Dynamische Programmierung
Einsatz von dynamischer Programmierung
Wann ist es sinnvoll, dynamische Programmierung einzusetzen?
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Minimale Anzahl an Münzen
Gegeben sei ein Betrag n und eine Liste von Münzen coins. Implementieren Sie eine naive rekursive Funktion minCoins(n: int, coins: list[int]) -> int, die die minimale Anzahl an Münzen zurückgibt, die benötigt wird, um den Betrag n zu erreichen.
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
Minimale Anzahl an Münzen mit dynamischer Programmierung
Stellen Sie die Funktion minCoins(n: int, coins: list[int]) -> int so um, dass sie dynamische Programmierung einsetzt.
MTAwMDAw:ZHvmMn2/Ihfhwd2hajtcT6WOdK87OqhCYYfAUr0WiMw=:R6NSBIt/fzNoMhrV:4k3VnYKjZXtYWtoCDoEx6Rf1zo0JOHFPvo6Wlp5+iRewUuD3ZjURqoTrdHY2rFtxnrKisWObLVLZjgnV+1NmZxg1JkJfSQjf/a2wft1WvU9ZiRPpmCZhKCBCrQudvMJwGO8AqYTCcLeEf1GUXKh/qJvDkxEU+KyHak4V+ZjqDGs9IqzaWrfifLvDH0ekKGe3sHqX6sFh9tMlxlB5Ne5PApVQDIlelp05128uhP2D+rCtwmcLqA8DhfhTZoemeqch5HVnSpaDr7WC4k7dPiILh4P0S7P1U9BPuNvuIDYTW8HTEc5SkQS52XcTcFUj3A+GwU+KX66WDAo9nTMLw/AClaiAL1hKOm59l8Ax2SKNy2k8EsHFlhiR1/wINhTfn/ghelM3jcAPhnEj7WikY2h6BLsT6xeMABh0jqHma5p1MW16JPnokuEoOs2QjpozuWN8DeJ0vOSWWaXaRZ/Gt/KSOXOUAjZtBW1Lj2U3KbH2kiDPuji8p/wN9wd86qFmfEDL3J+AJKkTQZY5qc2s0dKzfPLqQ3TbvvmwRROiskUtL11P/1jrOvMsgpEmxtUPQmXrQsJrtSjFyjknRVN/3yfPfo4M1ODoQgEG4v/CEhWh3BjgMtp7bC15RE06Jjn1wAnUH0hPkACXAk5cWJnMhhKON+H67X4ZfvRhFm0jxDMM8CfTkl7FKw/1+lYYkPSxHaGMMCxCFlp9WqqKHsJ5wExqSAhB6ESNm32qGnp+jS1KXyw6jzhrKlaAXLVCLMHtMQNqadx/qHJn7tlfW0qFxi+zYzakThECsF2Ufgo2E85zQ8Ve6T+DcOdn9Q1f51ztPCnW3E+8JcwYrAaYyRlldmPXGdaj3m2ZA4A1Rf1Maz8vvLNpdPBR1c3MiZv7ZvVAPCT8xwrSdrXF+hG9qeJntPuKtcBX3/JTU+KjDO/DShtA5awilZoAGWvtkEjYVOgiy3qBiEP93N88UbTiSvkovw+joS2xuf93KlpI2hSZ8YDR1qqyZTR9tM4z415PEdpWL32o+8GxVRnF6ucOO6O8UvI9xY7p5PDfd3wKuf4q21cBEATuhmOEpaJrVRrUzCDcugNwei0ecyH67w8qZYXSfsBbiXc8ay5lKYb5L1bjBChjrFPjB0BH78Iebaky6Wca6zg4VIDeCPup04N6WWPQhC2RaM6D3yKS8hVA85K4Xzqx74qOAWXAVBec9qGtyC06GqMZEaXSWswGdZd6rqiSxgMGoTo+3r15MZ+nZkQp4E4OPZAxHeg3L7MzCPG3DkbYQRrck22Fcm3VveHYT+y+ejUYYhEVbIIfAADRVGUDyhLTNkBla+sJLPU7D+agJbDrXas/ONIkCpwZvuX9HlKvFX1IHKxhMndm9ppVCFQaKCmrIAr11bmjWyI8q7UFGdZXR+ZASWWk4IGXXwV90zTaUu0gqxZ+521/BjFmSmZ9zu2y3OrsNoWwAfBPVGEOi44dJS8fmctAt/KbwQu55L4kZOI4maaQfGbdnDrG0bmod8CPU+OxUVeLW1neDj2uiCrNUBkBs9IBFXEDOzmvdSURT2Lf51MSbmXehSjNHjgYbGCez96Jp2bvXuRN4NN/mwuEEEuFYKgyDiGbe7QvCrL6A80qnrKFVVDT+0k+MeVpDT8xqV7QLi4wZ60IGbuS15eUHKp+Z98y2sojoTzlQ+kZrQn7lF9z4oRApIa5O+yS9aqg4mR4Wfthcr9OhQvVDzEEsox+snzTDVEMk9V1b7MrI+fDP8FzmoTMY6rrTRANwOFtOlgBLY4jiBTjBLPCP/upB4GB3HDM7GcWYWQjJDTu8BfSz0nkJ7SzIcgvDHwV6b4UZm3swOW5g0js1aff1TZxMsNAD7ikPY3zCqUo9fucweyiXs/aZLIbX3wgBOgzSr39eg51htnHZEsepgZvEMC9N6OQg2+erRyPXJjZN1dGM3167Dpptek84aTCu4Gb8fFe3BTGW+b5k6NOomAi3jialvxZuKqbQkq7UTHGhRET4TTEv9+l425qNxNtm6ki30L1pt/tA88gjg/4oNTRuYGsNAbTqpThsptehPJGm1Ml4Nxj76j9FqdEi1egYD0KS4FjYMGWoh2V2odXg0lk8JT+54FFWbcclF3IAEwYPsjHjs0I429IE/nXPJonDuMOrbWpt8yZ04sfHvPtF1r/Y2PbWfjR3TRcxXNqp5Z/Lx984qUXKL+gBtzlVEKal1nhZTTGATw6frRPoYpP+UEfEMXy4+JoDnVh3nERrPEbPE8Z36IhWa0RK1H3q6K6AOz7LPuz7hvG6Mg//e7PqeTB0Vo5KLV2qsQAG1zobi++NUxFXP2dHbFhEGfoebkk2U5fJNR53gijUGDh5Wv6v7fmp9xxPWyEZDrQb8AwlYxVCxw+DgDnzG/3HUvnE27JgXoxM6nj4IDEXdx+8h3wqD9AN4yVESp5GbSkyYUlndAigiAUFLFMwJ/mtw27i3bF9DBWR+7v6NblTf2ZkSGzr5HS25NNBS9u59y3+5TOJy2PP2kS1wd0urU9HSP3dxZ4MF5/PWJKYZqITNIm7xA/7Wjdtk7X4RHF7mcbDeZif55c5FPVWvCYwQ+KR2NC6FjH6ti37H115hNPHmTNWTne2vd+A7cTGijiRTdYfSEy7x3oppxuQCXjbqzZDcBmSL4mB7NvIqSi03A7ILMrH5/0nQOP9QEzdvK9qJcklqJ5EMNyP65hojki8HaruiIcTkw2ZfnZE970AZkCgfNR0/HuN/w9aUod0FGhFLB2kvqbA/SLib9EjKfopKhKARtvA5DNfdDT3f0yVTJXS1Bu31snU8w4cbWITyZDO1ULOyIN0ABoTxDHYSRL/Wq25QH0gQSvT0WWbn4ZuY/KjI5oHU0wot1IxVEn9b+JgKgDEd81wIsolQXCk/3dgbItjYUyhrbbhii//VfKD9eDIVLxBxM1Db98ryvzx67lyd9sVVVmapJ5lKERdHNI0qcJNE+fh75meBs89oL7niJYVLvOgBdekSnudylG6Ah2XVFdgoGwCY0Ln2osM7wpW8WL5155J9XAYBwSoWKLHROpF4P5prSgEYc03Ff87WsNq8aRorGG82EwnUjNn7jVZzgTMDfJ5lmcvosUOWhQK11cZSuQB6BfHbyiWUPBUZknEdqCw/05JHuq2xHLxcZ1zsFkREy8LqKln7c2jwO2t5CQHkDiHiCFwE9GwT8WFmUNkxu1sYn3EDvvOCUSeSVzCYo3dEboOpZCDkf/hz7sx0un+ftmgPHQWkZoZ0IVWxfLIQbaiOR604WgTHZfl3sDj97nZsYnSo1pxC2D186Hq6ZOTIrQCbBYjnPFSv4TLIsduCbZAm0OoC8FFNzTW3+oTypsy+x5L0OFEs+EbfWGJPaJAIiD/lp+Pi9HK2fRmmLueTpsJwROLQ0XYCokdtkPWWPZDUz5/l06fI6SITey2xS0+/xdzA2VcKY6qG/mnW/WCynZzrNs4rpLev44gJjPvd6hveU8XlE1a/CF5JiO5Kb6W394DkpIPdFNKCALgJ/Dq+N8UpX0suzhXdT0/wJhymoBYbPoU9ZJetVq1ThNK3gaOM/XfJA1HH5is1qJXfTvGWaH3cTk3ThetqQUcx8ybXajbgSbcMN1BPBs3S6qBGOAnwMlQPrFXmeBem/igYakNkm6JtOIWOkAmBQh8QcRWDYbWhbwz0w9paVCr7Dn3GgDkWiqboIc9EVc8WOFgEmISIYdEeIyiiMfN9BkSvuEIBmaQBXU5nCceIuCNRVLvalrDu1VbYHUEINuE88wSH0gcRm9HRhD+q0rZwfiEyU5xTRKYsFbi8+g99ZpSzLHR6hXlDentGS47Wqpwa9k7Gf724PHZFx/s+f9GpHIbJJ2hj8vhKQgvlpXrXy0pf+Rd0MzqoKhldW1Yfr8WZTVdiOR7lf5R+qMG2Hqea71sB4U/APm1L0OKKPFEB5vujwSuYMVixM2VsxOKaVCkZzeanduyEKWDLatCA3Y2eJ3YiJxGzQvFM8CeZe5Dx+iSZvV7h1QOmV3Yrdviu3I7FOcuU71nriLCuHyQn9n/U5iztyzzVtMOTkBgQNWjGy+rfmO7VUQRvc62xjtxsZCFP+euOfp+rcfy9dkGciBUkjtW61VyJ00hUohBuec8odlH91e8Okjw6UBEeqmiEYwgwGCQdmYB+PNmqKfyKAdf2wjuCdAQsLgDtWEZL6g+nwa/kLQJnWegNXvVRVtgdx8O1JNdKuGDVrdjagdcnlOdNyaoaW8pRwC7Qmm1kwvubnxkRVk3Z3NuPAIewdug4uB/Gb48JgYNQv9XE8/bUJzWQD75/yWwZwfeHoK3fDFPFq+1TwbK9KJAQu0EcmRs07GLgsNS0OnnBiwmWjKdUIc7Gp1F6PMCqdl+IDW0LQJ/gIpED5GCDDul9