compte rendu

COMPTE_RENDU.md

@@ -0,0 +1,78 @@
+# Dimitri SOLAR / Valentin LOISON / Kais BENS
+
+Empreinte           : ff68d260a7a58441
+
+real    2.11s
+user    2.11s
+sys     0.00s
+
+
+
+2. # Profiller 
+la fonction la plus couteuse est : trier_par_montant pourtant elle n'a pas la complexité la plys élévé .
+
+3. 
+F1 = O(n^2)  
+F2 = O(n^2)  
+F3 = O(n*c)  
+F4 = O(n*j)  
+F5 = O(j^2)  
+F6 = O(n^2)  
+F7 = O(n^2)    
+F8 O(2^k)  
+F9 M=14  
+F10 = O(n+L)
+
+
+
+```console
+└─$ ./evaluer.sh banque.c solar
+Empreinte correcte
+Temps (médiane de 5) : 13 ms
+Complexité cyclomatique : vérifiée par l'enseignant
+Ligne ajoutée à resultats.csv : solar;-;13
+
+```
+
+
+4. # Justification
+
+F1 (trier_par_montant)  
+Remplacement du tri à bulles en O(n^2) par le tri rapide standard qsort en O(n log n).  
+La fonction de comparaison dédiée traite la clé composite (montant puis identifiant) efficacement.
+
+F2 (nb_clients_distincts)  
+Remplacement de la double boucle imbriquée en O(n^2)par un tableau de présence (deja_vu).  
+Le calcul s'effectue désormais en un seul parcours linéaire O(n) grâce à des accès directs en O(1).
+
+F3 (total_par_client)  
+Suppression de la double boucle en O(clients * n) qui re-parcourait inutilement le tableau pour chaque client.
+Accumulation directe des montants sur chaque client au fil d'une passe unique en O(clients + n).
+
+F4 (total_par_jour)  
+Élimination du parcours complet de toutes les transactions pour chaque jour distinct en O(jours * n).  
+Parcours unique des transactions avec ajout immédiat au jour correspondant, réduisant le temps à O(jours + n).
+
+F5 (meilleure_periode)  
+Remplacement du calcul exhaustif de toutes les plages de jours consécutifs en O(n^3).  
+Application de l'algorithme de Kadane pour trouver la somme maximale en une seule passe linéaire O(n).  
+
+F6 (rechercher_par_id)  
+Remplacement de la recherche linéaire globale répétée en O(n) à la requête.  
+Mise en place d'une table d'indexation directe (cache statique) offrant un accès immédiat en O(1) par requête.  
+
+F7 (nb_paires_opposees)  
+Passage d'une comparaison de toutes les paires possibles en O(n^2) à un tri préalable des montants en O(n log n).  
+Utilisation de deux pointeurs convergents pour dénombrer les paires opposées en un parcours linéaire.
+
+F8 (nb_facons_rendre)  
+Remplacement de l'exploration récursive naïve souffrant d'une complexité temporelle exponentielle.  
+Adoption de la programmation dynamique via un tableau 1D en O(somme * nb_pieces).  
+
+F9 (categorie)  
+Structuration et modularisation des tests conditionnels via categorie_debit et categorie_credit.  
+Simplification de l'arbre de décision permettant de réduire les comparaisons et d'aider la prédiction de branchement.
+
+F10 (ajouter_ligne)  
+Suppression du recalcul de la longueur totale du rapport à chaque insertion, évite un coût global en O(n^2).  
+Maintien d'un pointeur mobile fin_rapport garantissant une écriture directe à la suite en O(longueur_ligne).  

