From ee548c8d2eed31e3c9cd0730e51eac24fcd8ca6e Mon Sep 17 00:00:00 2001 From: gghxq Date: Sat, 5 Oct 2024 18:04:05 +0300 Subject: [PATCH 01/12] Create lab0.cpp --- lab0.cpp | 30 ++++++++++++++++++++++++++++++ 1 file changed, 30 insertions(+) create mode 100644 lab0.cpp diff --git a/lab0.cpp b/lab0.cpp new file mode 100644 index 00000000..ec14d6a4 --- /dev/null +++ b/lab0.cpp @@ -0,0 +1,30 @@ +#include + +int secondLargest(int arr[], int size) { + int first = -1; + int second = -1; + + for (int i = 0; i < size; i++) { + if (arr[i] > first) { + second = first; + first = arr[i]; + } + else if (arr[i] > second and arr[i] != first) { + second = arr[i]; + } + } + + return second; +} + +int main() { + int array[] = {1, 5, 2, 54, 23, 56, 7}; + int size = sizeof(array) / sizeof(array[0]); + + int answer = secondLargest(array, size); + + std::cout << answer; + + return 0; + +} From 83a1cc284b46d54fd09e39880d6e9de892a41b95 Mon Sep 17 00:00:00 2001 From: gghxq Date: Sun, 20 Oct 2024 17:02:52 +0300 Subject: [PATCH 02/12] lab0 --- lab0.cpp | 30 ++++++++++++++++++++++++++++++ 1 file changed, 30 insertions(+) create mode 100644 lab0.cpp diff --git a/lab0.cpp b/lab0.cpp new file mode 100644 index 00000000..ec14d6a4 --- /dev/null +++ b/lab0.cpp @@ -0,0 +1,30 @@ +#include + +int secondLargest(int arr[], int size) { + int first = -1; + int second = -1; + + for (int i = 0; i < size; i++) { + if (arr[i] > first) { + second = first; + first = arr[i]; + } + else if (arr[i] > second and arr[i] != first) { + second = arr[i]; + } + } + + return second; +} + +int main() { + int array[] = {1, 5, 2, 54, 23, 56, 7}; + int size = sizeof(array) / sizeof(array[0]); + + int answer = secondLargest(array, size); + + std::cout << answer; + + return 0; + +} From 4e95fea10b4f0a7fb9b2310f3b282e49cffba999 Mon Sep 17 00:00:00 2001 From: gghxq Date: Tue, 14 Jan 2025 20:25:25 +0300 Subject: [PATCH 03/12] c3100_tregubov_vadim_lab3 leetcode 330 --- c3100_tregubov_vadim_lab3 | 34 ++++++++++++++++++++++++++++++++++ 1 file changed, 34 insertions(+) create mode 100644 c3100_tregubov_vadim_lab3 diff --git a/c3100_tregubov_vadim_lab3 b/c3100_tregubov_vadim_lab3 new file mode 100644 index 00000000..ff9e089f --- /dev/null +++ b/c3100_tregubov_vadim_lab3 @@ -0,0 +1,34 @@ +#include +#include +#include +#include +using namespace std; + +void fisherYatesShuffle(vector& arr) { + random_device rd; // O(1) + mt19937 gen(rd()); // O(1) + + for (int i = arr.size() - 1; i > 0; i--) { // O(N) + uniform_int_distribution<> dis(0, i); // O(1) + int j = dis(gen); // O(1) + swap(arr[i], arr[j]); // O(1) + } +} + +int main() { + int n = 10; // O(1) + vector arr(n); // O(N) + + for (int i = 0; i < n; i++) { // O(N) + arr[i] = i + 1; // O(1) + } + + fisherYatesShuffle(arr); // O(N) + + for (int num : arr) { // O(N) + cout << num << " "; // O(1) + } + cout << endl; // O(1) + + return 0; +} From c905923c3d9cea66289baf84c525cbfe83714206 Mon Sep 17 00:00:00 2001 From: gghxq Date: Fri, 17 Jan 2025 19:05:58 +0300 Subject: [PATCH 04/12] Create C3100_tregubov_vadim_lab4.cpp --- C3100_tregubov_vadim_lab4.cpp | 92 +++++++++++++++++++++++++++++++++++ 1 file changed, 92 insertions(+) create mode 100644 C3100_tregubov_vadim_lab4.cpp diff --git a/C3100_tregubov_vadim_lab4.cpp b/C3100_tregubov_vadim_lab4.cpp new file mode 100644 index 00000000..55d89156 --- /dev/null +++ b/C3100_tregubov_vadim_lab4.cpp @@ -0,0 +1,92 @@ +#include +#include +#include +#include +#include + +using namespace std; + +// Функция для подсчета суммы отклонений в кластере +double calculateClusterCost(const vector& arr, int start, int end) { + double mean = 0; + for (int i = start; i <= end; ++i) { + mean += arr[i]; + } + mean /= (end - start + 1); // Среднее значение кластера + + double cost = 0; + for (int i = start; i <= end; ++i) { + cost += abs(arr[i] - mean); // Сумма модулей отклонений + } + return cost; +} + +// Рекурсивная