ZBrRKVgDsI/z9o5v/Veeb+/2bA650g31jQXlI/7gtIY2g65iskmJagxtQJWKO5CPluXskB2+VIoSbqFgCF5Ldgjri2KdwSxFOjT0Js+wL+bsP0dLn/r8tLM3xZ6PaRd1yA//bZT1IJ1KtR5krog1HxbXUfbrr7tA7ljnGi8zhOAomEFlBLzILikwfO013GBUMbIBWUZ3d2hrw9IUwy4a0cAlmaTiW3oQnTr9v/mpIXhee1yp2qa5ghIrdTMYoh+1xQKMN2ojPp9WHIdjHadVopt+X51PahVAQlkor40Nm4qKjk5fIm1NsBq8NM2bblLtQSndaQWjNam0fvq4OgPoz9ogY7Txpj+TEXzjU2hpFUjrkUgu5B+EVxzK6i/rPhCtZYadt9w5FElpOEUZNHortzNAymRU0Txhld3qe60UNa/JStUDX3UyWUDV+4UssL8qremkb9HhU9e6/V3GLkLP6ydZ/0RAlvEbAG/XPU0PTtsJcdNxZOF8f8F918Rmy8qPcYuInjuIz+4AGHWfM+0WAAf2AGakySnEDz8ZDjw6eh3sIWwCDRhPWayBlUDW7tUoawWJCVdaXI6cHjbl2iX6zBwyopAtDcgc7btAL29v2Mh/p5/9OGce7wwDxLG5eRdmnqC56ssg2mV5WS0Kb91KVL9veFpglzNe0Ji0h0c2UrD2PsZsEgeTgth8QvmHYvrgo6O8/+MtWE4LKe3LTi62UBjmmEaAqdv2it+gKguBrrRx6/Y6wPz28VQBMmis+x7smPAwOVnBSZoEippKd+nLk948r2BeX80UTOSstZMI5yeV/CBgP6KKHPyFXacCQeuY6+LfZ747wRmfJWPs2WUFwboVZDY535nJxyBezaS3dY7CPh0KXuE23ReDCJNsmNgLNzTX9CF0uIfNxzo44HWDxE5T3LDvxiHTyzRjYPCvzmNAeYZzV3HBJvR8QLqqFnpCehNQrZ+fio1ZMKrhBsfHqTKskDEYTRW7Kr+g2eHA900u2adHYf2zK8COW2LCwsXouRSTyMYf51njV2ulXONuWt/3mQTxgCxkHBMIzPSoM2H6ZREXDX2bXmRCqUyr6DR3MOuzfR+SLHaqSm4Le8r+AVkuJdgnAOlYam8t/xazprDXSgf8k3pNnVm/6r5P6AAp+7eOm83VAKib6xTycFcwt2U0UVXHx7y2Rj0fn8RfytEER9CsBCHVeSx5TsWxcCO5qb/dFlIXJVxzwRUlnhhUfxtNmMVdkk//aVebtvIztWkk82SHU86IEw/yoC6shEFSAbqK4Z0uRv3P5DRWSA+DC7VN6KBulErgQp3vJHjyEuZu6elULA2hBPMSxhTsS1ih+vR/pDHPd4kKj6M7GJMf72r12FCzSVrOcOUcIbK97SQDVE851wLPupEsFVti8dbNY86Dc8wOScez6Cz2gIhpFb9jlj6qqo8qUUoz5EqAEQnCXScKIklwonVQ1MwqUENPa5FDmx4zpiM65jyr6ADUBsIdOucbhnK2wiZVB2TwDu7qALuO8AJeE+ldzg3gFTGYKMZPPKHhVIUtOA7sQkC3DtA667nOqTh96tbs0G7x26R2TNdrrm+vQevqaG2Kg33o6xZDbvRmlqUPh7GqyVlvP8dgjLtlibds8DP10OU57Z6i4mz35xVUEA8XvMlAfFpfAPJdItU6XBRSOAcSf7Xm39HLBJVkKaOnDsqDv/+VExWQocCUzymyayS9/Fpj7E69Jfo8Kw0NMiBhjbYgOab5v1LOSbQHlG3KBb/c3Oi+rt6/TcIOCY5u0VRiw9LTAfV7OcW3JBWAjJv4cixOR6pA9RBZs0OvvHah2eSTwY5Z/RAZDaKB81rAKFKMbXRxHnmlA7T8XFUN0GVin7BviOE2NXCcNlvwQH+RzfzGL+9wtSdtBY8EjQmWnFnRVeSaj6fkStHZtMaPOdDV82yGVnrCCtbClPzeo/RTAXHVM+kvBsnn0/yG8B6mQORCGZcj2fa0sUJtobtx2pmtKwobtTHMAP1PXMxZ31uYBullf+EOF8s7ODpB9X49Mv+8xO4EfRXQIyl8zp2rapz8q2bBkHIc+2OhiMY9Lt99vktDrsbeuPX3NOGu0yxw1VkMeIODxEMkPURxuEqIGvpkvDri+IxQfzA4lXMvIZ31Y18vnQpmD/kNWM1jhT2K90nuYePyX+MXdcEXgD9E9ArHF0Dvg2whRTJle9s02KdDA3ZFMQRtrzQhDoLavghajWnzAfumApTj1PTkPFN0/KfPGzvOhMM6qB9qwec0Q7vNwhe5Ke435ZJv6Y1bigjy0o31c2IDjMuHITSQKkHj+1GnhoIVXZyV1jglWWmGS7PIDWr9JaIEEPem3KEAMh9rkC+ZflTwkRf91bJUscJDIrP3J/YlNH8mqyY9fngTVy0VSI2nmLddT5x4SjQ72YbXhHRINotAqeCRYSt4OqTlxeI0tupXMq6nwJOyZFKhYhsQnO0H5zOpvZalbTrJOJ51ppnCKk07ki4+ck93bi3RZhMufJQARDVrNl5oEuZ6XoHrNPi6KL7RJmDKLIhVm0X0QKqhfAhwzG3sq8OkT4jHiJn9ry5