[{"data":1,"prerenderedAt":2976},["ShallowReactive",2],{"navigation":3,"\u002Fblog\u002Fege\u002Ftask16":386,"\u002Fblog\u002Fege\u002Ftask16-surround":2971},[4],{"title":5,"path":6,"stem":7,"children":8,"page":114},"Blog","\u002Fblog","blog",[9,115,184,329],{"title":10,"path":11,"stem":12,"children":13,"page":114},"Ege","\u002Fblog\u002Fege","blog\u002Fege",[14,18,22,26,30,34,38,42,46,50,54,58,62,66,70,74,78,82,86,90,94,98,102,106,110],{"title":15,"path":16,"stem":17},"ЕГЭ Задание 1","\u002Fblog\u002Fege\u002Ftask1","blog\u002Fege\u002Ftask1",{"title":19,"path":20,"stem":21},"ЕГЭ Задание 10","\u002Fblog\u002Fege\u002Ftask10","blog\u002Fege\u002Ftask10",{"title":23,"path":24,"stem":25},"ЕГЭ Задание 11","\u002Fblog\u002Fege\u002Ftask11","blog\u002Fege\u002Ftask11",{"title":27,"path":28,"stem":29},"ЕГЭ Задание 12","\u002Fblog\u002Fege\u002Ftask12","blog\u002Fege\u002Ftask12",{"title":31,"path":32,"stem":33},"ЕГЭ Задание 13","\u002Fblog\u002Fege\u002Ftask13","blog\u002Fege\u002Ftask13",{"title":35,"path":36,"stem":37},"ЕГЭ Задание 14","\u002Fblog\u002Fege\u002Ftask14","blog\u002Fege\u002Ftask14",{"title":39,"path":40,"stem":41},"ЕГЭ Задание 15","\u002Fblog\u002Fege\u002Ftask15","blog\u002Fege\u002Ftask15",{"title":43,"path":44,"stem":45},"ЕГЭ Задание 16","\u002Fblog\u002Fege\u002Ftask16","blog\u002Fege\u002Ftask16",{"title":47,"path":48,"stem":49},"ЕГЭ Задание 17","\u002Fblog\u002Fege\u002Ftask17","blog\u002Fege\u002Ftask17",{"title":51,"path":52,"stem":53},"ЕГЭ Задание 18","\u002Fblog\u002Fege\u002Ftask18","blog\u002Fege\u002Ftask18",{"title":55,"path":56,"stem":57},"ЕГЭ Задание 19, 20, 21","\u002Fblog\u002Fege\u002Ftask19_20_21","blog\u002Fege\u002Ftask19_20_21",{"title":59,"path":60,"stem":61},"ЕГЭ Задание 2","\u002Fblog\u002Fege\u002Ftask2","blog\u002Fege\u002Ftask2",{"title":63,"path":64,"stem":65},"ЕГЭ Задание 22","\u002Fblog\u002Fege\u002Ftask22","blog\u002Fege\u002Ftask22",{"title":67,"path":68,"stem":69},"ЕГЭ Задание 23","\u002Fblog\u002Fege\u002Ftask23","blog\u002Fege\u002Ftask23",{"title":71,"path":72,"stem":73},"ЕГЭ Задание 24","\u002Fblog\u002Fege\u002Ftask24","blog\u002Fege\u002Ftask24",{"title":75,"path":76,"stem":77},"ЕГЭ Задание 25","\u002Fblog\u002Fege\u002Ftask25","blog\u002Fege\u002Ftask25",{"title":79,"path":80,"stem":81},"ЕГЭ Задание 26","\u002Fblog\u002Fege\u002Ftask26","blog\u002Fege\u002Ftask26",{"title":83,"path":84,"stem":85},"ЕГЭ Задание 27","\u002Fblog\u002Fege\u002Ftask27","blog\u002Fege\u002Ftask27",{"title":87,"path":88,"stem":89},"ЕГЭ Задание 3","\u002Fblog\u002Fege\u002Ftask3","blog\u002Fege\u002Ftask3",{"title":91,"path":92,"stem":93},"ЕГЭ Задание 4","\u002Fblog\u002Fege\u002Ftask4","blog\u002Fege\u002Ftask4",{"title":95,"path":96,"stem":97},"ЕГЭ Задание 5","\u002Fblog\u002Fege\u002Ftask5","blog\u002Fege\u002Ftask5",{"title":99,"path":100,"stem":101},"ЕГЭ Задание 6","\u002Fblog\u002Fege\u002Ftask6","blog\u002Fege\u002Ftask6",{"title":103,"path":104,"stem":105},"ЕГЭ Задание 7","\u002Fblog\u002Fege\u002Ftask7","blog\u002Fege\u002Ftask7",{"title":107,"path":108,"stem":109},"ЕГЭ Задание 8","\u002Fblog\u002Fege\u002Ftask8","blog\u002Fege\u002Ftask8",{"title":111,"path":112,"stem":113},"ЕГЭ Задание 9","\u002Fblog\u002Fege\u002Ftask9","blog\u002Fege\u002Ftask9",false,{"title":116,"path":117,"stem":118,"children":119,"page":114},"Oge","\u002Fblog\u002Foge","blog\u002Foge",[120,124,128,132,136,140,144,148,152,156,160,164,168,172,176,180],{"title":121,"path":122,"stem":123},"ОГЭ Задание 1","\u002Fblog\u002Foge\u002Ftask1","blog\u002Foge\u002Ftask1",{"title":125,"path":126,"stem":127},"ОГЭ Задание 10","\u002Fblog\u002Foge\u002Ftask10","blog\u002Foge\u002Ftask10",{"title":129,"path":130,"stem":131},"ОГЭ Задание 11","\u002Fblog\u002Foge\u002Ftask11","blog\u002Foge\u002Ftask11",{"title":133,"path":134,"stem":135},"ОГЭ Задание 12","\u002Fblog\u002Foge\u002Ftask12","blog\u002Foge\u002Ftask12",{"title":137,"path":138,"stem":139},"ОГЭ Задание 13","\u002Fblog\u002Foge\u002Ftask13","blog\u002Foge\u002Ftask13",{"title":141,"path":142,"stem":143},"ОГЭ Задание 14","\u002Fblog\u002Foge\u002Ftask14","blog\u002Foge\u002Ftask14",{"title":145,"path":146,"stem":147},"ОГЭ Задание 15","\u002Fblog\u002Foge\u002Ftask15","blog\u002Foge\u002Ftask15",{"title":149,"path":150,"stem":151},"ОГЭ Задание 16","\u002Fblog\u002Foge\u002Ftask16","blog\u002Foge\u002Ftask16",{"title":153,"path":154,"stem":155},"ОГЭ Задание 2","\u002Fblog\u002Foge\u002Ftask2","blog\u002Foge\u002Ftask2",{"title":157,"path":158,"stem":159},"ОГЭ Задание 3","\u002Fblog\u002Foge\u002Ftask3","blog\u002Foge\u002Ftask3",{"title":161,"path":162,"stem":163},"ОГЭ Задание 4","\u002Fblog\u002Foge\u002Ftask4","blog\u002Foge\u002Ftask4",{"title":165,"path":166,"stem":167},"ОГЭ Задание 5","\u002Fblog\u002Foge\u002Ftask5","blog\u002Foge\u002Ftask5",{"title":169,"path":170,"stem":171},"ОГЭ Задание 6","\u002Fblog\u002Foge\u002Ftask6","blog\u002Foge\u002Ftask6",{"title":173,"path":174,"stem":175},"ОГЭ Задание 7","\u002Fblog\u002Foge\u002Ftask7","blog\u002Foge\u002Ftask7",{"title":177,"path":178,"stem":179},"ОГЭ Задание 8","\u002Fblog\u002Foge\u002Ftask8","blog\u002Foge\u002Ftask8",{"title":181,"path":182,"stem":183},"ОГЭ Задание 9","\u002Fblog\u002Foge\u002Ftask9","blog\u002Foge\u002Ftask9",{"title":185,"path":186,"stem":187,"children":188,"page":114},"Python","\u002Fblog\u002Fpython","blog\u002Fpython",[189,193,197,201,205,209,213,217,221,225,229,233,237,241,245,249,253,257,261,265,269,273,277,281,285,289,293,297,301,305,309,313,317,321,325],{"title":190,"path":191,"stem":192},"Знакомство с синтаксисом","\u002Fblog\u002Fpython\u002Fst1","blog\u002Fpython\u002Fst1",{"title":194,"path":195,"stem":196},"Отладка","\u002Fblog\u002Fpython\u002Fst10","blog\u002Fpython\u002Fst10",{"title":198,"path":199,"stem":200},"Модули и пакеты","\u002Fblog\u002Fpython\u002Fst11","blog\u002Fpython\u002Fst11",{"title":202,"path":203,"stem":204},"Кортежи","\u002Fblog\u002Fpython\u002Fst12","blog\u002Fpython\u002Fst12",{"title":206,"path":207,"stem":208},"Знакомство со списками","\u002Fblog\u002Fpython\u002Fst13","blog\u002Fpython\u002Fst13",{"title":210,"path":211,"stem":212},"Списки и циклы","\u002Fblog\u002Fpython\u002Fst14","blog\u002Fpython\u002Fst14",{"title":214,"path":215,"stem":216},"Использование списков ч.1","\u002Fblog\u002Fpython\u002Fst15","blog\u002Fpython\u002Fst15",{"title":218,"path":219,"stem":220},"Использование списков ч.2","\u002Fblog\u002Fpython\u002Fst16","blog\u002Fpython\u002Fst16",{"title":222,"path":223,"stem":224},"Использование списков ч.3","\u002Fblog\u002Fpython\u002Fst17","blog\u002Fpython\u002Fst17",{"title":226,"path":227,"stem":228},"Словари","\u002Fblog\u002Fpython\u002Fst18","blog\u002Fpython\u002Fst18",{"title":230,"path":231,"stem":232},"Множества","\u002Fblog\u002Fpython\u002Fst19","blog\u002Fpython\u002Fst19",{"title":234,"path":235,"stem":236},"Переменные","\u002Fblog\u002Fpython\u002Fst2","blog\u002Fpython\u002Fst2",{"title":238,"path":239,"stem":240},"Хеш-таблицы","\u002Fblog\u002Fpython\u002Fst20","blog\u002Fpython\u002Fst20",{"title":242,"path":243,"stem":244},"Решето Эратосфена","\u002Fblog\u002Fpython\u002Fst21","blog\u002Fpython\u002Fst21",{"title":246,"path":247,"stem":248},"Длинная арифметика","\u002Fblog\u002Fpython\u002Fst22","blog\u002Fpython\u002Fst22",{"title":250,"path":251,"stem":252},"Декораторы функций","\u002Fblog\u002Fpython\u002Fst23","blog\u002Fpython\u002Fst23",{"title":254,"path":255,"stem":256},"Знакомство с алгоритмами","\u002Fblog\u002Fpython\u002Fst24","blog\u002Fpython\u002Fst24",{"title":258,"path":259,"stem":260},"Бинарный поиск – примеры задач","\u002Fblog\u002Fpython\u002Fst25","blog\u002Fpython\u002Fst25",{"title":262,"path":263,"stem":264},"Сортировка выбором","\u002Fblog\u002Fpython\u002Fst26","blog\u002Fpython\u002Fst26",{"title":266,"path":267,"stem":268},"Рекурсия и стек","\u002Fblog\u002Fpython\u002Fst27","blog\u002Fpython\u002Fst27",{"title":270,"path":271,"stem":272},"Быстрая сортировка","\u002Fblog\u002Fpython\u002Fst28","blog\u002Fpython\u002Fst28",{"title":274,"path":275,"stem":276},"Поиск в ширину","\u002Fblog\u002Fpython\u002Fst29","blog\u002Fpython\u002Fst29",{"title":278,"path":279,"stem":280},"Работа со строками","\u002Fblog\u002Fpython\u002Fst3","blog\u002Fpython\u002Fst3",{"title":282,"path":283,"stem":284},"Поиск в глубину","\u002Fblog\u002Fpython\u002Fst30","blog\u002Fpython\u002Fst30",{"title":286,"path":287,"stem":288},"Сбалансированные деревья","\u002Fblog\u002Fpython\u002Fst31","blog\u002Fpython\u002Fst31",{"title":290,"path":291,"stem":292},"Алгоритм