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              <p>Lorsqu'on écrit un algorithme, trois problèmes se posent immédiatement. L'algorithme va-t-il donner une réponse ? C'est la question de la terminaison. Va-t-il donner la bonne réponse ? C'est la validité ou la correction de l'algorithme. Va-t-il donner la réponse en un temps acceptable ? Cela conduit à étudier la complexité de l'algorithme, en gros le nombre d'opérations élémentaires à effectuer en fonction de la taille des données. A travers l'étude détaillée d'exemples simples (Euclide, Fibonacci...), l'article tente de montrer que ces questions peuvent être étudiées de façon théorique, mais aussi expérimentale (mesure de temps de calcul), et que, outre leur intérêt dans le champ de l'informatique, elles motivent des questions qui figurent dans les programmes de mathématiques de lycée (notamment pour la logique ou l'étude des suites).</p>
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