Ue5M+r7nHi+pT3AsWkLzin93w1AEBc/zvYSmTt4Uk9tuIODYpT9+Z+vjMtVuGi61tPWHGiurPoGsoOBBW+tW5P+QlLg69jYoUeODfwRwO7CDozrPXhK5Zo006bClaH05lvcS+ilNu8d/ZFWyNhsoTYPQXswyy4d/aWwJ5XwFqA7ZB1KeIIS7jM30OzSEb+jdTfJRvloVPF14lBkpBk+SDc7tjFTmiWwwBDL2VJDzyL88DEGXel+Lfc2ZTMZmSb5f00HwJ0iutbSfQB6cgCzpBAjPAC+B+7K7bgfJh3rbdE5RFCyjspPdItKxB4JCJ/OpxAwXKd7wuiPffTjuplEmjKv2YS/ZWMTrV0HF3mzPa2xF7xOzpuP/ZG3mBJ2vF0VUf2Qg3iVMUG+q0PpvBLy5KYCOaSo4YAQ8IA6bRZ91qrlIBynoCggQgv996K7eQ1AcdiIugcb9JFlj+MVnKAzPJO8Jp83Jo0/NGMPzHQnUgvtrpd9f0OTnVVnmMruRyAA2+6IAPzbbQqEmrgCmChcHxv2TXfAQbQdTzl/EVE/9IlazZ6Igl8McMpOMku4HVkHnHFWQiT05jq/btiwejh2M7z2sDij4DHDwtpJH+hn+mkgfQlK2vOrTo1HlGmSNCFsHn6zEBoe+C7X2uoBuCdVnYsR1SiYBEeb2aNcJUu3cAE0hq0GNyJ6qBC4uRXgBDtZvb2cuWR/z8va2Y9tBNEJbtJHd3xM5/kFLftheP7LHLHti6JMh0AJ6POXLyEBybZKQlGgeD7LMpq84KvIA9t4msI5utDBPWx5ryF/Dps9qZkQz2ZbZg5IRHxeMDmCye9azOVOgKpSLYcK4cm3p3ucpmYvgwPya5XexE3xJXvfFSDKKrIrs2oCBoitckP9Ifan7sU3kBT60/1TFOi5Sm6YfgQhUFWOPCXyAmIWXQlNiAiJ0VjFJu59o7YyfVJSYlu/P01twNFr/WAxIXknBcM6c62GUCQ0p/AkQEq0ygrbRlfI4e/s0vteJkDqGrHHDxGtJSS/x3hn62Ye3NzZ7f/oseCmanKvsdEH0dNWq+GduwEDmDS49trra0I+Io1V9po7AjJIStZINIhEZszhow2iIeMWv10ZEFlHMxphjZR5T8BOr12nOEI2oyh7sJ8UWVlbAfBbAIGEMrt/DiDDQRyIBxXswfQ47FUSZTc/s0uF1Iz7wRKSyyhTM4KkL7Bag0Ks/q5SWs1bRUripSXJHFFp8y+7O/l1W891SXX3lij8ZQNaU+0bmpvsicAa8BiHm7N/zCRjCTBdIfyO8VmzVSjz4gVAj6pvRLih9dI9rzvFuPeDSG/vCpGdKpONZ+3t6o7pQc49IsdKUkyPJsjEdYD6g6ezJQsztmALLkfQa6IYB3UeRVLDXaw1vqACD/rElFszdIZgI37p/xra92cIgCswYx/a7ck3CVR20W8W8ODlKMymm98e8VakdsXdmCTe8KIQKsDm3+6R6d7IGNPFaqTh7suOJy7Q/Go7+B/QJBOPwG4PbDceh8gidUub4n7V74x1a9KeLWN4TZgNPJrAgmXoijk+dzx0eG8jsHc08xIaH20XCUy30cT0xR5n4kpGe4m0CgeCauG+xNzNG79sstS587Mv+UiD4ZnEja4x/lF/6W1rVovKSie7fFnkU2qJKB155djB4uJy5vyNj2QKFKF4uDeFoaP5gMv+4AZ4ZrUdORIU0UK7PJj0Th1zq8BpAxjoxqeUblxoNTsq2oPPmI2XgYt3A3wLPOl9+0PMqGOpU/DnyaveCrj2R7pq3NnNWrThKwbFc5RupCknlc6+WvLa32WKXm0qF/NxZpRLx+7iUQei3CLEPQK5LHHXb3brSfi/wmVBiMd7z7RQvPBuVkfi7frK6Ox33MlCU7WhOesGTB0WR7WNbuKjEvylYPEcA531+XzN8MxFB/zySqTYnGcd8zyCstzrq64z0PSeo9km/hW0ZzNKD82S1CB4C6Mv9f8zpCutrxbdrdN5gOCR8E1O6fGDkId4sH94HyNJ5y33kWvxQIvGLLalMdC9fxYlKaVhoQY7d4+SpbKZk3O4ZXAFh1PnZyrbBQBXiIy47WMydnYwZUe1S3KND7Pz75UK/QqVskFZaACbpMpJoiWzgR97MG3LFHyEfsfaXOIcR/vMCqgyPZT5SEma+HN2YiEk8GZuKdaDcm5WxlBU66dT0edKpl/Zpi1CN78fKqNuzSfs/sxO1vc9sjxTWiGwdlL1C9pfyM1WnM5xCMIHkr7fQTrnebM3IyvVZWkzVzo1kZsPEX+Hd05WZe6Q1cgP+9KVvwTxWXWOuE5FItAk0kD5r6ientEuY6sT+x5ecIfIypezQGXpmTpk5PmYA1Nbsp0tuCq2hylFYd/EeunhAF3PzdvkZ5xh/vHHHMIzWhg/oQSAKoIXlw1vNs8L3h2JT5NmsKt3L4TsA01JFbyymqBqC0xpo2afXdUacSofYvGm9/kH+OFkmDCMrpkbDwmAFEPgcmlMMeh/1h8KulNnjlO0/EX/eX2PODNltuTFkFigL9VICLpIHQnbWOf0/01yy22vnyMvAi7GUsLLg2uWaQ0