Дейкстры","\u002Fblog\u002Fpython\u002Fst32","blog\u002Fpython\u002Fst32",{"title":294,"path":295,"stem":296},"Жадные алгоритмы","\u002Fblog\u002Fpython\u002Fst33","blog\u002Fpython\u002Fst33",{"title":298,"path":299,"stem":300},"Динамическое программирование","\u002Fblog\u002Fpython\u002Fst34","blog\u002Fpython\u002Fst34",{"title":302,"path":303,"stem":304},"Алгоритм k ближайших соседей","\u002Fblog\u002Fpython\u002Fst35","blog\u002Fpython\u002Fst35",{"title":306,"path":307,"stem":308},"Типы данных","\u002Fblog\u002Fpython\u002Fst4","blog\u002Fpython\u002Fst4",{"title":310,"path":311,"stem":312},"О функциях","\u002Fblog\u002Fpython\u002Fst5","blog\u002Fpython\u002Fst5",{"title":314,"path":315,"stem":316},"Свойства и методы","\u002Fblog\u002Fpython\u002Fst6","blog\u002Fpython\u002Fst6",{"title":318,"path":319,"stem":320},"Определение функций","\u002Fblog\u002Fpython\u002Fst7","blog\u002Fpython\u002Fst7",{"title":322,"path":323,"stem":324},"Логика","\u002Fblog\u002Fpython\u002Fst8","blog\u002Fpython\u002Fst8",{"title":326,"path":327,"stem":328},"Циклы","\u002Fblog\u002Fpython\u002Fst9","blog\u002Fpython\u002Fst9",{"title":330,"path":331,"stem":332,"children":333,"page":114},"Toi","\u002Fblog\u002Ftoi","blog\u002Ftoi",[334,338,342,346,350,354,358,362,366,370,374,378,382],{"title":335,"path":336,"stem":337},"Информация и информационные процессы","\u002Fblog\u002Ftoi\u002Fst1","blog\u002Ftoi\u002Fst1",{"title":339,"path":340,"stem":341},"Электронные таблицы","\u002Fblog\u002Ftoi\u002Fst10","blog\u002Ftoi\u002Fst10",{"title":343,"path":344,"stem":345},"Система, её свойства и компоненты. Моделирование","\u002Fblog\u002Ftoi\u002Fst11","blog\u002Ftoi\u002Fst11",{"title":347,"path":348,"stem":349},"Представление информации в компьютере","\u002Fblog\u002Ftoi\u002Fst12","blog\u002Ftoi\u002Fst12",{"title":351,"path":352,"stem":353},"Средства информационно-коммуникационных технологий. Файловая система","\u002Fblog\u002Ftoi\u002Fst13","blog\u002Ftoi\u002Fst13",{"title":355,"path":356,"stem":357},"Комбинаторика","\u002Fblog\u002Ftoi\u002Fst2","blog\u002Ftoi\u002Fst2",{"title":359,"path":360,"stem":361},"Адресация в интернете","\u002Fblog\u002Ftoi\u002Fst3","blog\u002Ftoi\u002Fst3",{"title":363,"path":364,"stem":365},"Измерение количества информации","\u002Fblog\u002Ftoi\u002Fst4","blog\u002Ftoi\u002Fst4",{"title":367,"path":368,"stem":369},"Системы счисления","\u002Fblog\u002Ftoi\u002Fst5","blog\u002Ftoi\u002Fst5",{"title":371,"path":372,"stem":373},"Диаграммы Эйлера — Венна","\u002Fblog\u002Ftoi\u002Fst6","blog\u002Ftoi\u002Fst6",{"title":375,"path":376,"stem":377},"Условие Фано","\u002Fblog\u002Ftoi\u002Fst7","blog\u002Ftoi\u002Fst7",{"title":379,"path":380,"stem":381},"Теория графов","\u002Fblog\u002Ftoi\u002Fst8","blog\u002Ftoi\u002Fst8",{"title":383,"path":384,"stem":385},"Алгебра логики","\u002Fblog\u002Ftoi\u002Fst9","blog\u002Ftoi\u002Fst9",{"id":387,"title":43,"author":388,"body":393,"date":2963,"description":2964,"extension":2965,"image":2966,"meta":2967,"minRead":2968,"navigation":662,"num":865,"path":44,"seo":2969,"stem":45,"__hash__":2970},"ege\u002Fblog\u002Fege\u002Ftask16.md",{"name":389,"avatar":390},"Штана Альберт Игоревич",{"src":391,"alt":392},"me.jpg","@ashtana",{"type":394,"value":395,"toc":2903},"minimark",[396,401,409,415,424,432,437,446,451,461,464,469,477,482,690,695,699,702,708,714,717,720,723,881,886,890,893,899,1059,1062,1065,1234,1240,1245,1249,1252,1258,1261,1264,1267,1416,1421,1425,1427,1436,1439,1442,1445,1652,1657,1661,1663,1669,1672,1675,1678,1830,1841,1846,1850,1852,1858,1861,1864,1867,2032,2035,2040,2044,2047,2127,2130,2133,2246,2273,2278,2282,2284,2290,2293,2296,2299,2401,2431,2436,2440,2442,2447,2450,2453,2456,2609,2639,2643,2656,2661,2665,2668,2677,2680,2683,2686,2853,2877,2882,2893,2896,2900],[397,398,400],"h2",{"id":399},"типы-заданий-16","Типы заданий № 16",[402,403,404,405],"p",{},"В этой статье будет разобрано ",[406,407,408],"strong",{},"задание 16.",[402,410,411,412],{},"Рассмотрим типовые задачи из шестнадцатого задания ",[406,413,414],{},"ЕГЭ по информатике.",[402,416,417],{},[418,419,420,421],"em",{},"Данное задание относится к ",[406,422,423],{},"повышенному уровню сложности.",[402,425,426],{},[418,427,428,429],{},"Время выполнения задания ",[406,430,431],{},"≈ 5 минут.",[402,433,434],{},[418,435,436],{},"Данный тип задач проверяет умение вычислять рекуррентные выражения.",[402,438,439],{},[418,440,441,442],{},"В коде Python мы использовали декоратор функции. Подробнее о декораторах в статье: ",[443,444,445],"a",{"href":251},"Декораторы.",[447,448,450],"h4",{"id":449},"задача-1","Задача 1",[402,452,453,454,457,458,460],{},"Алгоритм вычисления значения функции F(n), где n – натуральное число, задан следующими соотношениями:\nF(1) = 1 ",[455,456],"br",{},"\nF(n) = n + F(n − 1), если n – чётно, ",[455,459],{},"\nF(n) = F(n–1) * n + F(n–2) * (n – 1), при n > 2 и при этом n – нечётно. \\",[402,462,463],{},"Чему равно значение функции F(12)?\nВ ответе запишите только натуральное число.",[465,466,468],"h5",{"id":467},"решение","Решение:",[470,471,472],"blockquote",{},[402,473,474],{},[418,475,476],{},"Данный тип задач можно анализировать и решать аналитически, но мы будем рассматривать только решение с помощью Python. Подразумевается что решать такую задачу на самом экзамене учащийся будет с помощью программирования за пяти минут.",[478,479,481],"h6",{"id":480},"решение-python","Решение Python",[483,484,489],"pre",{"className":485,"code":486,"language":487,"meta":488,"style":488},"language-python shiki shiki-themes github-light","# Функция, которая вызывает сама себя\ndef f(n):  # Названия функций в Python принято писать с маленькой буквы\n    if n == 1:\n        return 1\n    if n % 2 == 0:\n        return n + f(n - 1)\n    if n > 2 and n % 2 != 0:\n        return f(n - 1) * n + f(n - 2) * (n - 1)\n\n\n# Основная часть программы\nprint(f(12))\n","python","",[490,491,492,501,519,538,547,568,589,617,657,664,669,675],"code",{"__ignoreMap":488},[493,494,497],"span",{"class":495,"line":496},"line",1,[493,498,500],{"class":499},"sAwPA","# Функция, которая вызывает сама себя\n",[493,502,504,508,512,516],{"class":495,"line":503},2,[493,505,507],{"class":506},"sD7c4","def",[493,509,511],{"class":510},"s7eDp"," f",[493,513,515],{"class":514},"sgsFI","(n):  ",[493,517,518],{"class":499},"# Названия функций в Python принято писать с маленькой буквы\n",[493,520,522,525,528,531,535],{"class":495,"line":521},3,[493,523,524],{"class":506},"    if",[493,526,527],{"class":514}," n ",[493,529,530],{"class":506},"==",[493,532,534],{"class":533},"sYu0t"," 1",[493,536,537],{"class":514},":\n",[493,539,541,544],{"class":495,"line":540},4,[493,542,543],{"class":506},"        return",[493,545,546],{"class":533}," 1\n",[493,548,550,552,554,557,560,563,566],{"class":495,"line":549},5,[493,551,524],{"class":506},[493,553,527],{"class":514},[493,555,556],{"class":506},"%",[493,558,559],{"class":533}," 2",[493,561,562],{"class":506}," ==",[493,564,565],{"class":533}," 0",[493,567,537],{"class":514},[493,569,571,573,575,578,581,584,586],{"class":495,"line":570},6,[493,572,543],{"class":506},[493,574,527],{"class":514},[493,576,577],{"class":506},"+",[493,579,580],{"class":514}," f(n ",[493,582,583],{"class":506},"-",[493,585,534],{"class":533},[493,587,588],{"class":514},")\n",[493,590,592,594,596,599,601,604,606,608,610,613,615],{"class":495,"line":591},7,[493,593,524],{"class":506},[493,595,527],{"class":514},[493,597,598],{"class":506},">",[493,600,559],{"class":533},[493,602,603],{"class":506}," and",[493,605,527],{"class":514},[493,607,556],{"class":506},[493,609,559],{"class":533},[493,611,612],{"class":506}," !