banque.c

@@ -128,18 +128,21 @@ void total_par_jour(const Transaction *t, int n, long *totaux)
 long meilleure_periode(const long *totaux, int nb_jours, int *debut, int *fin)
 {
     long meilleur = totaux[0];
+    long somme_courante = totaux[0];
+    int debut_courant = 0;
     *debut = 0;
     *fin = 0;
-    for (int i = 0; i < nb_jours; i++) {
+    for (int j = 1; j < nb_jours; j++) {
-        for (int j = i; j < nb_jours; j++) {
+        if (somme_courante < 0) {
-            long somme = 0;
+            somme_courante = totaux[j];
-            for (int k = i; k <= j; k++)
+            debut_courant = j;
-                somme += totaux[k];
+        } else {
-            if (somme > meilleur) {
+            somme_courante += totaux[j];
-                meilleur = somme;
-                *debut = i;
-                *fin = j;
         }
+        if (somme_courante > meilleur) {
+            meilleur = somme_courante;
+            *debut = debut_courant;
+            *fin = j;
         }
     }
     return meilleur;
@@ -148,6 +151,19 @@ long meilleure_periode(const long *totaux, int nb_jours, int *debut, int *fin)
 /* F6 : retrouve une transaction à partir de son id */
 const Transaction *rechercher_par_id(const Transaction *t, int n, int id)
 {
+    static const Transaction *index[NB_TRANSACTIONS];
+    static const Transaction *transactions_indexees;
+    static int taille_indexee;
+
+    if (n <= NB_TRANSACTIONS && (t != transactions_indexees || n != taille_indexee)) {
+        for (int i = 0; i < n; i++)
+            index[t[i].id] = &t[i];
+        transactions_indexees = t;
+        taille_indexee = n;
+    }
+    if (n <= NB_TRANSACTIONS && id >= 0 && id < n && t == transactions_indexees)
+        return index[id];
+
     for (int i = 0; i < n; i++)
         if (t[i].id == id)
             return &t[i];
@@ -155,13 +171,56 @@ 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, y = *(const long *)b;
+    return (x > y) - (x < y);
+}
+
 long nb_paires_opposees(const Transaction *t, int n)
 {
-    long nb = 0;
+    if (n < 2)
+        return 0;
+
+    long *m = malloc(n * sizeof(long));
+    if (!m)
+        return 0;
     for (int i = 0; i < n; i++)
-        for (int j = i + 1; j < n; j++)
+        m[i] = t[i].montant;
-            if (t[i].montant + t[j].montant == 0)
+
-                nb++;
+    qsort(m, n, sizeof(long), cmp_long);          /* O(n log n) */
+
+    long nb = 0;
+
+    /* zéros : tous les montants nuls forment un bloc contigu */
+    int deb = 0;
+    while (deb < n && m[deb] < 0)
+        deb++;
+    int fin = deb;
+    while (fin < n && m[fin] == 0)
+        fin++;
+    long z = fin - deb;
+    nb += z * (z - 1) / 2;
+
+    /* deux pointeurs : négatifs depuis la fin de la zone négative,
+       positifs depuis le début de la zone positive (fin) */
+    int i = deb - 1;      /* plus grand négatif  : le plus proche de 0 */
+    int j = fin;          /* plus petit positif  : le plus proche de 0 */
+    while (i >= 0 && j < n) {
+        long neg = -m[i], pos = m[j];
+        if (neg < pos) {
+            i--;
+        } else if (neg > pos) {
+            j++;
+        } else {
+            long v = pos, a = 0, b = 0;
+            while (i >= 0 && -m[i] == v) { a++; i--; }
+            while (j < n && m[j] == v)   { b++; j++; }
+            nb += a * b;
+        }
+    }
+
+    free(m);
     return nb;
 }
 
@@ -171,66 +230,74 @@ static const int PIECES[] = {1, 2, 5, 10, 20, 50, 100, 200};
 
 long nb_facons_rendre(int somme, int nb_pieces)
 {
-    if (somme == 0)
+    if (somme < 0)
-        return 1;
-    if (somme < 0 || nb_pieces == 0)
         return 0;
-    return nb_facons_rendre(somme - PIECES[nb_pieces - 1], nb_pieces) +
+    if (nb_pieces == 0)
-           nb_facons_rendre(somme, nb_pieces - 1);
+        return somme == 0;
+
+    long dp[somme + 1];
+    for (int s = 0; s <= somme; s++)
+        dp[s] = 1;                   /* pièce de 1 : une seule façon */
+
+    for (int p = 1; p < nb_pieces; p++) {
+        int c = PIECES[p];
+        for (int s = c; s <= somme; s++)
+            dp[s] += dp[s - c];
+    }
+    return dp[somme];
 }
 
-/* F9 : catégorie d'une transaction (pour les statistiques) */
+static int categorie_debit(const Transaction *t)
-int categorie(const Transaction *t)
 {
-    if (t->montant < 0) {
     if (t->montant < -20000) {
         if (t->jour % 7 == 5 || t->jour % 7 == 6)
             return 1;
-            else
         return 2;
-        } else if (t->montant < -5000) {
+    }
+    if (t->montant < -5000)
         return 3;
-        } else {
     if (t->client % 10 == 0)
         return 4;
     return 5;
 }
-    } else if (t->montant == 0) {
+
-        return 0;
+static int categorie_credit(const Transaction *t)
-    } else {
+{
     if (t->montant > 30000) {
         if (t->client % 10 == 0 && t->jour % 7 < 5)
             return 6;
         return 7;
-        } else if (t->montant > 10000) {
+    }
+    if (t->montant > 10000)
         return 8;
-        } else if (t->montant > 1000) {
+    if (t->montant > 1000) {
         if (t->jour % 30 == 0)
             return 9;
         return 10;
     }
     return 11;
 }
+
+/* F9 : catégorie d'une transaction (pour les statistiques) */
+int categorie(const Transaction *t)
+{
+    if (t->montant < 0)
+        return categorie_debit(t);
+    if (t->montant == 0)
+        return 0;
+    return categorie_credit(t);
 }
 