ytNyMnIS/oFx6hAqNEuLKx0GjgliSqrgQdG6yM4aN98QYOiS2mcFU1Ey1FDR4Te3cy+RIusF+4myVT0xkL+c4/Qyg/H6z8+8ykt6A1e95iB3pmkhq0gomAqDebixawyzeUOcfqji0ta+U4AAUTS6J3YU3SE0yBStlu8qVwto+2zf9GusA6MMyejFc0vPivAs0c5v/OMfkw31s8m9EzDNySNhmFN87WIY1llpTXD9yUm5OFoVp5NT6reSN8q9JRCFEAGvfzWQvr7H94afgnoIjsxHtQec6V6M3nssRhhOWDIePb6kIwgY0FJF+zYOWgCx1I63nT4kmMXWqp9LPZaKooAHp8giQ8fxExbSHYeIS0XXHzi45HOzDUTynRSYjCQXZPGet++9mS7gXdoq+3VFAWXciLM380ys0x+muFuhaHMi6/a7tT4CDyeYymuzWbio7zPr7IrI7ZBhlu7Z6H0tvaH1MtJGpgmCm6Xv0tvhl+s2YKiv0gDyu9TPkOFaJNKz540soQvfGKLx/I9Bu0RqvSKLzxYKumQfCWWDlhLOenKCEj8OX7p3cKV19X+P+KgRmgre6ONEkzJxSmdWBznZ9O6eOzXwnKBW5dOU1RrmIU6P+G3DZWN6+cP1YICRH0aAvUYZIF47rXQ+HPheWkKC6xZE5X8Z+mD+S7h4LdpYKPE4ROZhbhS72FcS2CcPaSopFGSITGR739xani79W7v/dUclYsJSCsQzrJlcjukDJhIZ4n08H5PEFG+oCJwWq9Rm5MhHcfWbOjNUlPZI/r6MUbWZGF/WJyRgesNLxjii5J2B28REpQd8SWgdGf9ljuLAdGq4uAkabi/Biz5CCLC7u6M9U1tLOxOh9xI64njiGAov/lT6T4Q68WtVs/r56iaaOxDxkC4zgrLsEOrthRMxcQ+xU0BjfNeLCJeU59WjjtpPXc4TYnvygAu8XmcKk+uKCw2SLixYWSR/OzRNOWvJYUxxz2o9gJ4Z/Oi4sqbgGKFDc3iWxNGDs5hD+YWeRdcmhHLb2DjXYoPGsSDYRKfCge57HoML7D96cTibdVz+96QRaC+FSFgAU6JWqCdM6FzKx18il/1+q/bC6HJrpwsv2N1Gt4/hcSOVKkYktaZkdjr/Cguxu4LFjnONsUzrkM6I70l8xNDO/cYxvWN8nxPCoECRLgc6gpH6Gm/Bz1YUrVSH8RLarYBoq5k1u+GzcwBmaC5Y1AOBAHixHftjxbiUNFUzATQ3211n+oD4rK2zCTpoj7KdSa1L6Rgi6i+t0zXU759ewvuaov53AYBD8YwKWMsChszty7dDj6NlXL05R2198i8NZmjJYVSyAY0xCfxFjX7MrdB7/FwYZvI4LlS+nIV2ZtMlPbDD2Y4u1Sk9u/blp6Toc+ANtxA1YeUSmq9ZPclOKcYGG++cssxWQ47DzZorgsAZIR3OmsBHsBmGy9V62sADJjTViLBtiKiQZ1mZyCnty1yt/avcPAwV36XvizzM9VUcLSjLGWxhm65lGT0a6vWlvAnMoqswSJRkl8hNspD+yj5srSyc0GloQAlQ5NxTZZXFW3a1LIB1EewI1JDUPT/Bu8C4W1nECw+BAOn1X3nkuNrf157DUPlBwSxm5+dQUvFChtLIIRv46rx2EojrxtvYKKyxl492Dqg9XaPKl+Yi4ewbvvwW5IQJ0QPjx2wiLBmcvBOdbyu/sVU+7bYWzJqn+SuMN0L3UUarZz5aPYerUZ8NVvZ4Yu33uLNuNzgYPu00L+ncDrxRk7e7A4K9JT+4066EO9IKSS7BNLJIAcqRZM3vJJBCdaw8hY9ljbEZiLZSf14BQ8rPBovZ57RTAObbjeDoHqj51Vxy04kp6ctfiOXbscAMpw9U+Ko0usEYlVljebPHRMC1xh045nru6CKgxMBc+5vdFy4uh1RYwUJusu4XpWopLpJqUky/KQIXFrqvQOXukX8lZGXmsZXeKTZooEVN6XcTLFX1/9ZEhGAYAcrwgDAeT25o7wfZ5VCcUVy0/KUlvAvkKL3vICcjljiUPT32MHmUOER/kjC2SwqnufEyk0/qXcHs+tGhzXMBSJf7cA5D98CgbKStQldmEtYFbJjadWj2B++QgH4++ot2Ur1QJLNKV8htit/vtGIfTBDkmmy+GDrVhvIJocMIdrfogXEzgQAlkDDIaegAmJD9Bf9XXbl+Eg/5yYcCMDHdK6AdO/rYsbHREVzclizrVFYFfgE1MXDkdz/LLp69XNxLKUUozGJmwyXaRlvW0jx+HHXfQzyujXmLZScwWObN4d4mfT/8k0zET7FwG0R3cchRv2k2eaYYcr4J6P5Mqod+j9Mf1RWOe/nBazK2oQ+Re6yXA/vYYHl9i5UJlj1kttuL9c/WBarB72fSSTjNlOGO/wbjLnha0cenOFLrMEfgz9iHQVvXxvEVWzF9yRsPRUd/ZMwnSfIa0KzuD8FEe7+bvdedIDL4oJsFBVv/8afslH9BtyzFTkfSG9H7joTD2GCIKj5OgX5Xw618oba48fZaNi8ACQnIUQ4yuDVhE27HZEbjDO7ZX0i7HiUSof6YO6lNq/7BY/jj+KCF/moJEXnQt1CzAJCAcn+qsedBWLBbb7Ik5K50z4YGik+AGisdl+hoMNRl3TVeO7fpaG6NS6cjY7ryJ8LfOmxtNzlys8O1GKgpLu6p/eltlQVwPKcE1jrdu01qBFd22C/sCOij2IwoRF0ZXYotBwtBcd0rJXC2S9OK8Gxg1J+vWYgcJkCx3794IEJhb6nwe3nstl4BTxRW8HWCvH6PHvNQ1BiK0grqRT67KOo/Hh+X6+cLrMwct2JtZsKu4qfC1yYxDGW0QSsKQH014UdzEUhGkbc/Q8KTwBBNGBrZeH5Dp5nDZrFKQRkC/TKTIsDH6G28FM3hj/ZDN5SCdkTpukoMJFe9jlpeJs8S35BFqjFZOdAoregAr/h6HDWRQ2qJU2Of2hlLdeoIC47pwO7daljEsnHPV8Jc7c70X9iN90t0j7boM0pwPTGzi59Vz5vT3hhNil1S+5loMaTpTzyUF72bDBpZvd1S2inZAa4G7X2aMMVSRcmv7Va7dJw3Kzyb9I5nNMeJoB8pNYcLfbgSz8UTqRS3MSffw8z7tDOcmdccnHYpKu0iwzIYnunu3Kt0XsrB+QnK6z6+lJT2e+cVBl5tizOtGPfyB9ymespoRNRgicFLFS1wc+QKrJrbXjE7DffSFt2Dka4GI+l1hKY6pLC3C4fADS06XFt3J9TSF/MU4DNZN39wU6rZalJ988unl7LxwPPJwp4dYaelq32VLAqLnTrQ6h9oTtN6KS9WvTQx8oIQIovh8KsAAj/IPf+vLq0cYVBsD+gETLzOv2W/3/Pw2aaioBpO5rQyNj0AIGxx4O5c+fCtRyDzmRerHPw65VujrESujRS7t1BxpwvEDb+86qJcF9jQV1YyjsrC8YhMZt1DgJ7SBxQkLfeseRHD61WpkHZP/y0hK6Rw72LocVMdz+sTMdm00aMnoahwewoxEV0fzAiEHBjOys6jXxirraPQ4eCnXXkiAU26+USdtHxLOm/RcW3M/19R8ldRW01FBMgAmPtsw6UDb7/LZK58nPcdhH1Hx74Z8dcCiEFBaGzwjSQmqWbPvVnLxyTLuGatNZnCUm5nPn/W0/n5Nh3GodJa0YhAQneza5lF7xwUhNFZwZCwyWFI2YAf+G0IJN0uFi0M5jR2SihbDMfb/kTTHWgf3Xm9Xw8bwtg7mKcmQFlNLW213MNM9WfDgWQ4GBzuyNsSXPTrtUwIysok6VmAe3NL1SJ+5KBilS0HT/h+3Ri2WmNDrfFHBv2PtSvicPdxzQMQoFg0TSCuKAX1YOVPcc/ae/axcYMTi6CwlVGWaH45NiAAfJLFCc4RMLyDPX9pbCdDiUK/PFp5dYIRn20JAsy2eIl6mVZjbSs0h3wPHm7aqboFGpt+a1Z6bNoGhsa43cYesgApJYAS3c7gMHTA4FnzZPirNyueaVZgPih/5xQHGJP2we98VoWtWWSECxFcELwQv+6LtgY+dTXWwPQP6nlHKoIMlLSj6lY11Vf0AeU1LbV4oJrKmerSvk8YCITShWc77EsUdTe2eBM8nJrf6J/GuvGVR/HVBSaNZXwg/yJlcgPW5U0UOB8MNZlhkh6v8peFhYfahZkouoiNbRke593WZcguw+c+pn4rqwzuo85A1nRiicBQ5Ru8xjkMnFtT13MQamii4sC7zYrlP2Tr/gRQozi00TSGQvRRTRrqaE2Si3T1zIE57FEMpSB9+czwlkLvoQyOmZyU61h6ppd0/BxgAcLp7kc1PJEmPbkk1xDIK+A8bURghgm9Wq0eE/q965lPKhvSpDoTBRg83KckzqqHPqRKfF/V0vfZT5oRSknO5VWTsDcJ8y9lGk/Pw6iDki55hSdUQvWdSELVmaVO7PQwXZ/Wu3vk0+S6O/4oJqRihYHmHbwWGRaR0qyefviucOaI/MBmkG9cxUry4U13bJg7Pz+nSWAlNDOpXsiMX4tsj04IeZgfPNyNDzSm6JjWOucBSIKW7GMietddHSXpk6Hgom4MRL774y7cD0rBErstWcj3w9II/2v+QC6ZbR1JFjcl26Q9CSHvvgwHpggRlK33XMIvHki92X3UxGA3gEYcLc8gRKVcEnxgy8khZ9Q8wEoC17wQNwPh3QG3kgsLAwJRStOaehit5H2mhHKW8hIGOG/pHLysyHDMA55SFrQJ2PaZRCPwiOjhBCrZS5DIJPuD6Fj3hLUyp0quAtl2HWLa3//F8TPXMAd7pKji8n50mMWn6BakfGHlARgX8H6tVGu71fRGomUVx1OkgqYEEImihHzkeYAmGCLO3txwe57ZHn470T0me2BVqnxmm02DIMf6VQxvaDTPXW/DK2Z6chST38kilGDbnrsaBvTmRY6Pm4RXf4JzWGvwMpKibAd6KR9zi1Fe/0ldtlKgrMiFw7ElokPnDGXx0mvxI4hBV1gvqGeEIuNULfEsbckcMcpYec7yxp2HxRhHYxnrCHhO2w8HwFdv3sZLHjiWcZdeOy0C5yCFuTHcPrAYwA5Bo/GgVbbG7SKqNnM2sVSOlIQkoYB2X4BVlrqmDofWxpGyE5l2HeoKPEk2GzKxUnvUjh9nPRIbQrlPPB9nOPU68ep