=",[493,614,565],{"class":533},[493,616,537],{"class":514},[493,618,620,622,624,626,628,631,634,636,638,640,642,644,646,648,651,653,655],{"class":495,"line":619},8,[493,621,543],{"class":506},[493,623,580],{"class":514},[493,625,583],{"class":506},[493,627,534],{"class":533},[493,629,630],{"class":514},") ",[493,632,633],{"class":506},"*",[493,635,527],{"class":514},[493,637,577],{"class":506},[493,639,580],{"class":514},[493,641,583],{"class":506},[493,643,559],{"class":533},[493,645,630],{"class":514},[493,647,633],{"class":506},[493,649,650],{"class":514}," (n ",[493,652,583],{"class":506},[493,654,534],{"class":533},[493,656,588],{"class":514},[493,658,660],{"class":495,"line":659},9,[493,661,663],{"emptyLinePlaceholder":662},true,"\n",[493,665,667],{"class":495,"line":666},10,[493,668,663],{"emptyLinePlaceholder":662},[493,670,672],{"class":495,"line":671},11,[493,673,674],{"class":499},"# Основная часть программы\n",[493,676,678,681,684,687],{"class":495,"line":677},12,[493,679,680],{"class":533},"print",[493,682,683],{"class":514},"(f(",[493,685,686],{"class":533},"12",[493,688,689],{"class":514},"))\n",[402,691,692],{},[406,693,694],{},"Ответ: 568907",[447,696,698],{"id":697},"задача-2","Задача 2",[402,700,701],{},"Алгоритм вычисления значения функций F(n) и G(n), где n — натуральное число, задан следующими соотношениями:",[402,703,704,705,707],{},"F(n) = 0, если n \u003C= 2, ",[455,706],{},"\nF(n) = G(n - 2), если n > 2",[402,709,710,711,713],{},"G(n) = 0, n \u003C= 1, ",[455,712],{},"\nG(n) = F(n - 1) + n, если n > 1",[402,715,716],{},"Чему равно значение функции F(8)? В ответе запишите только натуральное число.",[465,718,468],{"id":719},"решение-1",[478,721,481],{"id":722},"решение-python-1",[483,724,726],{"className":485,"code":725,"language":487,"meta":488,"style":488},"# Функции вызывающие друг друга\ndef f(n):\n    if n \u003C= 2: \n        return 0\n    if n > 2: \n        return G(n - 2)\n\n\ndef G(n):\n    if n \u003C= 1: \n        return 0\n    if n > 1: \n        return f(n - 1) + n\n\n\n# Запуск\nprint(f(8))\n",[490,727,728,733,742,756,763,775,788,792,796,805,817,823,835,853,858,863,869],{"__ignoreMap":488},[493,729,730],{"class":495,"line":496},[493,731,732],{"class":499},"# Функции вызывающие друг друга\n",[493,734,735,737,739],{"class":495,"line":503},[493,736,507],{"class":506},[493,738,511],{"class":510},[493,740,741],{"class":514},"(n):\n",[493,743,744,746,748,751,753],{"class":495,"line":521},[493,745,524],{"class":506},[493,747,527],{"class":514},[493,749,750],{"class":506},"\u003C=",[493,752,559],{"class":533},[493,754,755],{"class":514},": \n",[493,757,758,760],{"class":495,"line":540},[493,759,543],{"class":506},[493,761,762],{"class":533}," 0\n",[493,764,765,767,769,771,773],{"class":495,"line":549},[493,766,524],{"class":506},[493,768,527],{"class":514},[493,770,598],{"class":506},[493,772,559],{"class":533},[493,774,755],{"class":514},[493,776,777,779,782,784,786],{"class":495,"line":570},[493,778,543],{"class":506},[493,780,781],{"class":514}," G(n ",[493,783,583],{"class":506},[493,785,559],{"class":533},[493,787,588],{"class":514},[493,789,790],{"class":495,"line":591},[493,791,663],{"emptyLinePlaceholder":662},[493,793,794],{"class":495,"line":619},[493,795,663],{"emptyLinePlaceholder":662},[493,797,798,800,803],{"class":495,"line":659},[493,799,507],{"class":506},[493,801,802],{"class":510}," G",[493,804,741],{"class":514},[493,806,807,809,811,813,815],{"class":495,"line":666},[493,808,524],{"class":506},[493,810,527],{"class":514},[493,812,750],{"class":506},[493,814,534],{"class":533},[493,816,755],{"class":514},[493,818,819,821],{"class":495,"line":671},[493,820,543],{"class":506},[493,822,762],{"class":533},[493,824,825,827,829,831,833],{"class":495,"line":677},[493,826,524],{"class":506},[493,828,527],{"class":514},[493,830,598],{"class":506},[493,832,534],{"class":533},[493,834,755],{"class":514},[493,836,838,840,842,844,846,848,850],{"class":495,"line":837},13,[493,839,543],{"class":506},[493,841,580],{"class":514},[493,843,583],{"class":506},[493,845,534],{"class":533},[493,847,630],{"class":514},[493,849,577],{"class":506},[493,851,852],{"class":514}," n\n",[493,854,856],{"class":495,"line":855},14,[493,857,663],{"emptyLinePlaceholder":662},[493,859,861],{"class":495,"line":860},15,[493,862,663],{"emptyLinePlaceholder":662},[493,864,866],{"class":495,"line":865},16,[493,867,868],{"class":499},"# Запуск\n",[493,870,872,874,876,879],{"class":495,"line":871},17,[493,873,680],{"class":533},[493,875,683],{"class":514},[493,877,878],{"class":533},"8",[493,880,689],{"class":514},[402,882,883],{},[406,884,885],{},"Ответ: 9",[447,887,889],{"id":888},"задача-3","Задача 3",[402,891,892],{},"Алгоритм вычисления значения функции F(n), где n – натуральное число, задан следующими соотношениями:",[402,894,895,896,898],{},"F(n) = 2, если n = 1, ",[455,897],{},"\nF(n) = 2 · F(n – 1), если n > 1.",[402,900,901,902],{},"Чему равно значение выражения ",[903,904,908],"mjx-container",{"className":905,"jax":907},[906],"MathJax","SVG",[909,910,919,963],"svg",{"style":911,"xmlns":912,"width":913,"height":914,"role":915,"focusable":916,"viewBox":917,"xmlnsXLink":918},"vertical-align: -0.566ex;","http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","14.697ex","2.452ex","img","false","0 -833.9 6496.2 1083.9","http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink",[920,921,922,927,931,935,939,943,947,951,955,959],"defs",{},[923,924],"path",{"id":925,"d":926},"MJX-1-TEX-I-1D439","M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z",[923,928],{"id":929,"d":930},"MJX-1-TEX-N-28","M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z",[923,932],{"id":933,"d":934},"MJX-1-TEX-N-31","M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z",[923,936],{"id":937,"d":938},"MJX-1-TEX-N-39","M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z",[923,940],{"id":941,"d":942},"MJX-1-TEX-N-30","M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z",[923,944],{"id":945,"d":946},"MJX-1-TEX-N-29","M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z",[923,948],{"id":949,"d":950},"MJX-1-TEX-N-2F","M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z",[923,952],{"id":953,"d":954},"MJX-1-TEX-N-32","M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z",[923,956],{"id":957,"d":958},"MJX-1-TEX-N-38","M70 417T70 494T124 618T248 666Q319 666 374 624T429 515Q429 485 418 459T392 417T361 389T335 371T324 363L338 354Q352 344 366 334T382 323Q457 264 457 174Q457 95 399 37T249 -22Q159 -22 101 29T43 155Q43 263 172 335L154 348Q133 361 127 368Q70 417 70 494ZM286 386L292 390Q298 394 301 396T311 403T323 413T334 425T345 438T355 454T364 471T369 491T371 513Q371 556 342 586T275 624Q268 625 242 625Q201 625 165 599T128 534Q128 511 141 492T167 463T217 431Q224 426 228 424L286 386ZM250 21Q308 21 350 55T392 137Q392 154 387 169T375 194T353 216T330 234T301 253T274 270Q260 279 244 289T218 306L210 311Q204 311 181 294T133 239T107 157Q107 98 150 60T250 21Z",[923,960],{"id":961,"d":962},"MJX-1-TEX-N-3F","M226 668Q190 668 162 656T124 632L114 621Q116 621 119 620T130 616T145 607T157 591T162 567Q162 544 147 529T109 514T71 528T55 566Q55 625 100 661T199 704Q201 704 210 704T224 705H228Q281 705 320 692T378 656T407 612T416 567Q416 503 361 462Q267 395 247 303Q242 279 242 241V224Q242 205 239 202T222 198T205 201T202 218V249Q204 320 220 371T255 445T292 491T315 537Q317 546 317 574V587Q317 604 315 615T304 640T277 661T226 668ZM162 61Q162 89 180 105T224 121Q247 119 264 104T281 61Q281 31 264 16T222 1Q197 1 180 16T162 61Z",[964,965,969],"g",{"stroke":966,"fill":966,"stroke-width":967,"transform":968},"currentColor","0","scale(1,-1)",[964,970,972,980,988,1009,1016,1027,1052],{"dataMmlNode":971},"math",[964,973,975],{"dataMmlNode":974},"mi",[976,977],"use",{"dataC":978,"xLinkHref":979},"1D439","#MJX-1-TEX-I-1D439",[964,981,984],{"dataMmlNode":982,"transform":983},"mo","translate(749,0)",[976,985],{"dataC":986,"xLinkHref":987},"28","#MJX-1-TEX-N-28",[964,989,992,996,1001,1006],{"dataMmlNode":990,"transform":991},"mn","translate(1138,0)",[976,993],{"dataC":994,"xLinkHref":995},"31","#MJX-1-TEX-N-31",[976,997],{"dataC":998,"xLinkHref":999,"transform":1000},"39","#MJX-1-TEX-N-39","translate(500,0)",[976,1002],{"dataC":1003,"xLinkHref":1004,"transform":1005},"30","#MJX-1-TEX-N-30","translate(1000,0)",[976,1007],{"dataC":1003,"xLinkHref":1004,"transform":1008},"translate(1500,0)",[964,1010,1012],{"dataMmlNode":982,"transform":1011},"translate(3138,0)",[976,1013],{"dataC":1014,"xLinkHref":1015},"29","#MJX-1-TEX-N-29",[964,1017,1021],{"dataMmlNode":1018,"dataMjxTexclass":1019,"transform":1020},"TeXAtom","ORD","translate(3527,0)",[964,1022,1023],{"dataMmlNode":982},[976,1024],{"dataC":1025,"xLinkHref":1026},"2F","#MJX-1-TEX-N-2F",[964,1028,1031,1037],{"dataMmlNode":1029,"transform":1030},"msup","translate(4027,0)",[964,1032,1033],{"dataMmlNode":990},[976,1034],{"dataC":1035,"xLinkHref":1036},"32","#MJX-1-TEX-N-32",[964,1038,1040],{"dataMmlNode":1018,"transform":1039,"dataMjxTexclass":1019},"translate(533,363) scale(0.707)",[964,1041,1042,1044,1048,1050],{"dataMmlNode":990},[976,1043],{"dataC":994,"xLinkHref":995},[976,1045],{"dataC":1046,"xLinkHref":1047,"transform":1000},"38","#MJX-1-TEX-N-38",[976,1049],{"dataC":998,"xLinkHref":999,"transform":1005},[976,1051],{"dataC":1003,"xLinkHref":1004,"transform":1008},[964,1053,1055],{"dataMmlNode":982,"transform":1054},"translate(6024.2,0)",[976,1056],{"dataC":1057,"xLinkHref":1058},"3F","#MJX-1-TEX-N-3F",[465,1060,468],{"id":1061},"решение-2",[478,1063,481],{"id":1064},"решение-python-2",[483,1066,1068],{"className":485,"code":1067,"language":487,"meta":488,"style":488},"from