La Résistance, ou décoder des messages Morse
Valentin PORTAIL - Prép'ISIMA 1 - 2021/2022
Figure 1 : Table rappelant les caractères du code Morse international
Table des matières
1 Enoncé du problème
L'objectif de cet exercice est de déchiffrer des messages codés en Morse, un système de codage des lettres de l'alphabet par des points et des traits. (L'encodage de ces différentes lettres est visible dans la figure ci-dessus.)
Cependant, aucun espace n'a été encodé et un même message peut donc avoir plusieurs significations. Ainsi, la séquence -….–.-. peut correspondre aux mots suivants : BAC, BANN, DUC, DU TETTE…
Le programme devra déterminer le nombre de messages différents qu'il est possible d'obtenir à partir d'une séquence de Morse et d'un dictionnaire donné.
Il prend en argument :
- Une séquence Morse notée L.
- Un entier N correspondant au nombre de mots du dictionnaire.
- Les différents mots du dictionnaire de longueur maximale M et n'apparaissant qu'une seule fois dans le dictionnaire.
Il doit renvoyer un entier R correspondant au nombre de messages qu'il est possible de générer.
2 Méthode de résolution
2.1 Stocker les données
La séquence Morse est stockée dans une chaîne de caractères L et le nombre de mots dans un entier N.
On stockera dans un tableau de chaînes de caractères morse l'encodage en Morse des différentes lettres de l'alphabet dans l'ordre (A, B, C, …, Y, Z).
Les mots du dictionnaire seront, dans un premier temps, stockés dans une chaîne de caractères word, puis encodés en Morse grâce au tableau morse. On les stockera ensuite dans un tableau de chaînes de caractères que l'on appellera words.
Cela permet de gagner du temps lors de l'exécution de la fonction.
On crée également une variable R qui contiendra le nombre de messages possibles.
2.2 Analyser la séquence Morse
On va parcourir la séquence Morse et compter le nombre de messages possibles en utilisant les techniques de récursivité et de mémoïsation.
On utilisera une fonction messages qui prend en argument :
- Une chaîne de caractères txt qui pointera vers la séquence en Morse.
- Un entier debut qui indiquera l'endroit à partir duquel il faudra commencer l'analyse de txt.
- Un tableau d'entiers memo qui contiendra les résultats des différents appels de fonction.
- Un tableau de chaînes de caractères dico qui contiendra les mots du dictionnaire encodés en Morse.
- Un entier size_dico qui contiendra la taille du dictionnaire.
…et qui renvoie le nombre de messages possibles pour la séquence txt entre debut et le dernier caractère de txt (d'indice longueur(txt)-1).
En entrant dans la fonction, trois cas sont possibles.
- Si l'indice debut est égal à la longueur de txt (indice invalide), cela signifie que nous avons atteint la fin du texte et que le mot précédent rentre parfaitement. (Il ne dépasse pas de la chaîne.) On renvoie 1. (Il est peu probable que l'on tombe sur ce cas en dehors d'un appel récursif.)
- Si la valeur memo[debut] est différente de -1, cela signifie que nous avons déjà traité ce cas précédemment. On renvoie la valeur de memo[debut] (C'est là que s'applique le principe de mémoïsation.)
- Sinon, on analyse la séquence.
Pour analyser la séquence, on commence par créer une variable nb_messages initialisée à 0.
Pour chaque mot dico[i] du dictionnaire encodé en Morse, on compare le résultat avec le début de la séquence. Si les deux sont identiques, on appelle la fonction messages avec l'argument debut égal à debut + longueur(dico[i]). (C'est là que s'applique le principe de récursivité.) On ajoute le résultat de cet appel à nb_messages.
Dans le programme principal, on crée le tableau memo_messages qui contiendra les résultats des appels de la fonction messages.
On appelle ensuite la fonction messages avec l'argument debut à 0 et avec les différents arguments associés à des variables adéquates. On stocke le résultat dans la variable R, puis on l'affiche.