/Qh2IZkqhDKuUEdQHOifhdE8EoHgTRtrT3N+u6eUPHqFgoBXLW+W6ln3DHwBoeainR9gmAkfDaa0gUGphDDPST0j2FbHMNeq5gef7w49bFtbUQbPwcG7K7lJvVlaVuDk8/gBGnq+rpSJAv5EBJaGa1Nl7dTJFZfHUoc4NF+qoKXjq5vW2XEaS/sWOlYzRLu7CjgBlqqjnZzuOGZY6z7j/UGBFYIPnsLdxAvNRk8CrHDXBTmhoLzb7TFt3ncEryZ5kRSEG/yh/YUf0qhZsIN79gItvEJYe8llsGCGFIi3dYLH0gP/YOKvalm4FL4+qDRgbICXCrkMp7GskwgePtj/CQa3gv5I6V7SrTMBuargnE53tpaFDtkVXI6tfwV1yO4o4mOZBIy46RYxDmE+EMsUm9UqmY25ETH2i6NOrLe2ruyaMi7ecMUQkBIBnhBlsWnkScJd/07UsKnyI2G111PqZmqjT2KTr2irYkykM5//pN4Uvn9Tb+LIgddfj5rLOKY/zsZJooq77e+ADU4gIazHnsMKto9amEufEWKmDxr0vgmDRLmEELi8Kibiw3qC6evNJFIYoNTvi8vr+kpwNmKGt/bIuB88MW5lDAy6M1OT/jEy/MPD69FVGct6QYvI2LS4NRX+3CJLt4qar3Hw4EN2eR2t+Jpigs4RmlZWMgTLvsQtFBfellBa/5fd4SXwHBfagE7v4cP/WYaJnpMt21tN8bn4BRWcipufFErFO97PdWRzJJFA5tvzAKsBGtGHnt+yXwLV3JMhugdpMumshWkLiWDXjDkZKz6YytPfj+OX+5TtRsAwTzPIsP/XXnlAsTUPmDFIGy9lIPpLW1505qrsYzBEZ8SB9JWzd7rZyBAo2exyvdFJRKX96FQQDW2NBCmymVc58f6QJQS91rV471uKl4OcjfWnicdNoH6dcIVbBGHiUC603bGPpyh6V3OnbRTASfKFWh/VugIo2WrPGS3tR5/Skbjjtr1aHBBKHYncwm28I0l3o3/ro6k2t+xc8CJkIRkdE9t/ItSNJJnZjSckMNcZlbglcfkAyCRuAmG6XQf2yQQS9iNWfOW8Qjdcr4m9Zs0jIKxRJVC8euN6nVs3BU3UrpFJZV211CINkLKnhe2ouE/L0helEWWMM6u2ZD9RvrCidWG/CwDZ23EVS2bn/c3l0wTH9Yw5QIo4kA9j3xRJosUVDU9KR6H0o02ANKBF+/DevWGcAK7NYzz4p9dck59lhr2NicpaURey5nCfic+aMRSg73VDg9YAVgB1QXcMYmPmpS6SQZNKmyd6+85hmuk3uzgLXHsU0p6bCv+sD76FrSf0dw2oxqYdhdlkF9j0F4BTZubmvGAel0v9OB+g3lJT5oIzlqXQQpSJPTTxhECB4ebIvFAFOFLdQ2UD9laYkFg/1v/ZdWAKvtXVx0YGibm1Nrr2MLWqRMZncbNhQHVKdFWyNXR0qBDhaPDgdwWpLBhcxL9zyCnjw21j0foHuCdx2/e1KiMHjPYRx6aIV0GQALaz86W+gF2jiu1FILxwxQhIwNACJ4YFrZbzKtLMqjQhkHhQW/KApEf4ay0qk8iNpfi/Ohw7Q+RTq5lNM2dlp9h4VYuCeU4qe7xtUvDXOFHGDmybKlCSRGZ4sCADiDCV8n+ihYCbDbJTwZtwqFU+ig6XzPAh/MRAcQV/DSwXJlBl/bq0pfyPsOyWs8aT6zsEzlqqa7qZ7PH4nOL9z78jFFwm0Y2xiaotz4qiCTLJfaqfreulvBQdIOLPaXnGgYWT3pIDmy7xtjKebQcaOhQBL/gq+12ko8u3z3ObODU3uFCpwZ1FudMC/P/QPG1TghOHfi3pap2L5Qr1iLDKiF2G5s/fPlNuZyv9hU8kgDApeUEw7u0TxQGL2mS0b4cZ4CLSbMOTsoI8IGBtSOscvD2xwpwpixSje9QYCs/0X+l6lWiwTaId6lzYH49k2bmN/qGs7UnFDL7h8zw/UHo516yWWKxtlaknI9jmOsHURqunY9nZxgI4fJ67B+n0yuyapVDjbmpkWOb/DghMCSWLGnaqd3yquEx/aXLJkIVnjjX150sq2LH1bocsecElceIDKFfuahnzxO48z7FJ2m5GGv6PvTU/qW0+l7r8MRxCGgZ5/mi500k7neGfpMaGFnANeFUxiGS9R/u7NBhLhwTEyL7s528BObPb7boPbkIoJpFnviTwxGEJcjsp2HYbQeftFq/GkCmzWcM4PdfUK63H70S6GAb58YFs2g5yio7j84nHEScpjBxXCk1/tsVLCgPNA47gJX5aowNQ6aDkt1Ngu5CRvl7IxgH4DSk1BjhvtZ8UsZD31kl6W6A2X/+05I84228ArhHHr3GFDJGqsIpttf+e1fghjrkbK0t19s3vscbVHVftJpH7P9ngNEMp3ySTkYm67O4koEWXae0NhW1kJ6wBRAObWxRldQ6xgFMl97+hybcfvIzhd6NHjqd5y+8zZkWEU91TPLM5P5r367XQxosfOmtg/UPcxkc88dKkgXTpmokWpGxlfpONAJnkzVsF746ApeJ0ldS80tFpEg1Dd+qUue1sQjwlpBqzI