functools import lru_cache\n\n\n@lru_cache(None)\ndef f(n):\n    if n == 1: \n        return 2\n    if n > 1: \n        return 2 * f(n - 1)\n\n\nfor i in range(2, 1900):\n    f(i)\n\nprint(int(f(1900) \u002F 2 ** 1890))\n",[490,1069,1070,1084,1088,1092,1105,1113,1125,1132,1144,1161,1165,1169,1197,1202,1206],{"__ignoreMap":488},[493,1071,1072,1075,1078,1081],{"class":495,"line":496},[493,1073,1074],{"class":506},"from",[493,1076,1077],{"class":514}," functools ",[493,1079,1080],{"class":506},"import",[493,1082,1083],{"class":514}," lru_cache\n",[493,1085,1086],{"class":495,"line":503},[493,1087,663],{"emptyLinePlaceholder":662},[493,1089,1090],{"class":495,"line":521},[493,1091,663],{"emptyLinePlaceholder":662},[493,1093,1094,1097,1100,1103],{"class":495,"line":540},[493,1095,1096],{"class":510},"@lru_cache",[493,1098,1099],{"class":514},"(",[493,1101,1102],{"class":533},"None",[493,1104,588],{"class":514},[493,1106,1107,1109,1111],{"class":495,"line":549},[493,1108,507],{"class":506},[493,1110,511],{"class":510},[493,1112,741],{"class":514},[493,1114,1115,1117,1119,1121,1123],{"class":495,"line":570},[493,1116,524],{"class":506},[493,1118,527],{"class":514},[493,1120,530],{"class":506},[493,1122,534],{"class":533},[493,1124,755],{"class":514},[493,1126,1127,1129],{"class":495,"line":591},[493,1128,543],{"class":506},[493,1130,1131],{"class":533}," 2\n",[493,1133,1134,1136,1138,1140,1142],{"class":495,"line":619},[493,1135,524],{"class":506},[493,1137,527],{"class":514},[493,1139,598],{"class":506},[493,1141,534],{"class":533},[493,1143,755],{"class":514},[493,1145,1146,1148,1150,1153,1155,1157,1159],{"class":495,"line":659},[493,1147,543],{"class":506},[493,1149,559],{"class":533},[493,1151,1152],{"class":506}," *",[493,1154,580],{"class":514},[493,1156,583],{"class":506},[493,1158,534],{"class":533},[493,1160,588],{"class":514},[493,1162,1163],{"class":495,"line":666},[493,1164,663],{"emptyLinePlaceholder":662},[493,1166,1167],{"class":495,"line":671},[493,1168,663],{"emptyLinePlaceholder":662},[493,1170,1171,1174,1177,1180,1183,1185,1188,1191,1194],{"class":495,"line":677},[493,1172,1173],{"class":506},"for",[493,1175,1176],{"class":514}," i ",[493,1178,1179],{"class":506},"in",[493,1181,1182],{"class":533}," range",[493,1184,1099],{"class":514},[493,1186,1187],{"class":533},"2",[493,1189,1190],{"class":514},", ",[493,1192,1193],{"class":533},"1900",[493,1195,1196],{"class":514},"):\n",[493,1198,1199],{"class":495,"line":837},[493,1200,1201],{"class":514},"    f(i)\n",[493,1203,1204],{"class":495,"line":855},[493,1205,663],{"emptyLinePlaceholder":662},[493,1207,1208,1210,1212,1215,1217,1219,1221,1224,1226,1229,1232],{"class":495,"line":860},[493,1209,680],{"class":533},[493,1211,1099],{"class":514},[493,1213,1214],{"class":533},"int",[493,1216,683],{"class":514},[493,1218,1193],{"class":533},[493,1220,630],{"class":514},[493,1222,1223],{"class":506},"\u002F",[493,1225,559],{"class":533},[493,1227,1228],{"class":506}," **",[493,1230,1231],{"class":533}," 1890",[493,1233,689],{"class":514},[402,1235,1236,1237,1239],{},"В данной и подобных задачах используем кэширование с помощью декоратора функции ",[406,1238,1096],{}," из встроенного пакета functools.\nВ задаче функция вызывает сама себя на значение n-1 и т.д. За счёт этого происходят длинные вычисления для каждого числа n. Если n будет большим числом, то без кэширования(сохранения вычисленных результатов) мы не сможем получить результат вызова функции с большим числом n.\nИспользуем декоратор @lru_cache для рекурсивной функции, затем пробегаемся в цикле по значениям n в возрастающем порядке, и для каждого значения сохраняем в кэше результат функции. Таким образом, вычисляя очередное значение, интерпретатор python будет опираться на уже готовый результат из кэша, и тем самым цепочка вызовов функции будет меньше.",[402,1241,1242],{},[406,1243,1244],{},"Ответ: 1024",[447,1246,1248],{"id":1247},"задача-4","Задача 4",[402,1250,1251],{},"Алгоритм вычисления значения функции F(n), где n — натуральное число, задан следующими соотношениями:",[402,1253,1254,1255,1257],{},"F(n) = 1 при n ≤ 2; ",[455,1256],{},"\nF(n) = n * F(n - 2), если n > 2.",[402,1259,1260],{},"Чему равно значение выражение F(3000)\u002FF(2996) ?",[465,1262,468],{"id":1263},"решение-3",[478,1265,481],{"id":1266},"решение-python-3",[483,1268,1270],{"className":485,"code":1269,"language":487,"meta":488,"style":488},"from functools import lru_cache\n\n\n@lru_cache(None)\ndef f(n):\n    if n \u003C= 2:\n        return 1\n    if n > 2:\n        return n * f(n - 2)\n\n\nfor i in range(2, 3000):\n    f(i)\n\nprint(int(f(3000) \u002F f(2996)))\n",[490,1271,1272,1282,1286,1290,1300,1308,1320,1326,1338,1354,1358,1362,1383,1387,1391],{"__ignoreMap":488},[493,1273,1274,1276,1278,1280],{"class":495,"line":496},[493,1275,1074],{"class":506},[493,1277,1077],{"class":514},[493,1279,1080],{"class":506},[493,1281,1083],{"class":514},[493,1283,1284],{"class":495,"line":503},[493,1285,663],{"emptyLinePlaceholder":662},[493,1287,1288],{"class":495,"line":521},[493,1289,663],{"emptyLinePlaceholder":662},[493,1291,1292,1294,1296,1298],{"class":495,"line":540},[493,1293,1096],{"class":510},[493,1295,1099],{"class":514},[493,1297,1102],{"class":533},[493,1299,588],{"class":514},[493,1301,1302,1304,1306],{"class":495,"line":549},[493,1303,507],{"class":506},[493,1305,511],{"class":510},[493,1307,741],{"class":514},[493,1309,1310,1312,1314,1316,1318],{"class":495,"line":570},[493,1311,524],{"class":506},[493,1313,527],{"class":514},[493,1315,750],{"class":506},[493,1317,559],{"class":533},[493,1319,537],{"class":514},[493,1321,1322,1324],{"class":495,"line":591},[493,1323,543],{"class":506},[493,1325,546],{"class":533},[493,1327,1328,1330,1332,1334,1336],{"class":495,"line":619},[493,1329,524],{"class":506},[493,1331,527],{"class":514},[493,1333,598],{"class":506},[493,1335,559],{"class":533},[493,1337,537],{"class":514},[493,1339,1340,1342,1344,1346,1348,1350,1352],{"class":495,"line":659},[493,1341,543],{"class":506},[493,1343,527],{"class":514},[493,1345,633],{"class":506},[493,1347,580],{"class":514},[493,1349,583],{"class":506},[493,1351,559],{"class":533},[493,1353,588],{"class":514},[493,1355,1356],{"class":495,"line":666},[493,1357,663],{"emptyLinePlaceholder":662},[493,1359,1360],{"class":495,"line":671},[493,1361,663],{"emptyLinePlaceholder":662},[493,1363,1364,1366,1368,1370,1372,1374,1376,1378,1381],{"class":495,"line":677},[493,1365,1173],{"class":506},[493,1367,1176],{"class":514},[493,1369,1179],{"class":506},[493,1371,1182],{"class":533},[493,1373,1099],{"class":514},[493,1375,1187],{"class":533},[493,1377,1190],{"class":514},[493,1379,1380],{"class":533},"3000",[493,1382,1196],{"class":514},[493,1384,1385],{"class":495,"line":837},[493,1386,1201],{"class":514},[493,1388,1389],{"class":495,"line":855},[493,1390,663],{"emptyLinePlaceholder":662},[493,1392,1393,1395,1397,1399,1401,1403,1405,1407,1410,1413],{"class":495,"line":860},[493,1394,680],{"class":533},[493,1396,1099],{"class":514},[493,1398,1214],{"class":533},[493,1400,683],{"class":514},[493,1402,1380],{"class":533},[493,1404,630],{"class":514},[493,1406,1223],{"class":506},[493,1408,1409],{"class":514}," f(",[493,1411,1412],{"class":533},"2996",[493,1414,1415],{"class":514},")))\n",[402,1417,1418],{},[406,1419,1420],{},"Ответ: 8994000",[447,1422,1424],{"id":1423},"задача-5","Задача 5",[402,1426,1251],{},[402,1428,1429,1430,1432,1433,1435],{},"F(n) = 1 при n = 1; ",[455,1431],{},"\nF(n) = 2 при n = 2; ",[455,1434],{},"\nF(n) = n * (n - 1) + F(n - 1) + F(n - 2), если n > 2.",[402,1437,1438],{},"Чему равно значение функции F(2023) - F(2021) - 2 * F(2020) - F(2019)?",[465,1440,468],{"id":1441},"решение-4",[478,1443,481],{"id":1444},"решение-python-4",[483,1446,1448],{"className":485,"code":1447,"language":487,"meta":488,"style":488},"from functools import lru_cache\n\n\n@lru_cache(None)\ndef f(n):\n    if n == 1: \n        return 1\n    if n == 2: \n        return 2\n    if n > 2: \n        return n * (n - 1) + f(n - 1) + f(n - 2)\n\n\nfor i in range(2, 2023):\n    f(i)\n\nprint(int(f(2023) - f(2021) - 2 * f(2020) - f(2019)))\n",[490,1449,1450,1460,1464,1468,1478,1486,1498,1504,1516,1522,1534,1570,1574,1578,1599,1603,1607],{"__ignoreMap":488},[493,1451,1452,1454,1456,1458],{"class":495,"line":496},[493,1453,1074],{"class":506},[493,1455,1077],{"class":514},[493,1457,1080],{"class":506},[493,1459,1083],{"class":514},[493,1461,1462],{"class":495,"line":503},[493,1463,663],{"emptyLinePlaceholder":662},[493,1465,1466],{"class":495,"line":521},[493,1467,663],{"emptyLinePlaceholder":662},[493,1469,1470,1472,1474,1476],{"class":495,"line":540},[493,1471,1096],{"class":510},[493,1473,1099],{"class":514},[493,1475,1102],{"class":533},[493,1477,588],{"class":514},[493,1479,1480,1482,1484],{"class":495,"line":549},[493,1481,507],{"class":506},[493,1483,511],{"class":510},[493,1485,741],{"class":514},[493,1487,1488,1490,1492,1494,1496],{"class":495,"line":570},[493,1489,524],{"class":506},[493,1491,527],{"class":514},[493,1493,530],{"class":506},[493,1495,534],{"class":533},[493,1497,755],{"class":514},[493,1499,1500,1502],{"class":495,"line":591},[493,1501,543],{"class":506},[493,1503,546],{"class":533},[493,1505,1506,1508,1510,1512,1514],{"class":495,"line":619},[493,1507,524],{"class":506},[493,1509,527],{"class":514},[493,1511,530],{"class":506},[493,1513,559],{"class":533},[493,1515,755],{"class":514},[493,1517,1518,1520],{"class":495,"line":659},[493,1519,543],{"class":506},[493,1521,1131],{"class":533},[493,1523,1524,1526,1528,1530,1532],{"class":495,"line":666},[493,1525,524],{"class":506},[493,1527,527],{"class":514},[493,1529,598],{"class":506},[493,1531,559],{"class":533},[493,1533,755],{"class":514},[493,1535,1536,1538,1540,1542,1544,1546,1548,1550,1552,1554,1556,1558,1560,1562,1564,1566,1568],{"class":495,"line":671},[493,1537,543],{"class":506},[493,1539,527],{"class":514},[493,1541,633],{"class":506},[493,1543,650],{"class":514},[493,1545,583],{"class":506},[493,1547,534],{"class":533},[493,1549,630],{"class":514},[493,1551,577],{"class":506},[493,1553,580],{"class":514},[493,1555,583],{"class":506},[493,1557,534],{"class":533},[493,1559,630],{"class":514},[493,1561,577],{"class":506},[493,1563,580],{"class":514},[493,1565,583],{"class":506},[493,1567,559],{"class":533},[493,1569,588],{"class":514},[493,1571,1572],{"class":495,"line":677},[493,1573,663],{"emptyLinePlaceholder":662},[493,1575,1576],{"class":495,"line":837},[493,1577,663],{"emptyLinePlaceholder":662},[493,1579,1580,1582,1584,1586,1588,1590,1592,1594,1597],{"class":495,"line":855},[493,1581,1173],{"class":506},[493,1583,1176],{"class":514},[493,1585,1179],{"class":506},[493,1587,1182],{"class":533},[493,1589,1099],{"class":514},[493,1591,1187],{"class":533},[493,1593,1190],{"class":514},[493,1595,1596],{"class":533},"2023",[493,1598,1196],{"class":514},[493,1600,1601],{"class":495,"line":860},[493,1602,1201],{"class":514},[493,1604,1605],{"class":495,"line":865},[493,1606,663],{"emptyLinePlaceholder":662},[493,1608,1609,1611,1613,1615,1617,1619,1621,1623,1625,1628,1630,1632,1634,1636,1638,1641,1643,1645,1647,1650],{"class":495,"line":871},[493,1610,680],{"class":533},[493,1612,1099],{"class":514},[493,1614,1214],{"class":533},[493,1616,683],{"class":514},[493,1618,1596],{"class":533},[493,1620,630],{"class":514},[493,1622,583],{"class":506},[493,1624,1409],{"class":514},[493,1626,1627],{"class":533},"2021",[493,1629,630],{"class":514},[493,1631,583],{"class":506},[493,1633,559],{"class":533},[493,1635,1152],{"class":506},[493,1637,1409],{"class":514},[493,1639,1640],{"class":533},"2020",[493,1642,630],{"class":514},[493,1644,583],{"class":506},[493,1646,1409],{"class":514},[493,1648,1649],{"class":533},"2019",[493,1651,1415],{"class":514},[402,1653,1654],{},[406,1655,1656],{},"Ответ: 12259388",[447,1658,1660],{"id":1659},"задача-6","Задача 6",[402,1662,892],{},[402,1664,1665,1666,1668],{},"F(n) = n при n ≥ 2025; ",[455,1667],{},"\nF(n) = n + F(n + 2), если n \u003C 2025.",[402,1670,1671],{},"Чему равно значение выражения F(2020) - F(2023)?",[465,1673,468],{"id":1674},"решение-5",[478,1676,481],{"id":1677},"решение-python-5",[483,1679,1681],{"className":485,"code":1680,"language":487,"meta":488,"style":488},"from functools import lru_cache\n\n\n@lru_cache(None)\ndef f(n):\n    if n >= 2025: \n        return n\n    if n \u003C 2025: \n        return n + f(n + 2)\n\n\nfor i in range(2025, 0, -1):\n    f(i)\n\nprint(f(2020) - f(2023))\n",[490,1682,1683,1693,1697,1701,1711,1719,1733,1739,1752,1768,1772,1776,1804,1808,1812],{"__ignoreMap":488},[493,1684,1685,1687,1689,1691],{"class":495,"line":496},[493,1686,1074],{"class":506},[493,1688,1077],{"class":514},[493,1690,1080],{"class":506},[493,1692,1083],{"class":514},[493,1694,1695],{"class":495,"line":503},[493,1696,663],{"emptyLinePlaceholder":662},[493,1698,1699],{"class":495,"line":521},[493,1700,663],{"emptyLinePlaceholder":662},[493,1702,1703,1705,1707,1709],{"class":495,"line":540},[493,1704,1096],{"class":510},[493,1706,1099],{"class":514},[493,1708,1102],{"class":533},[493,1710,588],{"class":514},[493,1712,1713,1715,1717],{"class":495,"line":549},[493,1714,507],{"class":506},[493,1716,511],{"class":510},[493,1718,741],{"class":514},[493,1720,1721,1723,1725,1728,1731],{"class":495,"line":570},[493,1722,524],{"class":506},[493,1724,527],{"class":514},[493,1726,1727],{"class":506},">=",[493,1729,1730],{"class":533}," 2025",[493,1732,755],{"class":514},[493,1734,1735,1737],{"class":495,"line":591},[493,1736,543],{"class":506},[493,1738,852],{"class":514},[493,1740,1741,1743,1745,1748,1750],{"class":495,"line":619},[493,1742,524],{"class":506},[493,1744,527],{"class":514},[493,1746,1747],{"class":506},"\u003C",[493,1749,1730],{"class":533},[493,1751,755],{"class":514},[493,1753,1754,1756,1758,1760,1762,1764,1766],{"class":495,"line":659},[493,1755,543],{"class":506},[493,1757,527],{"class":514},[493,1759,577],{"class":506},[493,1761,580],{"class":514},[493,1763,577],{"class":506},[493,1765,559],{"class":533},[493,1767,588],{"class":514},[493,1769,1770],{"class":495,"line":666},[493,1771,663],{"emptyLinePlaceholder":662},[493,1773,1774],{"class":495,"line":671},[493,1775,663],{"emptyLinePlaceholder":662},[493,1777,1778,1780,1782,1784,1786,1788,1791,1793,1795,1797,1799,1802],{"class":495,"line":677},[493,1779,1173],{"class":506},[493,1781,1176],{"class":514},[493,1783,1179],{"class":506},[493,1785,1182],{"class":533},[493,1787,1099],{"class":514},[493,1789,1790],{"class":533},"2025",[493,1792,1190],{"class":514},[493,1794,967],{"class":533},[493,1796,1190],{"class":514},[493,1798,583],{"class":506},[493,1800,1801],{"class":533},"1",[493,1803,1196],{"class":514},[493,1805,1806],{"class":495,"line":837},[493,1807,1201],{"class":514},[493,1809,1810],{"class":495,"line":855},[493,1811,663],{"emptyLinePlaceholder":662},[493,1813,1814,1816,1818,1820,1822,1824,1826,1828],{"class":495,"line":860},[493,1815,680],{"class":533},[493,1817,683],{"class":514},[493,1819,1640],{"class":533},[493,1821,630],{"class":514},[493,1823,583],{"class":506},[493,1825,1409],{"class":514},[493,1827,1596],{"class":533},[493,1829,689],{"class":514},[402,1831,1832,1833,1836,1837,1840],{},"Здесь мы видим что функция запускается с достаточно большими числами n, поэтому решаем с помощью декоратора функции @lru_cache.\nФункция возрастающая, поэтому запускаем функцию в цикле в начале с большими числами, а потом числа убывают (на это указывает третий параметр: шаг ",[406,1834,1835],{},"-1",") функции ",[406,1838,1839],{},"range",".",[402,1842,1843],{},[406,1844,1845],{},"Ответ: 4044",[447,1847,1849],{"id":1848},"задача-7","Задача 7",[402,1851,892],{},[402,1853,1854,1855,1857],{},"F(n) = 2 * n * n * n + 1, при n > 25 ",[455,1856],{},"\nF(n) = F(n + 2) + 2 * F(n + 3), при n ≤ 25",[402,1859,1860],{},"Определите количество натуральных значений n из отрезка [1; 1000], для которых значение F(n) кратно 11.",[465,1862,468],{"id":1863},"решение-6",[478,1865,481],{"id":1866},"решение-python-6",[483,1868,1870],{"className":485,"code":1869,"language":487,"meta":488,"style":488},"def f(n):\n    if n > 25: \n        return 2 * n * n * n + 1\n    if n \u003C= 25: \n        return f(n + 2) + 2 * f(n + 3)\n\n\nk = 0\nfor i in range(1, 1001):\n    if f(i) % 11 == 0:\n        k += 1\n\nprint(k)\n",[490,1871,1872,1880,1893,1915,1927,1954,1958,1962,1972,1993,2011,2021,2025],{"__ignoreMap":488},[493,1873,1874,1876,1878],{"class":495,"line":496},[493,1875,507],{"class":506},[493,1877,511],{"class":510},[493,1879,741],{"class":514},[493,1881,1882,1884,1886,1888,1891],{"class":495,"line":503},[493,1883,524],{"class":506},[493,1885,527],{"class":514},[493,1887,598],{"class":506},[493,1889,1890],{"class":533}," 