3 Implémentation en C
3.1 Description pas à pas
On commence par définir les variables L (la séquence Morse), N (le nombre de mots du dictionnaire), morse (l'encodage en Morse des lettres de l'alphabet dans l'ordre), word (un mot du dictionnaire non-encodé), words (les mots du dictionnaire encodés en Morse), et R (le résultat final). Elles correspondant aux entrées et aux sorties du programme. Les variables en entrée seront complétées par CodinGame, puis traitées si nécessaire (notamment pour words).
On définit aussi deux variables i et j qui nous serviront de compteurs pour les boucles for.
Remarque : Afin d'éviter les débordements de mémoire, R pouvant être compris entre 0 et 263, il faut utiliser le type long long int et non int.
Remarque : Chaque mot du dictionnaire fait au maximum 20 caractères. Comme les lettres encodées en Morse ont une taille d'au plus 4 caractères, il faut donc prévoir 80 caractères pour stocker un mot du dictionnaire encodé en Morse.
int i, j; char * L = malloc(100001 * sizeof(char)); scanf("%s", L); int N; scanf("%d", &N); char * morse[26] = {".-", "-...", "-.-.", "-..", ".", "..-.", "--.", "....", "..", ".---", "-.-", ".-..", "--", "-.", "---", ".--.", "--.-", ".-.", "...", "-", "..-", "...-", ".--", "-..-", "-.--", "--.."}; char word[21]; char ** words = (char **) malloc(N * sizeof(char *)); for (i = 0; i < N; i++) { scanf("%s", word); words[i] = (char *) malloc(80 * sizeof(char)); strcpy(words[i], ""); for (j = 0; j < strlen(word); ++j) { strcat(words[i], morse[word[j] - 'A']); } } long long int R;
On définit ensuite la fonction messages qui est l’élément central du programme. Elle prend en argument une séquence en Morse txt, un indice de départ debut, un tableau memo pour la mémoïsation, un dictionnaire encodé en Morse dico et la taille de ce dictionnaire size_dico. Elle renverra le nombre de messages possibles.
long long int messages(char * txt, int debut, long long int * memo, char ** dico, int size_dico) { long long int nb_messages; long long int nb_messages_suiv; int i; int len_w_morse; if (debut == strlen(txt)) { nb_messages = 1; } else if (memo[debut] != -1) { nb_messages = memo[debut]; } else { nb_messages = 0; for (i = 0; i < size_dico; ++i) { len_w_morse = strlen(dico[i]); if ((!strncmp(&txt[debut], dico[i], len_w_morse)) && (debut + len_w_morse <= strlen(txt))) { nb_messages_suiv = messages(txt, debut + len_w_morse, memo, dico, size_dico); nb_messages += nb_messages_suiv; } } memo[debut] = nb_messages; } return nb_messages; }
On définit ensuite un tableau d'entiers memo_messages qui contiendra les résultats des appels successifs de la fonction messages. Toutes les valeurs du tableau sont initialisées à -1, une valeur impossible à obtenir lors d'une utilisation normale de la fonction messages. Ce tableau est nécessaire pour pouvoir utiliser la fonction.
long long int * memo_messages = (long long int *) malloc(strlen(L) * sizeof(long long int)); for (i = 0; i < strlen(L); ++i) { memo_messages[i] = -1; // Valeur impossible }
Enfin, on calcule le nombre de messages possibles grâce à la fonction messages, on le stocke dans la variable R, on libère la mémoire utilisée par les variables, puis on affiche enfin la valeur contenue dans R.