5T679mspa4wXgqiaShbJ+wo6Fb4SlN0P3r1NbVBfX0ViHbZnc8pSOzsT+evKvwnPDrvSS/1cp0BUE+oU5018hUinqCyFuFmLFh53yz0zPSxG7ratS3lM7Ek7MFhfLaMY7qXQgMgHGtiO64gcNek9TYq1DKF8hBjZV6q58o0nwRVoK3bfKG6/R0kbJMX4jGEbMOR3lqM8ulJ6iOqKGn44FdagXSWdYaAh5AJeBRSs24HuWfL9SdjSK22TdhrHgFy5QPPrmWSzVzAE+yO1YhE8wyII97V96gMWzLIXRJseILyjST/BfwavqZEvvb2t0LuEp/Q3416aHPJ3N5LwOBeTqxuCYg1dzyCb3vpe8Eoii9oyLZ2jxs9npCAKqT1JBxHLYBj2dJxBb
Folgen
wichtige Grenzwerte
Wie Sie die Grenzwerte der folgenden Folgen:
\begin{equation*}
\lim_{{n \to \infty}} {q^n \over n!}\quad \text{für} \; \ q \in \mathbb{C}
\end{equation*}
\begin{equation*}
\lim_{{n \to \infty}} \sqrt[n]{n}
\end{equation*}
MTAwMDAw:kDjmlUmzmzRd+N/iUYt3J52nRacHV3E9rd6nK7oRuHI=:tfeThoVwQOYm1T1V:JJw4tmGnTRo3+GnKqg3tunMBLiETvJjqfkLxYmQz7QyqFOjuTuivmiy8l4/b+jZOdi9JHQFmT4JW+tzern+jDjLlUqZqXFvCS3qoAwF8EEQZTNFgT3XfwS/dnFSH6lOq5EpTiDmfJcxyvFJ5d8qQdlRYrLrTH2hHmgPN0ANoBvXFolm51SkdowBjm4gI4BE=
Konvergenz einer Folge
Gegen welchen Wert konvergiert die Folge:
\begin{equation*}
a_n = n^3+n^2+1\over n^4
\end{equation*}
Wie gehen Sie vor, um den Grenzwert einer Folge zu bestimmen?
MTAwMDAw:OGxfrfkmgvM28e92dsHjIgO/XnK1Orqo6CsAAArH+4E=:z7bwD/80hAiJjy5E:PR5guhJH4QZs5fDtTwoAFTJslUm99aXcAXFfTwkh7LNKb8txDI2114+/BTjrOVqIxPJbwoQdTej+F27JYcWNxfnitmLu3E0sgrnx/hjTPP8rUybmJOtRrAUYVy1eNNU746FCDXmveG2e48oxrKA4YS0AILc+tu0rKRtEl3ciJm2xMnPxa935iXWeH5dPH63KSwh4wfGXt1JIvqoH7M6Y5AxIHNW9c8XxD9M+W1be5YaBX0eBdr9MQ5sYLNW8pHqm6iGM59Bt2o8vVap7N1ODW0R9zc8LsWa9bQ81ty71DqNqSn28uwCB3c4N7V8fPN8t/k4HCe1ZuuyDRgaFzR9TX9JmkIDYVmzVPvLjSK4S55+AFg+sSL7OURoMMW2XccbkKDpQvXaR5rMl9aFJQb9q8lwYl3quh+/jiyWnSDceLYVpIe0q+i4U7g==
Analyse des asymptotischen Verhaltens
Asymptotisches Verhalten
Bestimmen Sie das asymptotische Verhalten der folgenden Funktionen:
\begin{equation*}
f(x) = \frac{\ln x}{\log_2 x} \quad \text{für} \; x \rightarrow \infty
\end{equation*}
MTAwMDAw:cGP9LunJdX9GJQhb+7fHxhUhZnnExZi76gBpt93vRgg=:KJn/jyoEsriJVJcr:iQjG+xW36FCXsAGTXlMaEOzM9hbJ6khlLjjQFqdqZQovLwSsW3uEHQ17eCSclt2WcNoysU0RJTHcZsh19/DU92p1UuWBlrG6v0G/S2gA5j6EZwIKeSpD8fj7yLuNkE8Ad5UCffGBdmnMVyEpiyFFNYuohY94Z0b9QZSAZ7YzbZDoLSBMOiiFt5qkcMJT3zFqPsXc/V7QzmUprwHurAFRL0rjJ1vwtsPgoDfb/QRgogrhxgULV2yo6OW8A+nPAc/gTUNZBv+7KglcytqyyGjk/o8BBOvxxzPUSOzBaEGF1OIWLAQ9iU7IHeTKdNMfleSFS+pFk9xWx+jt+Mvs8w==
Rekurrenz-Gleichungen und das Master Theorem
Anwendung des Master-Theorems
Analysieren Sie die folgenden Rekurrenz-Gleichungen mit Hilfe des Master-Theorems:
Gegeben sei: \(T(n) = 9 \cdot T(n/3) + 3n^2\log_2n\).
Gegeben sei: \(T(n) = 1 \cdot T(n/4) + \frac{1}{3}n^2\).
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