25",[493,1892,755],{"class":514},[493,1894,1895,1897,1899,1901,1903,1905,1907,1909,1911,1913],{"class":495,"line":521},[493,1896,543],{"class":506},[493,1898,559],{"class":533},[493,1900,1152],{"class":506},[493,1902,527],{"class":514},[493,1904,633],{"class":506},[493,1906,527],{"class":514},[493,1908,633],{"class":506},[493,1910,527],{"class":514},[493,1912,577],{"class":506},[493,1914,546],{"class":533},[493,1916,1917,1919,1921,1923,1925],{"class":495,"line":540},[493,1918,524],{"class":506},[493,1920,527],{"class":514},[493,1922,750],{"class":506},[493,1924,1890],{"class":533},[493,1926,755],{"class":514},[493,1928,1929,1931,1933,1935,1937,1939,1941,1943,1945,1947,1949,1952],{"class":495,"line":549},[493,1930,543],{"class":506},[493,1932,580],{"class":514},[493,1934,577],{"class":506},[493,1936,559],{"class":533},[493,1938,630],{"class":514},[493,1940,577],{"class":506},[493,1942,559],{"class":533},[493,1944,1152],{"class":506},[493,1946,580],{"class":514},[493,1948,577],{"class":506},[493,1950,1951],{"class":533}," 3",[493,1953,588],{"class":514},[493,1955,1956],{"class":495,"line":570},[493,1957,663],{"emptyLinePlaceholder":662},[493,1959,1960],{"class":495,"line":591},[493,1961,663],{"emptyLinePlaceholder":662},[493,1963,1964,1967,1970],{"class":495,"line":619},[493,1965,1966],{"class":514},"k ",[493,1968,1969],{"class":506},"=",[493,1971,762],{"class":533},[493,1973,1974,1976,1978,1980,1982,1984,1986,1988,1991],{"class":495,"line":659},[493,1975,1173],{"class":506},[493,1977,1176],{"class":514},[493,1979,1179],{"class":506},[493,1981,1182],{"class":533},[493,1983,1099],{"class":514},[493,1985,1801],{"class":533},[493,1987,1190],{"class":514},[493,1989,1990],{"class":533},"1001",[493,1992,1196],{"class":514},[493,1994,1995,1997,2000,2002,2005,2007,2009],{"class":495,"line":666},[493,1996,524],{"class":506},[493,1998,1999],{"class":514}," f(i) ",[493,2001,556],{"class":506},[493,2003,2004],{"class":533}," 11",[493,2006,562],{"class":506},[493,2008,565],{"class":533},[493,2010,537],{"class":514},[493,2012,2013,2016,2019],{"class":495,"line":671},[493,2014,2015],{"class":514},"        k ",[493,2017,2018],{"class":506},"+=",[493,2020,546],{"class":533},[493,2022,2023],{"class":495,"line":677},[493,2024,663],{"emptyLinePlaceholder":662},[493,2026,2027,2029],{"class":495,"line":837},[493,2028,680],{"class":533},[493,2030,2031],{"class":514},"(k)\n",[402,2033,2034],{},"В начале формируем функцию f. Затем перебираем числа из диапазона от 1 до 1000.\nКаждое число подставляем в функцию f. Если значение функции f делится на 11, то мы зачитываем такое значение i.",[402,2036,2037],{},[406,2038,2039],{},"Ответ: 91",[447,2041,2043],{"id":2042},"задача-8","Задача 8",[402,2045,2046],{},"Определите сколько символов * выведет эта функция при вызове f(35):",[483,2048,2050],{"className":485,"code":2049,"language":487,"meta":488,"style":488},"def f(n):\n    print(\"*\")\n    if n >= 1:\n        print(\"*\")\n        f(n - 1)\n        f(n - 2)\n        print(\"*\")\n",[490,2051,2052,2060,2073,2085,2096,2107,2117],{"__ignoreMap":488},[493,2053,2054,2056,2058],{"class":495,"line":496},[493,2055,507],{"class":506},[493,2057,511],{"class":510},[493,2059,741],{"class":514},[493,2061,2062,2065,2067,2071],{"class":495,"line":503},[493,2063,2064],{"class":533},"    print",[493,2066,1099],{"class":514},[493,2068,2070],{"class":2069},"sYBdl","\"*\"",[493,2072,588],{"class":514},[493,2074,2075,2077,2079,2081,2083],{"class":495,"line":521},[493,2076,524],{"class":506},[493,2078,527],{"class":514},[493,2080,1727],{"class":506},[493,2082,534],{"class":533},[493,2084,537],{"class":514},[493,2086,2087,2090,2092,2094],{"class":495,"line":540},[493,2088,2089],{"class":533},"        print",[493,2091,1099],{"class":514},[493,2093,2070],{"class":2069},[493,2095,588],{"class":514},[493,2097,2098,2101,2103,2105],{"class":495,"line":549},[493,2099,2100],{"class":514},"        f(n ",[493,2102,583],{"class":506},[493,2104,534],{"class":533},[493,2106,588],{"class":514},[493,2108,2109,2111,2113,2115],{"class":495,"line":570},[493,2110,2100],{"class":514},[493,2112,583],{"class":506},[493,2114,559],{"class":533},[493,2116,588],{"class":514},[493,2118,2119,2121,2123,2125],{"class":495,"line":591},[493,2120,2089],{"class":533},[493,2122,1099],{"class":514},[493,2124,2070],{"class":2069},[493,2126,588],{"class":514},[465,2128,468],{"id":2129},"решение-7",[478,2131,481],{"id":2132},"решение-python-7",[483,2134,2136],{"className":485,"code":2135,"language":487,"meta":488,"style":488},"def f(n):\n    global s\n    s += 1\n    if n >= 1:\n        s += 1\n        f(n - 1)\n        f(n - 2)\n        s += 1\n\n\ns = 0\nf(35)\nprint(s)\n",[490,2137,2138,2146,2154,2163,2175,2184,2194,2204,2212,2216,2220,2229,2239],{"__ignoreMap":488},[493,2139,2140,2142,2144],{"class":495,"line":496},[493,2141,507],{"class":506},[493,2143,511],{"class":510},[493,2145,741],{"class":514},[493,2147,2148,2151],{"class":495,"line":503},[493,2149,2150],{"class":506},"    global",[493,2152,2153],{"class":514}," s\n",[493,2155,2156,2159,2161],{"class":495,"line":521},[493,2157,2158],{"class":514},"    s ",[493,2160,2018],{"class":506},[493,2162,546],{"class":533},[493,2164,2165,2167,2169,2171,2173],{"class":495,"line":540},[493,2166,524],{"class":506},[493,2168,527],{"class":514},[493,2170,1727],{"class":506},[493,2172,534],{"class":533},[493,2174,537],{"class":514},[493,2176,2177,2180,2182],{"class":495,"line":549},[493,2178,2179],{"class":514},"        s ",[493,2181,2018],{"class":506},[493,2183,546],{"class":533},[493,2185,2186,2188,2190,2192],{"class":495,"line":570},[493,2187,2100],{"class":514},[493,2189,583],{"class":506},[493,2191,534],{"class":533},[493,2193,588],{"class":514},[493,2195,2196,2198,2200,2202],{"class":495,"line":591},[493,2197,2100],{"class":514},[493,2199,583],{"class":506},[493,2201,559],{"class":533},[493,2203,588],{"class":514},[493,2205,2206,2208,2210],{"class":495,"line":619},[493,2207,2179],{"class":514},[493,2209,2018],{"class":506},[493,2211,546],{"class":533},[493,2213,2214],{"class":495,"line":659},[493,2215,663],{"emptyLinePlaceholder":662},[493,2217,2218],{"class":495,"line":666},[493,2219,663],{"emptyLinePlaceholder":662},[493,2221,2222,2225,2227],{"class":495,"line":671},[493,2223,2224],{"class":514},"s ",[493,2226,1969],{"class":506},[493,2228,762],{"class":533},[493,2230,2231,2234,2237],{"class":495,"line":677},[493,2232,2233],{"class":514},"f(",[493,2235,2236],{"class":533},"35",[493,2238,588],{"class":514},[493,2240,2241,2243],{"class":495,"line":837},[493,2242,680],{"class":533},[493,2244,2245],{"class":514},"(s)\n",[402,2247,2248,2249,2252,2253,2256,2257,2259,2260,2262,2263,2266,2267,2269,2270,2272],{},"Внутри функции ссылаемся на глобальную переменную ",[406,2250,2251],{},"s"," через оператор ",[406,2254,2255],{},"global",", которая будет подсчитывать количество напечатанных звёздочек.\nЗа счёт оператора ",[406,2258,2255],{}," переменную ",[406,2261,2251],{}," интерпретатору видно при любом вызове функции, и при каждом вызове функции она будет одна и та же.\nВместо печати звёздочек пишем конструкцию ",[406,2264,2265],{},"s += 1",", чтобы посчитать.\nВ основной части программы перед первым запуском функции переменной ",[406,2268,2251],{}," присваиваем ",[406,2271,967],{},".