R = messages(L, 0, memo_messages, words, N); for (i = 0; i < N; ++i) { free(words[i]); } free(words); free(memo_messages); printf("%lli\n", R);
3.2 Code complet
#include <stdio.h> #include <stdlib.h> #include <string.h> long long int messages(char * txt, int debut, long long int * memo, char ** dico, int size_dico) { long long int nb_messages; long long int nb_messages_suiv; int i; int len_w_morse; if (debut == strlen(txt)) { nb_messages = 1; } else if (memo[debut] != -1) { nb_messages = memo[debut]; } else { nb_messages = 0; for (i = 0; i < size_dico; ++i) { len_w_morse = strlen(dico[i]); if ((!strncmp(&txt[debut], dico[i], len_w_morse)) && (debut + len_w_morse <= strlen(txt))) { nb_messages_suiv = messages(txt, debut + len_w_morse, memo, dico, size_dico); nb_messages += nb_messages_suiv; } } memo[debut] = nb_messages; } return nb_messages; } int main () { int i, j; char * L = malloc(100001 * sizeof(char)); scanf("%s", L); int N; scanf("%d", &N); char * morse[26] = {".-", "-...", "-.-.", "-..", ".", "..-.", "--.", "....", "..", ".---", "-.-", ".-..", "--", "-.", "---", ".--.", "--.-", ".-.", "...", "-", "..-", "...-", ".--", "-..-", "-.--", "--.."}; char word[21]; char ** words = (char **) malloc(N * sizeof(char *)); for (i = 0; i < N; i++) { scanf("%s", word); words[i] = (char *) malloc(80 * sizeof(char)); strcpy(words[i], ""); for (j = 0; j < strlen(word); ++j) { strcat(words[i], morse[word[j] - 'A']); } } long long int R; long long int * memo_messages = (long long int *) malloc(strlen(L) * sizeof(long long int)); for (i = 0; i < strlen(L); ++i) { memo_messages[i] = -1; // Valeur impossible } R = messages(L, 0, memo_messages, words, N); for (i = 0; i < N; ++i) { free(words[i]); } free(words); free(memo_messages); printf("%lli\n", R); return 0; }
4 Tests
4.1 Test 1
Entrée :
-.- 6 A B C HELLO K WORLD
Sortie attendue :
1
Test réussi
4.2 Test 2
Entrée :
–.--–—.. 5 GOD GOOD MORNING G HELLO
Sortie attendue :
1
Test réussi
4.3 Test 3
Entrée :
……-…-..—.–—.-..-..-.. 5 HELL HELLO OWORLD WORLD TEST
Sortie attendue :
2
Test réussi
4.4 Test 4
Entrée :
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SOVNI YWZNRG MENBP VXNMR YYNUI XBYLR UKIJN KXFJT LFXCV HRASESC OXGFXW VZYIYL GEBSY EMORSEESTCO UTFHO VLSOC UEKWS YWVIC MAYXO JLAMA KQVPV CWNDQ VERSUNCB EXTELAIDE HXKCL MSMPC YRZFG KMAJF JYMSI UAFJD OOIWD IBOJVV WHTZI KUTWID GBVEG CJAUG BBUBN PNQXE ZDLWZR IHNNR FKUIQ ETQGI RNZAT AKVQL CZOSY TGABV KYZJR CWZIA PZUDL KIZHN VUBMC EZANX NEWNX CZSBW AQHZZV XVSDR SIIMK QTXZS VRGWI JDBOUQ CRXWU SUGWE AJMUU DEONTE BPEHQ KNYIC NTERMITTENT XSOWK OISLK RSLFG PUZSG OFPPC UKIQY YOOZX HLJLQ WHBWB DIAMQ CZCJO WDBWBD JPYVE JKJRRZ XDCZY GJOAG OYVLZ AOKODF BOXTU AUFJM XIUME AFBOE QTFSL LZCGA YXITB IHNSJ ZHLPH JTXDT PZPGH ACVYS AYQPR YLNRB AINESETLE UWKPA TOQCK OUUNGESTEC ZDIHY SMLTQ OYFPW UYMVO BUIVR LSGLT AMRDZ JPEZI BVFOI REYXPI DDOEK XTKYM ZIQTA UDBBW VSEVMP WFAKU VKDAX LYHPI WVFDS TTXJL
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4.5 Test 5
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-.-..—.-..—.-..– 5 CAT KIM TEXT TREM CEM
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4.6 Test 6
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………………………………………. 2 E I
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5 Description d'une autre solution
Cette solution a été proposée sur CodinGame par l'utilisateur "0006-IVH" :