+
 /* F10 : ajoute une ligne à la fin du rapport */
-int longueur(const char *s)
+void ajouter_ligne(char **fin_rapport, const char *ligne)
 {
-    int n = 0;
+    while (*ligne != '\0') {
-    while (s[n] != '\0')
+        **fin_rapport = *ligne;
-        n++;
+        (*fin_rapport)++;
-    return n;
+        ligne++;
     }
-
+    **fin_rapport = '\0';
-void ajouter_ligne(char *rapport, const char *ligne)
-{
-    int fin = longueur(rapport);
-    int i = 0;
-    while (ligne[i] != '\0') {
-        rapport[fin + i] = ligne[i];
-        i++;
-    }
-    rapport[fin + i] = '\0';
 }
 
 /* ------------------------------------------------------------------ */
@@ -251,6 +318,7 @@ int main(void)
 {
     Transaction *t = generer_transactions(NB_TRANSACTIONS);
     char *rapport = malloc(1 << 20);
+    char *fin_rapport = rapport;
     char ligne[128];
     rapport[0] = '\0';
 
@@ -286,30 +354,30 @@ int main(void)
 
     /* rapport */
     snprintf(ligne, sizeof(ligne), "clients distincts;%d\n", nb_clients);
-    ajouter_ligne(rapport, ligne);
+    ajouter_ligne(&fin_rapport, ligne);
     snprintf(ligne, sizeof(ligne), "somme des requetes;%ld\n", somme_requetes);
-    ajouter_ligne(rapport, ligne);
+    ajouter_ligne(&fin_rapport, ligne);
     snprintf(ligne, sizeof(ligne), "meilleure periode;%d;%d;%ld\n", debut, fin, meilleure);
-    ajouter_ligne(rapport, ligne);
+    ajouter_ligne(&fin_rapport, ligne);
     snprintf(ligne, sizeof(ligne), "paires opposees;%ld\n", nb_paires);
-    ajouter_ligne(rapport, ligne);
+    ajouter_ligne(&fin_rapport, ligne);
     snprintf(ligne, sizeof(ligne), "facons de rendre %d;%ld\n", MONTANT_MONNAIE, nb_facons);
-    ajouter_ligne(rapport, ligne);
+    ajouter_ligne(&fin_rapport, ligne);
     for (int c = 0; c < 12; c++) {
         snprintf(ligne, sizeof(ligne), "categorie;%d;%d\n", c, categories[c]);
-        ajouter_ligne(rapport, ligne);
+        ajouter_ligne(&fin_rapport, ligne);
     }
     for (int c = 0; c < NB_CLIENTS; c++) {
         snprintf(ligne, sizeof(ligne), "client;%d;%ld\n", c, totaux_clients[c]);
-        ajouter_ligne(rapport, ligne);
+        ajouter_ligne(&fin_rapport, ligne);
     }
     for (int j = 0; j < NB_JOURS; j++) {
         snprintf(ligne, sizeof(ligne), "jour;%d;%ld\n", j, totaux_jours[j]);
-        ajouter_ligne(rapport, ligne);
+        ajouter_ligne(&fin_rapport, ligne);
     }
     for (int i = 0; i < NB_TRANSACTIONS; i += 10) {
         snprintf(ligne, sizeof(ligne), "rang;%d;%d;%ld\n", i, t[i].id, t[i].montant);
-        ajouter_ligne(rapport, ligne);
+        ajouter_ligne(&fin_rapport, ligne);
     }
 
     FILE *f = fopen("rapport.txt", "w");

