Quiz — 1613454490_89983_Exercice5 _ puissance(algo)_ok.pdf

Question 1 sur 10 20:00

[{"id":34770,"question":"Quel est le nombre minimal d'opérations nécessaires pour calculer a^16 avec l'algorithme naïf ?","option_a":"15","option_b":"16","option_c":"17","option_d":"18","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'algorithme naïf multiplie a par lui-même 16 fois pour obtenir a^16, donc 16 opérations.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"15\", \"b\": \"16\", \"c\": \"17\", \"d\": \"18\"}}","_debug_options_count":4},{"id":34771,"question":"L'exponentiation rapide utilise la décomposition binaire de l'exposant pour réduire le nombre d'opérations.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est exact : l'exponentiation rapide exploite la décomposition binaire de l'exposant pour optimiser les calculs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":34772,"question":"Quel est le résultat de l'exponentiation rapide pour calculer 3^8 ?","option_a":"6561","option_b":"64","option_c":"512","option_d":"243","option_e":"","option_f":"","bonne_reponse":"c","explication":"3^8 = 6561, mais l'exponentiation rapide calcule d'abord 3^2=9, puis 9^2=81, puis 81^2=6561 en 3 étapes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"6561\", \"b\": \"64\", \"c\": \"512\", \"d\": \"243\"}}","_debug_options_count":4},{"id":34773,"question":"L'algorithme naïf est plus efficace que l'exponentiation rapide pour calculer a^2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour a^2, l'algorithme naïf et l'exponentiation rapide effectuent le même nombre d'opérations (1 multiplication).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":34774,"question":"Quel est le temps d'exécution de l'exponentiation rapide en fonction de la taille de l'exposant n ?","option_a":"O(n)","option_b":"O(log n)","option_c":"O(n^2)","option_d":"O(1)","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'exponentiation rapide a une complexité temporelle de O(log n) grâce à la décomposition binaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"O(n)\", \"b\": \"O(log n)\", \"c\": \"O(n^2)\", \"d\": \"O(1)\"}}","_debug_options_count":4},{"id":34775,"question":"Peut-on utiliser l'exponentiation rapide pour calculer a^0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, car a^0 = 1 pour tout a ≠ 0, ce qui est un cas de base simple.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":34776,"question":"Quel est le résultat de l'algorithme naïf pour calculer 2^5 ?","option_a":"10","option_b":"25","option_c":"32","option_d":"16","option_e":"","option_f":"","bonne_reponse":"c","explication":"2^5 = 2 × 2 × 2 × 2 × 2 = 32.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"10\", \"b\": \"25\", \"c\": \"32\", \"d\": \"16\"}}","_debug_options_count":4},{"id":34777,"question":"L'exponentiation rapide nécessite toujours moins d'opérations que l'algorithme naïf.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Non, pour de très petites valeurs de n (comme n=1 ou n=2), les deux méthodes effectuent le même nombre d'opérations.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":34778,"question":"Quel est l'avantage principal de l'exponentiation rapide par rapport à l'algorithme naïf ?","option_a":"Moins de lignes de code","option_b":"Moins de mémoire utilisée","option_c":"Moins d'opérations de multiplication","option_d":"Plus lisible","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'avantage majeur est la réduction du nombre d'opérations de multiplication, surtout pour les grands exposants.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Moins de lignes de code\", \"b\": \"Moins de mémoire utilisée\", \"c\"","_debug_options_count":4},{"id":34779,"question":"Peut-on appliquer l'exponentiation rapide à des exposants négatifs ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Non, car l'exponentiation rapide repose sur des multiplications successives, qui ne sont pas définies pour des exposants négatifs dans ce contexte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]