\nПрограмма может медленно работать из-за большой глубины рекурсии, но через минуту выведет ответ.",[402,2274,2275],{},[406,2276,2277],{},"Ответ: 96631265",[447,2279,2281],{"id":2280},"задача-9-демоверсия-егэ-2024","Задача 9 (Демоверсия ЕГЭ 2024)",[402,2283,892],{},[402,2285,2286,2287,2289],{},"F(n) = n при n > 2024; ",[455,2288],{},"\nF(n) = n × F(n + 1), если n ≤ 2024.",[402,2291,2292],{},"Чему равно значение выражения F(2022) \u002F F(2024)?",[465,2294,468],{"id":2295},"решение-8",[478,2297,481],{"id":2298},"решение-python-8",[483,2300,2302],{"className":485,"code":2301,"language":487,"meta":488,"style":488},"from functools import lru_cache\n\n@lru_cache(None)\ndef f(n):\n    if n > 2024:\n        return n\n    return n * f(n + 1)\n    \nprint(int(f(2022) \u002F f(2024)))\n",[490,2303,2304,2314,2318,2328,2336,2349,2355,2372,2377],{"__ignoreMap":488},[493,2305,2306,2308,2310,2312],{"class":495,"line":496},[493,2307,1074],{"class":506},[493,2309,1077],{"class":514},[493,2311,1080],{"class":506},[493,2313,1083],{"class":514},[493,2315,2316],{"class":495,"line":503},[493,2317,663],{"emptyLinePlaceholder":662},[493,2319,2320,2322,2324,2326],{"class":495,"line":521},[493,2321,1096],{"class":510},[493,2323,1099],{"class":514},[493,2325,1102],{"class":533},[493,2327,588],{"class":514},[493,2329,2330,2332,2334],{"class":495,"line":540},[493,2331,507],{"class":506},[493,2333,511],{"class":510},[493,2335,741],{"class":514},[493,2337,2338,2340,2342,2344,2347],{"class":495,"line":549},[493,2339,524],{"class":506},[493,2341,527],{"class":514},[493,2343,598],{"class":506},[493,2345,2346],{"class":533}," 2024",[493,2348,537],{"class":514},[493,2350,2351,2353],{"class":495,"line":570},[493,2352,543],{"class":506},[493,2354,852],{"class":514},[493,2356,2357,2360,2362,2364,2366,2368,2370],{"class":495,"line":591},[493,2358,2359],{"class":506},"    return",[493,2361,527],{"class":514},[493,2363,633],{"class":506},[493,2365,580],{"class":514},[493,2367,577],{"class":506},[493,2369,534],{"class":533},[493,2371,588],{"class":514},[493,2373,2374],{"class":495,"line":619},[493,2375,2376],{"class":514},"    \n",[493,2378,2379,2381,2383,2385,2387,2390,2392,2394,2396,2399],{"class":495,"line":659},[493,2380,680],{"class":533},[493,2382,1099],{"class":514},[493,2384,1214],{"class":533},[493,2386,683],{"class":514},[493,2388,2389],{"class":533},"2022",[493,2391,630],{"class":514},[493,2393,1223],{"class":506},[493,2395,1409],{"class":514},[493,2397,2398],{"class":533},"2024",[493,2400,1415],{"class":514},[402,2402,2403,2404,2406,2407,2410,2411,2414,2415,2418,2419,2422,2423,2426,2427,2430],{},"Чтобы уменьшить цепочку вызовов функции, используется декоратор ",[406,2405,1096],{}," из встроенного модуля ",[406,2408,2409],{},"functools",".\nЕсли его не использовать, то получим ошибку: ",[406,2412,2413],{},"RecursionError: maximum recursion depth exceeded in comparison",".\nФункцию пишем с двумя условиями(как по условию задачи) и что функция в одном из случаев вызывает сама себя.\nНе забываем декорировать её(сразу перед её определением) как ",[406,2416,2417],{},"@lru_cache(None)",".\nОпять же достаточно прописать одно условие где ",[406,2420,2421],{},"n > 2024",", второе указать как инструкцию ",[406,2424,2425],{},"return",", потому что рассматриваются все возможные значения ",[406,2428,2429],{},"n"," только с обратным знаком(тогда нет смысла прописывать новое условие можно просто записать return).",[402,2432,2433],{},[406,2434,2435],{},"Ответ: 4090506",[447,2437,2439],{"id":2438},"задача-10-демоверсия-егэ-2025","Задача 10 (Демоверсия ЕГЭ 2025)",[402,2441,892],{},[402,2443,1429,2444,2446],{},[455,2445],{},"\nF(n) = (n – 1)× F(n − 1), если n > 1.",[402,2448,2449],{},"Чему равно значение выражения (F(2024) + 2 × F(2023)) \u002F F(2022)?",[465,2451,468],{"id":2452},"решение-9",[478,2454,481],{"id":2455},"решение-python-9",[483,2457,2459],{"className":485,"code":2458,"language":487,"meta":488,"style":488},"from functools import lru_cache\n\n\n@lru_cache(None)\ndef f(n):\n    if n == 1:\n        return 1\n    return (n - 1) * f(n - 1)\n\n\nfor i in range(1, 2024):\n    f(i)\n\nprint(int((f(2024) + 2 * f(2023)) \u002F f(2022)))\n",[490,2460,2461,2471,2475,2479,2489,2497,2509,2515,2537,2541,2545,2565,2569,2573],{"__ignoreMap":488},[493,2462,2463,2465,2467,2469],{"class":495,"line":496},[493,2464,1074],{"class":506},[493,2466,1077],{"class":514},[493,2468,1080],{"class":506},[493,2470,1083],{"class":514},[493,2472,2473],{"class":495,"line":503},[493,2474,663],{"emptyLinePlaceholder":662},[493,2476,2477],{"class":495,"line":521},[493,2478,663],{"emptyLinePlaceholder":662},[493,2480,2481,2483,2485,2487],{"class":495,"line":540},[493,2482,1096],{"class":510},[493,2484,1099],{"class":514},[493,2486,1102],{"class":533},[493,2488,588],{"class":514},[493,2490,2491,2493,2495],{"class":495,"line":549},[493,2492,507],{"class":506},[493,2494,511],{"class":510},[493,2496,741],{"class":514},[493,2498,2499,2501,2503,2505,2507],{"class":495,"line":570},[493,2500,524],{"class":506},[493,2502,527],{"class":514},[493,2504,530],{"class":506},[493,2506,534],{"class":533},[493,2508,537],{"class":514},[493,2510,2511,2513],{"class":495,"line":591},[493,2512,543],{"class":506},[493,2514,546],{"class":533},[493,2516,2517,2519,2521,2523,2525,2527,2529,2531,2533,2535],{"class":495,"line":619},[493,2518,2359],{"class":506},[493,2520,650],{"class":514},[493,2522,583],{"class":506},[493,2524,534],{"class":533},[493,2526,630],{"class":514},[493,2528,633],{"class":506},[493,2530,580],{"class":514},[493,2532,583],{"class":506},[493,2534,534],{"class":533},[493,2536,588],{"class":514},[493,2538,2539],{"class":495,"line":659},[493,2540,663],{"emptyLinePlaceholder":662},[493,2542,2543],{"class":495,"line":666},[493,2544,663],{"emptyLinePlaceholder":662},[493,2546,2547,2549,2551,2553,2555,2557,2559,2561,2563],{"class":495,"line":671},[493,2548,1173],{"class":506},[493,2550,1176],{"class":514},[493,2552,1179],{"class":506},[493,2554,1182],{"class":533},[493,2556,1099],{"class":514},[493,2558,1801],{"class":533},[493,2560,1190],{"class":514},[493,2562,2398],{"class":533},[493,2564,1196],{"class":514},[493,2566,2567],{"class":495,"line":677},[493,2568,1201],{"class":514},[493,2570,2571],{"class":495,"line":837},[493,2572,663],{"emptyLinePlaceholder":662},[493,2574,2575,2577,2579,2581,2584,2586,2588,2590,2592,2594,2596,2598,2601,2603,2605,2607],{"class":495,"line":855},[493,2576,680],{"class":533},[493,2578,1099],{"class":514},[493,2580,1214],{"class":533},[493,2582,2583],{"class":514},"((f(",[493,2585,2398],{"class":533},[493,2587,630],{"class":514},[493,2589,577],{"class":506},[493,2591,559],{"class":533},[493,2593,1152],{"class":506},[493,2595,1409],{"class":514},[493,2597,1596],{"class":533},[493,2599,2600],{"class":514},")) ",[493,2602,1223],{"class":506},[493,2604,1409],{"class":514},[493,2606,2389],{"class":533},[493,2608,1415],{"class":514},[402,2610,2403,2611,2406,2613,2410,2615,2617,2618,2621,2622,2624,2625,2422,2628,2426,2630,2632,2633,2635,2636,2638],{},[406,2612,1096],{},[406,2614,2409],{},[406,2616,2413],{},". Поэтому вначале напишем ",[406,2619,2620],{},"from functools import lru_cache",".\nФункцию пишем с двумя условиями(как по условию задачи) и что функция в одном из случаев вызывает сама себя. Не забываем декорировать её(сразу перед её определением) как ",[406,2623,2417],{},". Опять же достаточно прописать одно условие где ",[406,2626,2627],{},"n == 1",[406,2629,2425],{},[406,2631,2429],{},".\nПробегаемся в цикле по значениям ",[406,2634,2429],{}," в возрастающем порядке, и для каждого значения сохраняем результаты функции.\nВ конце в функции ",[406,2637,680],{}," делаем вызов согласно условию из выражения задачи и получаем ответ.",[478,2640,2642],{"id":2641},"аналитическое-решение-задачи","Аналитическое решение задачи:",[402,2644,2645,2646,2649,2650,2652,2653],{},"Начнём расписывать выражение с функциями(p.s. Необходимо упростить выражение делая вызовы функций, которые больше чем знаменатель): ",[406,2647,2648],{},"(F(2024) + 2 * F(2023)) \u002F F(2022)"," ",[455,2651],{},"\nПолучается: ",[406,2654,2655],{},"(F(2024) + 2 * F(2023)) \u002F F(2022) = (2023 * F(2023) + 2 * F(2023)) \u002F F(2022) = (2023 * 2022 * F(2022) + 2 * 2022 * F(2022)) \u002F F(2022) = 2023 * 2022 + 2 * 2022 = 4090506 + 4044 = 4094550",[402,2657,2658],{},[406,2659,2660],{},"Ответ: 4094550",[447,2662,2664],{"id":2663},"задача-11-демоверсия-егэ-2026","Задача 11 (Демоверсия ЕГЭ 2026)",[402,2666,2667],{},"Алгоритм вычисления значения функции F(n) и G(n), где n – целое число, задан следующими соотношениями:",[402,2669,2670,2671,2673,2674,2676],{},"F(n) = 2 × (G(n-3)+8); ",[455,2672],{},"\nG(n) = 2 × n, если n \u003C 10; ",[455,2675],{},"\nG(n) = G(n-2) + 1, если n ≥ 10.",[402,2678,2679],{},"Чему равно значение выражения F(15548)?",[465,2681,468],{"id":2682},"решение-10",[478,2684,481],{"id":2685},"решение-python-10",[483,2687,2689],{"className":485,"code":2688,"language":487,"meta":488,"style":488},"from functools import lru_cache\n\n@lru_cache(None)\ndef g(n):\n    if n >= 10:\n        return g(n - 2) + 1\n    return 2 * n\n\n@lru_cache(None)\ndef f(n):\n    return 2 * (g(n - 3) + 8)\n\nfor i in range(15548):\n    f(i)\n\nprint(int(f(15548)))\n",[490,2690,2691,2701,2705,2715,2724,2737,2754,2764,2768,2778,2786,2810,2814,2831,2835,2839],{"__ignoreMap":488},[493,2692,2693,2695,2697,2699],{"class":495,"line":496},[493,2694,1074],{"class":506},[493,2696,1077],{"class":514},[493,2698,1080],{"class":506},[493,2700,1083],{"class":514},[493,2702,2703],{"class":495,"line":503},[493,2704,663],{"emptyLinePlaceholder":662},[493,2706,2707,2709,2711,2713],{"class":495,"line":521},[493,2708,1096],{"class":510},[493,2710,1099],{"class":514},[493,2712,1102],{"class":533},[493,2714,588],{"class":514},[493,2716,2717,2719,2722],{"class":495,"line":540},[493,2718,507],{"class":506},[493,2720,2721],{"class":510}," g",[493,2723,741],{"class":514},[493,2725,2726,2728,2730,2732,2735],{"class":495,"line":549},[493,2727,524],{"class":506},[493,2729,527],{"class":514},[493,2731,1727],{"class":506},[493,2733,2734],{"class":533}," 