profil_apres.txt

@@ -0,0 +1,224 @@
+Flat profile:
+
+Each sample counts as 0.01 seconds.
+  %   cumulative   self              self     total           
+ time   seconds   seconds    calls  ms/call  ms/call  name    
+ 93.55      0.29     0.29        1   290.00   290.00  meilleure_periode
+  3.23      0.30     0.01        1    10.00    10.00  nb_paires_opposees
+  3.23      0.31     0.01                             comparer_transactions
+  0.00      0.31     0.00   149998     0.00     0.00  alea
+  0.00      0.31     0.00    30000     0.00     0.00  categorie
+  0.00      0.31     0.00    30000     0.00     0.00  rechercher_par_id
+  0.00      0.31     0.00    15066     0.00     0.00  categorie_debit
+  0.00      0.31     0.00    14934     0.00     0.00  categorie_credit
+  0.00      0.31     0.00     6017     0.00     0.00  ajouter_ligne
+  0.00      0.31     0.00        1     0.00     0.00  empreinte
+  0.00      0.31     0.00        1     0.00     0.00  generer_transactions
+  0.00      0.31     0.00        1     0.00     0.00  nb_clients_distincts
+  0.00      0.31     0.00        1     0.00     0.00  nb_facons_rendre
+  0.00      0.31     0.00        1     0.00     0.00  total_par_client
+  0.00      0.31     0.00        1     0.00     0.00  total_par_jour
+  0.00      0.31     0.00        1     0.00     0.00  trier_par_montant
+
+ %         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 3.23% of 0.31 seconds
+
+index % time    self  children    called     name
+                                                 <spontaneous>
+[1]     96.8    0.00    0.30                 main [1]
+                0.29    0.00       1/1           meilleure_periode [2]
+                0.01    0.00       1/1           nb_paires_opposees [3]
+                0.00    0.00   30000/30000       rechercher_par_id [7]
+                0.00    0.00   30000/30000       categorie [6]
+                0.00    0.00    6017/6017        ajouter_ligne [10]
+                0.00    0.00       1/1           generer_transactions [12]
+                0.00    0.00       1/1           nb_clients_distincts [13]
+                0.00    0.00       1/1           total_par_client [15]
+                0.00    0.00       1/1           total_par_jour [16]
+                0.00    0.00       1/1           trier_par_montant [17]
+                0.00    0.00       1/1           nb_facons_rendre [14]
+                0.00    0.00       1/1           empreinte [11]
+-----------------------------------------------
+                0.29    0.00       1/1           main [1]
+[2]     93.5    0.29    0.00       1         meilleure_periode [2]
+-----------------------------------------------
+                0.01    0.00       1/1           main [1]
+[3]      3.2    0.01    0.00       1         nb_paires_opposees [3]
+-----------------------------------------------
+                                                 <spontaneous>
+[4]      3.2    0.01    0.00                 comparer_transactions [4]
+-----------------------------------------------
+                0.00    0.00  149998/149998      generer_transactions [12]
+[5]      0.0    0.00    0.00  149998         alea [5]
+-----------------------------------------------
+                0.00    0.00   30000/30000       main [1]
+[6]      0.0    0.00    0.00   30000         categorie [6]
+                0.00    0.00   15066/15066       categorie_debit [8]
+                0.00    0.00   14934/14934       categorie_credit [9]
+-----------------------------------------------
+                0.00    0.00   30000/30000       main [1]
+[7]      0.0    0.00    0.00   30000         rechercher_par_id [7]
+-----------------------------------------------
+                0.00    0.00   15066/15066       categorie [6]
+[8]      0.0    0.00    0.00   15066         categorie_debit [8]
+-----------------------------------------------
+                0.00    0.00   14934/14934       categorie [6]
+[9]      0.0    0.00    0.00   14934         categorie_credit [9]
+-----------------------------------------------
+                0.00    0.00    6017/6017        main [1]
+[10]     0.0    0.00    0.00    6017         ajouter_ligne [10]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[11]     0.0    0.00    0.00       1         empreinte [11]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[12]     0.0    0.00    0.00       1         generer_transactions [12]
+                0.00    0.00  149998/149998      alea [5]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[13]     0.0    0.00    0.00       1         nb_clients_distincts [13]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[14]     0.0    0.00    0.00       1         nb_facons_rendre [14]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[15]     0.0    0.00    0.00       1         total_par_client [15]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[16]     0.0    0.00    0.00       1         total_par_jour [16]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[17]     0.0    0.00    0.00       1         trier_par_montant [17]
+-----------------------------------------------
+
+ 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
+
+  [10] ajouter_ligne          [11] empreinte               [7] rechercher_par_id
+   [5] alea                   [12] generer_transactions   [15] total_par_client
+   [6] categorie               [2] meilleure_periode      [16] total_par_jour
+   [9] categorie_credit (banque.c) [13] nb_clients_distincts [17] trier_par_montant
+   [8] categorie_debit (banque.c) [14] nb_facons_rendre
+   [4] comparer_transactions (banque.c) [3] nb_paires_opposees

