13]
+                0.00    0.00       1/1           generer_transactions [16]
+                0.00    0.00       1/1           empreinte [15]
+-----------------------------------------------
+                5.20    0.00       1/1           main [1]
+[2]     43.8    5.20    0.00       1         trier_par_montant [2]
+-----------------------------------------------
+                1.82    0.00       1/1           main [1]
+[3]     15.3    1.82    0.00       1         nb_paires_opposees [3]
+-----------------------------------------------
+                             266723738             nb_facons_rendre [4]
+                1.52    0.00       1/1           main [1]
+[4]     12.8    1.52    0.00       1+266723738 nb_facons_rendre [4]
+                             266723738             nb_facons_rendre [4]
+-----------------------------------------------
+                1.45    0.00   30000/30000       main [1]
+[5]     12.2    1.45    0.00   30000         rechercher_par_id [5]
+-----------------------------------------------
+                0.00    0.72    6017/6017        main [1]
+[6]      6.1    0.00    0.72    6017         ajouter_ligne [6]
+                0.72    0.00    6017/6017        longueur [7]
+-----------------------------------------------
+                0.72    0.00    6017/6017        ajouter_ligne [6]
+[7]      6.1    0.72    0.00    6017         longueur [7]
+-----------------------------------------------
+                0.48    0.00       1/1           main [1]
+[8]      4.0    0.48    0.00       1         meilleure_periode [8]
+-----------------------------------------------
+                0.23    0.00       1/1           main [1]
+[9]      1.9    0.23    0.00       1         nb_clients_distincts [9]
+-----------------------------------------------
+                0.19    0.00       1/1           main [1]
+[10]     1.6    0.19    0.00       1         total_par_client [10]
+-----------------------------------------------
+                                                 <spontaneous>
+[11]     1.0    0.12    0.00                 _init [11]
+-----------------------------------------------
+                0.10    0.00       1/1           main [1]
+[12]     0.8    0.10    0.00       1         total_par_jour [12]
+-----------------------------------------------
+                0.04    0.00   30000/30000       main [1]
+[13]     0.4    0.04    0.00   30000         categorie [13]
+-----------------------------------------------
+                0.00    0.00  149998/149998      generer_transactions [16]
+[14]     0.0    0.00    0.00  149998         alea [14]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[15]     0.0    0.00    0.00       1         empreinte [15]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[16]     0.0    0.00    0.00       1         generer_transactions [16]
+                0.00    0.00  149998/149998      alea [14]
+-----------------------------------------------
+
+ This table describes the call tree of the program, and was sorted by
+ the total amount of time spent in each function and its children.
+
+ Each entry in this table consists of several lines.  The line with the
+ index number at the left hand margin lists the current function.
+ The lines above it list the functions that called this function,
+ and the lines below it list the functions this one called.
+ This line lists:
+     index	A unique number given to each element of the table.
+		Index numbers are sorted numerically.
+		The index number is printed next to every function name so
+		it is easier to look up where the function is in the table.
+
+     % time	This is the percentage of the `total' time that was spent
+		in this function and its children.  Note that due to
+		different viewpoints, functions excluded by options, etc,
+		these numbers will NOT add up to 100%.
+
+     self	This is the total amount of time spent in this function.
+
+     children	This is the total amount of time propagated into this
+		function by its children.
+
+     called	This is the number of times the function was called.
+		If the function called itself recursively, the number
+		only includes non-recursive calls, and is followed by
+		a `+' and the number of recursive calls.
+
+     name	The name of the current function.  The index number is
+		printed after it.  If the function is a member of a
+		cycle, the cycle number is printed between the
+		function's name and the index number.
+
+
+ For the function's parents, the fields have the following meanings:
+
+     self	This is the amount of time that was propagated directly
+		from the function into this parent.
+
+     children	This is the amount of time that was propagated from
+		the function's children into this parent.
+
+     called	This is the number of times this parent called the
+		function `/' the total number of times the function
+		was called.  Recursive calls to the function are not
+		included in the number after the `/'.
+
+     name	This is the name of the parent.  The parent's index
+		number is printed after it.  If the parent is a
+		member of a cycle, the cycle number is printed between
+		the name and the index number.
+
+ If the parents of the function cannot be determined, the word
+ `<spontaneous>' is printed in the `name' field, and all the other
+ fields are blank.
+
+ For the function's children, the fields have the following meanings:
+
+     self	This is the amount of time that was propagated directly
+		from the child into the function.
+
+     children	This is the amount of time that was propagated from the
+		child's children to the function.
+
+     called	This is the number of times the function called
+		this child `/' the total number of times the child
+		was called.  Recursive calls by the child are not
+		listed in the number after the `/'.
+
+     name	This is the name of the child.  The child's index
+		number is printed after it.  If the child is a
+		member of a cycle, the cycle number is printed
+		between the name and the index number.
+
+ If there are any cycles (circles) in the call graph, there is an
+ entry for the cycle-as-a-whole.  This entry shows who called the
+ cycle (as parents) and the members of the cycle (as children.)
+ The `+' recursive calls entry shows the number of function calls that
+ were internal to the cycle, and the calls entry for each member shows,
+ for that member, how many times it was called from other members of
+ the cycle.
+
+Copyright (C) 2012-2026 Free Software Foundation, Inc.
+
+Copying and distribution of this file, with or without modification,
+are permitted in any medium without royalty provided the copyright
+notice and this notice are preserved.
+
+Index by function name
+
+  [11] _init                  [16] generer_transactions    [3] nb_paires_opposees
+   [6] ajouter_ligne           [7] longueur                [5] rechercher_par_id
+  [14] alea                    [8] meilleure_periode      [10] total_par_client
+  [13] categorie               [9] nb_clients_distincts   [12] total_par_jour
+  [15] empreinte               [4] nb_facons_rendre        [2] trier_par_montant