10",[493,2736,537],{"class":514},[493,2738,2739,2741,2744,2746,2748,2750,2752],{"class":495,"line":570},[493,2740,543],{"class":506},[493,2742,2743],{"class":514}," g(n ",[493,2745,583],{"class":506},[493,2747,559],{"class":533},[493,2749,630],{"class":514},[493,2751,577],{"class":506},[493,2753,546],{"class":533},[493,2755,2756,2758,2760,2762],{"class":495,"line":591},[493,2757,2359],{"class":506},[493,2759,559],{"class":533},[493,2761,1152],{"class":506},[493,2763,852],{"class":514},[493,2765,2766],{"class":495,"line":619},[493,2767,663],{"emptyLinePlaceholder":662},[493,2769,2770,2772,2774,2776],{"class":495,"line":659},[493,2771,1096],{"class":510},[493,2773,1099],{"class":514},[493,2775,1102],{"class":533},[493,2777,588],{"class":514},[493,2779,2780,2782,2784],{"class":495,"line":666},[493,2781,507],{"class":506},[493,2783,511],{"class":510},[493,2785,741],{"class":514},[493,2787,2788,2790,2792,2794,2797,2799,2801,2803,2805,2808],{"class":495,"line":671},[493,2789,2359],{"class":506},[493,2791,559],{"class":533},[493,2793,1152],{"class":506},[493,2795,2796],{"class":514}," (g(n ",[493,2798,583],{"class":506},[493,2800,1951],{"class":533},[493,2802,630],{"class":514},[493,2804,577],{"class":506},[493,2806,2807],{"class":533}," 8",[493,2809,588],{"class":514},[493,2811,2812],{"class":495,"line":677},[493,2813,663],{"emptyLinePlaceholder":662},[493,2815,2816,2818,2820,2822,2824,2826,2829],{"class":495,"line":837},[493,2817,1173],{"class":506},[493,2819,1176],{"class":514},[493,2821,1179],{"class":506},[493,2823,1182],{"class":533},[493,2825,1099],{"class":514},[493,2827,2828],{"class":533},"15548",[493,2830,1196],{"class":514},[493,2832,2833],{"class":495,"line":855},[493,2834,1201],{"class":514},[493,2836,2837],{"class":495,"line":860},[493,2838,663],{"emptyLinePlaceholder":662},[493,2840,2841,2843,2845,2847,2849,2851],{"class":495,"line":865},[493,2842,680],{"class":533},[493,2844,1099],{"class":514},[493,2846,1214],{"class":533},[493,2848,683],{"class":514},[493,2850,2828],{"class":533},[493,2852,1415],{"class":514},[402,2854,2403,2855,2406,2857,2410,2859,2617,2861,2863,2864,2624,2866,2422,2869,2426,2871,2632,2873,2635,2875,2638],{},[406,2856,1096],{},[406,2858,2409],{},[406,2860,2413],{},[406,2862,2620],{},".\nФункции пишем с условиями(как по условию задачи) и что функция в одном из случаев вызывает сама себя. Не забываем декорировать её(сразу перед её определением) как ",[406,2865,2417],{},[406,2867,2868],{},"n >= 10",[406,2870,2425],{},[406,2872,2429],{},[406,2874,2429],{},[406,2876,680],{},[402,2878,2879],{},[406,2880,2881],{},"Ответ: 15588",[402,2883,2884,2885,2888,2889,2892],{},"Попробуйте сами запустить код в окне ниже с интерпретатором Python и повторите примеры из статьи чтобы самим увидеть и понять как всё это работает. Для этого в ячейке с кодом нажмите клавиши на клавиатуре ",[406,2886,2887],{},"Shift+Enter"," или запустите код через ",[406,2890,2891],{},"кнопку Run"," по значку ▶.",[2894,2895],"jypiter",{},[2897,2898,2899],"style",{},"\nmjx-container[jax=\"SVG\"] {\n  direction: ltr;\n}\n\nmjx-container[jax=\"SVG\"] > svg {\n  overflow: visible;\n  min-height: 1px;\n  min-width: 1px;\n}\n\nmjx-container[jax=\"SVG\"] > svg a {\n  fill: blue;\n  stroke: blue;\n}\n\nmjx-container[jax=\"SVG\"][display=\"true\"] {\n  display: block;\n  text-align: center;\n  margin: 1em 0;\n}\n\nmjx-container[jax=\"SVG\"][display=\"true\"][width=\"full\"] {\n  display: flex;\n}\n\nmjx-container[jax=\"SVG\"][justify=\"left\"] {\n  text-align: left;\n}\n\nmjx-container[jax=\"SVG\"][justify=\"right\"] {\n  text-align: right;\n}\n\ng[data-mml-node=\"merror\"] > g {\n  fill: red;\n  stroke: red;\n}\n\ng[data-mml-node=\"merror\"] > rect[data-background] {\n  fill: yellow;\n  stroke: none;\n}\n\ng[data-mml-node=\"mtable\"] > line[data-line], svg[data-table] > g > line[data-line] {\n  stroke-width: 70px;\n  fill: none;\n}\n\ng[data-mml-node=\"mtable\"] > rect[data-frame], svg[data-table] > g > rect[data-frame] {\n  stroke-width: 70px;\n  fill: none;\n}\n\ng[data-mml-node=\"mtable\"] > .mjx-dashed, svg[data-table] > g > .mjx-dashed {\n  stroke-dasharray: 140;\n}\n\ng[data-mml-node=\"mtable\"] > .mjx-dotted, svg[data-table] > g > .mjx-dotted {\n  stroke-linecap: round;\n  stroke-dasharray: 0,140;\n}\n\ng[data-mml-node=\"mtable\"] > g > svg {\n  overflow: visible;\n}\n\n[jax=\"SVG\"] mjx-tool {\n  display: inline-block;\n  position: relative;\n  width: 0;\n  height: 0;\n}\n\n[jax=\"SVG\"] mjx-tool > mjx-tip {\n  position: absolute;\n  top: 0;\n  left: 0;\n}\n\nmjx-tool > mjx-tip {\n  display: inline-block;\n  padding: .2em;\n  border: 1px solid #888;\n  font-size: 70%;\n  background-color: #F8F8F8;\n  color: black;\n  box-shadow: 2px 2px 5px #AAAAAA;\n}\n\ng[data-mml-node=\"maction\"][data-toggle] {\n  cursor: pointer;\n}\n\nmjx-status {\n  display: block;\n  position: fixed;\n  left: 1em;\n  bottom: 1em;\n  min-width: 25%;\n  padding: .2em .4em;\n  border: 1px solid #888;\n  font-size: 90%;\n  background-color: #F8F8F8;\n  color: black;\n}\n\nforeignObject[data-mjx-xml] {\n  font-family: initial;\n  line-height: normal;\n  overflow: visible;\n}\n\nmjx-container[jax=\"SVG\"] path[data-c], mjx-container[jax=\"SVG\"] use[data-c] {\n  stroke-width: 3;\n}\n",[2897,2901,2902],{},"html pre.shiki code .sAwPA, html code.shiki .sAwPA{--shiki-default:#6A737D}html pre.shiki code .sD7c4, html code.shiki .sD7c4{--shiki-default:#D73A49}html pre.shiki code .s7eDp, html code.shiki .s7eDp{--shiki-default:#6F42C1}html pre.shiki code .sgsFI, html code.shiki .sgsFI{--shiki-default:#24292E}html pre.shiki code .sYu0t, html code.shiki .sYu0t{--shiki-default:#005CC5}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html pre.shiki code .sYBdl, html code.shiki .sYBdl{--shiki-default:#032F62}",{"title":488,"searchDepth":503,"depth":549,"links":2904},[2905],{"id":399,"depth":503,"text":400,"children":2906},[2907,2912,2917,2922,2927,2932,2937,2942,2947,2952,2958],{"id":449,"depth":540,"text":450,"children":2908},[2909],{"id":467,"depth":549,"text":468,"children":2910},[2911],{"id":480,"depth":570,"text":481},{"id":697,"depth":540,"text":698,"children":2913},[2914],{"id":719,"depth":549,"text":468,"children":2915},[2916],{"id":722,"depth":570,"text":481},{"id":888,"depth":540,"text":889,"children":2918},[2919],{"id":1061,"depth":549,"text":468,"children":2920},[2921],{"id":1064,"depth":570,"text":481},{"id":1247,"depth":540,"text":1248,"children":2923},[2924],{"id":1263,"depth":549,"text":468,"children":2925},[2926],{"id":1266,"depth":570,"text":481},{"id":1423,"depth":540,"text":1424,"children":2928},[2929],{"id":1441,"depth":549,"text":468,"children":2930},[2931],{"id":1444,"depth":570,"text":481},{"id":1659,"depth":540,"text":1660,"children":2933},[2934],{"id":1674,"depth":549,"text":468,"children":2935},[2936],{"id":1677,"depth":570,"text":481},{"id":1848,"depth":540,"text":1849,"children":2938},[2939],{"id":1863,"depth":549,"text":468,"children":2940},[2941],{"id":1866,"depth":570,"text":481},{"id":2042,"depth":540,"text":2043,"children":2943},[2944],{"id":2129,"depth":549,"text":468,"children":2945},[2946],{"id":2132,"depth":570,"text":481},{"id":2280,"depth":540,"text":2281,"children":2948},[2949],{"id":2295,"depth":549,"text":468,"children":2950},[2951],{"id":2298,"depth":570,"text":481},{"id":2438,"depth":540,"text":2439,"children":2953},[2954],{"id":2452,"depth":549,"text":468,"children":2955},[2956,2957],{"id":2455,"depth":570,"text":481},{"id":2641,"depth":570,"text":2642},{"id":2663,"depth":540,"text":2664,"children":2959},[2960],{"id":2682,"depth":549,"text":468,"children":2961},[2962],{"id":2685,"depth":570,"text":481},"2025-09-04","Рекурсивные алгоритмы","md","images\u002Fblog\u002Fege\u002Ftask16\u002Fimg.png",{},18,{"title":43,"description":2964},"-bcaRrfrZX6U16eBiG1MC6aQsfouP_fdqN5_xLRvmOw",[2972,2974],{"title":39,"path":40,"stem":41,"description":2973,"children":-1},"Преобразование логических выражений",{"title":47,"path":48,"stem":49,"description":2975,"children":-1},"Обработка числовой последовательности в файле",1780737504481]