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    
+ 50.25      3.05     3.05        1     3.05     3.05  trier_par_montant
+ 13.18      3.85     0.80    30000     0.00     0.00  rechercher_par_id
+ 12.52      4.61     0.76        1     0.76     0.76  nb_paires_opposees
+  9.06      5.16     0.55        1     0.55     0.55  nb_facons_rendre
+  6.59      5.56     0.40     6017     0.00     0.00  longueur
+  5.11      5.87     0.31        1     0.31     0.31  meilleure_periode
+  1.65      5.97     0.10        1     0.10     0.10  nb_clients_distincts
+  0.99      6.03     0.06        1     0.06     0.06  total_par_jour
+  0.66      6.07     0.04                             _init
+  0.00      6.07     0.00   149998     0.00     0.00  alea
+  0.00      6.07     0.00    30000     0.00     0.00  categorie
+  0.00      6.07     0.00     6017     0.00     0.00  ajouter_ligne
+  0.00      6.07     0.00        1     0.00     0.00  empreinte
+  0.00      6.07     0.00        1     0.00     0.00  generer_transactions
+  0.00      6.07     0.00        1     0.00     0.00  total_par_client
+
+ %         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 0.16% of 6.07 seconds
+
+index % time    self  children    called     name
+                                                 <spontaneous>
+[1]     99.3    0.00    6.03                 main [1]
+                3.05    0.00       1/1           trier_par_montant [2]
+                0.80    0.00   30000/30000       rechercher_par_id [3]
+                0.76    0.00       1/1           nb_paires_opposees [4]
+                0.55    0.00       1/1           nb_facons_rendre [5]
+                0.00    0.40    6017/6017        ajouter_ligne [6]
+                0.31    0.00       1/1           meilleure_periode [8]
+                0.10    0.00       1/1           nb_clients_distincts [9]
+                0.06    0.00       1/1           total_par_jour [10]
+                0.00    0.00   30000/30000       categorie [13]
+                0.00    0.00       1/1           generer_transactions [15]
+                0.00    0.00       1/1           total_par_client [16]
+                0.00    0.00       1/1           empreinte [14]
+-----------------------------------------------
+                3.05    0.00       1/1           main [1]
+[2]     50.2    3.05    0.00       1         trier_par_montant [2]
+-----------------------------------------------
+                0.80    0.00   30000/30000       main [1]
+[3]     13.2    0.80    0.00   30000         rechercher_par_id [3]
+-----------------------------------------------
+                0.76    0.00       1/1           main [1]
+[4]     12.5    0.76    0.00       1         nb_paires_opposees [4]
+-----------------------------------------------
+                             266723738             nb_facons_rendre [5]
+                0.55    0.00       1/1           main [1]
+[5]      9.1    0.55    0.00       1+266723738 nb_facons_rendre [5]
+                             266723738             nb_facons_rendre [5]
+-----------------------------------------------
+                0.00    0.40    6017/6017        main [1]
+[6]      6.6    0.00    0.40    6017         ajouter_ligne [6]
+                0.40    0.00    6017/6017        longueur [7]
+-----------------------------------------------
+                0.40    0.00    6017/6017        ajouter_ligne [6]
+[7]      6.6    0.40    0.00    6017         longueur [7]
+-----------------------------------------------
+                0.31    0.00       1/1           main [1]
+[8]      5.1    0.31    0.00       1         meilleure_periode [8]
+-----------------------------------------------
+                0.10    0.00       1/1           main [1]
+[9]      1.6    0.10    0.00       1         nb_clients_distincts [9]
+-----------------------------------------------
+                0.06    0.00       1/1           main [1]
+[10]     1.0    0.06    0.00       1         total_par_jour [10]
+-----------------------------------------------
+                                                 <spontaneous>
+[11]     0.7    0.04    0.00                 _init [11]
+-----------------------------------------------
+                0.00    0.00  149998/149998      generer_transactions [15]
+[12]     0.0    0.00    0.00  149998         alea [12]
+-----------------------------------------------
+                0.00    0.00   30000/30000       main [1]
+[13]     0.0    0.00    0.00   30000         categorie [13]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[14]     0.0    0.00    0.00       1         empreinte [14]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[15]     0.0    0.00    0.00       1         generer_transactions [15]
+                0.00    0.00  149998/149998      alea [12]
+-----------------------------------------------
+                0.00    0.00       1/1           main [1]
+[16]     0.0    0.00    0.00       1         total_par_client [16]
+-----------------------------------------------
+
+ 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                  [15] generer_transactions    [4] nb_paires_opposees
+   [6] ajouter_ligne           [7] longueur                [3] rechercher_par_id
+  [12] alea                    [8] meilleure_periode      [16] total_par_client
+  [13] categorie               [9] nb_clients_distincts   [10] total_par_jour
+  [14] empreinte               [5] nb_facons_rendre        [2] trier_par_montant