#include <stdlib.h> #include <stdio.h> #include <string.h> #define MAX_LEN 20 #define MAX_LINE 100000 /* Implementation of the solution: -Create a binary tree to store words(not balanced), "."-> go left, "-" -> go right, storing 0 values in intermediates nodes, adding 1 to final leaf nodes (correspond to a word) nodes not explored are null terminated (can be improved) -Use dynamic programming to solve the problem: -store nb of combinations and pointers to node in the tree for each subline L[0..i-1], i; [0, n] -use the recurrence relation to find the nb of combinations for line L[0..i] */ typedef struct s_node { // loose structure to store the words int nb; struct s_node *left; struct s_node *right; } t_node; t_node *create_node(void) { //create and malloc a node t_node *res; res = (t_node *)malloc(sizeof(t_node)); res->nb = 0; res->left = NULL; res->right = NULL; return res; } t_node *append_node(t_node *root, char c) { //append a node if it doesnt exist, return the child if it already exists t_node *to_append; if (c == '.') { if (root->left == NULL) { to_append = create_node(); root->left = to_append; } else to_append = root->left; } else { if (root->right == NULL) { to_append = create_node(); root->right = to_append; } else to_append = root->right; } return to_append; } t_node *find_next(char c, t_node *node) { //find the next node in the tree structure given '.' or '-' if (node == NULL) return NULL; if (c == '.') return node->left; return node->right; } unsigned long long int find_combinations(t_node *root, char *L) { unsigned long long int values[MAX_LINE]; // nb of combinations for slices of lines L[0..i] i <= n t_node **nodes = (t_node **)malloc(sizeof(t_node *)*MAX_LINE); // stored pointers for words in the tree for (int i; i < MAX_LINE; i++) { nodes[i] = root; values[i] = 0; } int i = 0; char c; unsigned long long int res; while ((c = L[i]) != '\0') { nodes[0] = find_next(c, nodes[0]); // find next node and update it in the pointers array if (nodes[0] != NULL) res = (nodes[0])->nb; // initialise result with nb of possible words of size i else res = 0; for (int j = 1; j <= i; j++) { nodes[j] = find_next(c, nodes[j]); // update the pointer in the tree if (nodes[j] != NULL) res += ((nodes[j])->nb * values[j -1]); // recurrence relation } values[i] = res; // store the nb of combinations for subproblem i i++; } return values[i - 1]; // return the nb of combinations for i = line.size() } int main() { char *dict[] = {".-", "-...", "-.-.", "-..", ".", "..-.", "--.", "....", "..", ".---", "-.-", ".-..", "--", "-.", "---", ".--.","--.-", ".-.", "...", "-", "..-", "...-", ".--", "-..-", "-.--", "--.."}; t_node *root = create_node(); // root of the tree char L[MAX_LINE + 1]; scanf("%s", L); int N; int idx; scanf("%d", &N); t_node *current; for (int i = 0; i < N; i++) { // place each word in the tree structure char W[21]; scanf("%s", W); current = root; int j = 0; while (W[j] != '\0') { int k = 0; idx = W[j] -'A'; // find the index of the letter in dict to have its morse code while (dict[idx][k] != '\0') { current = append_node(current, dict[idx][k]); k++; } j++; } current->nb += 1; //add 1 to the node to show that the word exists } printf("%llu", find_combinations(root, L)); // find total number of combinations return 0; }
Cette solution a un fonctionnement assez différent de la mienne. En effet, elle utilise un arbre binaire pour stocker les mots du dictionnaire :
- Lorsqu'on trouve un point, on va à gauche et lorsqu'on trouve un trait, on va à droite
- Un nœud correspondant à la fin d'un mot prend la valeur 1 alors que les autres prennent la valeur 0.
Ainsi, au lieu de comparer chaque entrée du dictionnaire avec la séquence, on parcourt la séquence et on regarde si on tombe sur un mot du dictionnaire.
Le reste du programme est similaire et utilise la récursivité et la mémoïsation pour trouver le nombre de messages possibles.
Ainsi, cette solution est plus efficace que la mienne. En effet, rien qu'en parcourant la séquence Morse, on peut savoir s'il s'agit d'un mot du dictionnaire ou non.
En revanche, cette solution est plus difficile à comprendre sans lire les commentaires et est plus longue.
6 Conclusion
Lors de cet exercice, j'ai pu :
- affronter mon premier exercice de difficulté "Très difficile" sur CodinGame.
- manier les tableaux de chaînes de caractères (tableaux de caractères en 2 dimensions).
- corriger et optimiser mon programme afin de limiter les erreurs d'exécution et de réduire le temps d'exécution.