функция для полного перебора кластеров +double findOptimalClustering(const vector& arr, int k, int start, vector>& memo) { + if (k == 1) { + // Базовый случай: один кластер от start до конца массива + return calculateClusterCost(arr, start, arr.size() - 1); + } + if (memo[start][k] != -1) { + // Используем мемоизацию для предотвращения повторных вычислений + return memo[start][k]; + } + + double minCost = numeric_limits::max(); // Инициализируем минимальную стоимость большим значением + + // Перебираем все возможные позиции разделения кластера + for (int i = start; i < arr.size() - (k - 1); ++i) { + double currentCost = calculateClusterCost(arr, start, i) + + findOptimalClustering(arr, k - 1, i + 1, memo); + minCost = min(minCost, currentCost); + } + + return memo[start][k] = minCost; // Сохраняем результат в таблицу мемоизации +} + +// Основная функция кластеризации +// Параметры: +// arr - массив чисел, k - количество кластеров +// Возвращает минимальную сумму отклонений + +double clusterArray(const vector& arr, int k) { + int n = arr.size(); + + // Таблица мемоизации размером O(N * K) + vector> memo(n, vector(k + 1, -1)); + + return findOptimalClustering(arr, k, 0, memo); +} + +int main() { + // Пример ввода + vector arr = {1, -2, 3, 4, -5, 6}; // Массив чисел + int k = 3; // Количество кластеров + + // Вызов алгоритма кластеризации + double result = clusterArray(arr, k); + + // Вывод результата + cout << "Минимальная сумма отклонений: " << result << endl; + + return 0; +} + +/* +Память: +1. memo (N * (K + 1)): каждый double занимает 8 байт. Пример: N = 6, K = 3 -> 6 * 4 * 8 = 192 байта. +2. Локальные переменные (на вызов): 36 байт (4 double и int). + +В сумме: +- memo: 192 байта. +- Переменные: 36 байт. +Итого: ~228 байт. + +Время: +1. Перебор всех разбиений O(2^N). +2. Мемоизация ускоряет, но не убирает O(2^N). + +Ограничения: +1. Максимум 25 элементов в массиве. +2. K намного меньше N. +*/ From b131c4721b34974c91bee5531405ef10959cd93b Mon Sep 17 00:00:00 2001 From: gghxq Date: Fri, 17 Jan 2025 19:15:23 +0300 Subject: [PATCH 05/12] Create C3100_tregubov_vadim_lab4.cpp --- C3100_tregubov_vadim_lab4.cpp | 92 +++++++++++++++++++++++++++++++++++ 1 file changed, 92 insertions(+) create mode 100644 C3100_tregubov_vadim_lab4.cpp diff --git a/C3100_tregubov_vadim_lab4.cpp b/C3100_tregubov_vadim_lab4.cpp new file mode 100644 index 00000000..55d89156 --- /dev/null +++ b/C3100_tregubov_vadim_lab4.cpp @@ -0,0 +1,92 @@ +#include +#include +#include +#include +#include + +using namespace std; + +// Функция для подсчета суммы отклонений в кластере +double calculateClusterCost(const vector& arr, int start, int end) { + double mean = 0; + for (int i = start; i <= end; ++i) { + mean += arr[i]; + } + mean /= (end - start + 1); // Среднее значение кластера + + double cost = 0; + for (int i = start; i <= end; ++i) { + cost += abs(arr[i] - mean); // Сумма модулей отклонений + } + return cost; +} + +// Рекурсивная функция для полного перебора кластеров +double findOptimalClustering(const vector& arr, int k, int start, vector>& memo) { + if (k == 1) { + // Базовый случай: один кластер от start до конца массива + return calculateClusterCost(arr, start, arr.size() - 1); + } + if (memo[start][k] != -1) { + // Используем мемоизацию для предотвращения повторных вычислений + return memo[start][k]; + } + + double minCost = numeric_limits::max(); // Инициализируем минимальную стоимость большим значением + + // Перебираем все возможные позиции разделения кластера + for (int i = start; i < arr.size() - (k - 1); ++i) { + double currentCost = calculateClusterCost(arr, start, i) + + findOptimalClustering(arr, k - 1, i + 1, memo); + minCost = min(minCost, currentCost); + } + + return memo[start][k] = minCost; // Сохраняем результат в таблицу мемоизации +} + +// Основная функция кластеризации +// Параметры: +// arr - массив чисел, k - количество кластеров +// Возвращает минимальную сумму отклонений + +double clusterArray(const vector& arr, int k) { + int n = arr.size(); + + // Таблица мемоизации размером O(N * K) + vector> memo(n, vector(k + 1, -1)); + + return findOptimalClustering(arr, k, 0, memo); +} + +int main() { + // Пример ввода + vector arr = {1, -2, 3, 4, -5, 6}; // Массив чисел + int k = 3; // Количество кластеров + + // Вызов алгоритма кластеризации + double result = clusterArray(arr, k); + + // Вывод результата + cout << "Минимальная сумма отклонений: " << result << endl; + + return 0; +} + +/* +Память: +1. memo (N * (K + 1)): каждый double занимает 8 байт. Пример: N = 6, K = 3 -> 6 * 4 * 8 = 192 байта. +2. Локальные переменные (на вызов): 36 байт (4 double и int). + +В сумме: +- memo: 192 байта. +- Переменные: 36 байт. +Итого: ~228 байт. + +Время: +1. Перебор всех разбиений O(2^N). +2. Мемоизация ускоряет, но не убирает O(2^N). + +Ограничения: +1. Максимум 25 элементов в массиве. +2. K намного меньше N. +*/ From d42580b1a384852387b106b285133db90e2fb209 Mon Sep 17 00:00:00 2001 From: gghxq Date: Fri, 17 Jan 2025 19:55:59 +0300 Subject: [PATCH 06/12] Create lab5.cpp --- lab5.cpp | 167 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 167 insertions(+) create mode 100644 lab5.cpp diff --git a/lab5.cpp b/lab5.cpp new file mode 100644 index 00000000..6069d1a8 --- /dev/null +++ b/lab5.cpp @@ -0,0 +1,167 @@ +#include +#include +#include +#include +#include +#include + +using namespace std; + +// Сортировка методом Bucket Sort +void bucketSort(vector& arr) { + int n = arr.size(); + vector> buckets(n); + + for (double num : arr) { + int bucketIndex = static_cast(num * n); + buckets[bucketIndex].push_back(num); + } + + for (auto& bucket : buckets) { + sort(bucket.begin(), bucket.end()); + } + + int index = 0; + for (const auto& bucket : buckets) { + for (double num : bucket) { + arr[index++] = num; + } + } +} + +// Память и сложность Bucket Sort: +/* +Память: +1. Вектора для корзин: O(n). +2. Исходный массив: O(n). +Итого: O(n). + +Время: +1. Распределение по корзинам: O(n). +2. Сортировка каждой корзины: O(n log(n/k)), где k - средний размер корзины. +Итого: O(n + n log(n/k)) ≈ O(n log n) в худшем случае. +*/ + +// Сортировка методом Heap Sort +void heapify(vector& arr, int n, int i) { + int largest = i; + int left = 2 * i + 1; + int right = 2 * i + 2; + + if (left < n && arr[left] > arr[largest]) + largest = left; + + if (right < n && arr[right] > arr[largest]) + largest = right; + + if (largest != i) { + swap(arr[i], arr[largest]); + heapify(arr, n, largest); + } +} + +void heapSort(vector& arr) { + int n = arr.size(); + + for (int i = n / 2 - 1; i >= 0; i--) + heapify(arr, n, i); + + for (int i = n - 1; i >= 0; i--) { + swap(arr[0], arr[i]); + heapify(arr, i, 0); + } +} + +// Память и сложность Heap Sort: +/* +Память: +1. Исходный массив: O(n). +2. Дополнительный стек для рекурсии в heapify: O(log n). +Итого: O(n). + +Время: +1. Построение кучи: O(n). +2. Извлечение элементов: O(n log n). +Итого: O(n log n). +*/ + +// Сортировка методом Shaker Sort +void shakerSort(vector& arr) { + bool swapped = true; + int start = 0; + int end = arr.size() - 1; + + while (swapped) { + swapped = false; + + for (int i = start; i < end; ++i) { + if (arr[i] > arr[i + 1]) { + swap(arr[i], arr[i + 1]); + swapped = true; + } + } + + if (!swapped) + break; + + swapped = false; + --end; + + for (int i = end - 1; i >= start; --i) { + if (arr[i] > arr[i + 1]) { + swap(arr[i], arr[i + 1]); + swapped = true; + } + } + ++start; + } +} + +// Память и сложность Shaker Sort: +/* +Память: +1. Исходный массив: O(n). +2. Дополнительные переменные: O(1). +Итого: O(n). + +Время: +1. Худший случай: O(n^2) (если массив сильно неупорядочен). +2. Лучший случай: O(n) (если массив уже отсортирован). +*/ + +int main() { + // Пример для Bucket Sort + vector bucketArr = {0.78, 0.17, 0.39, 0.26, 0.72, 0.94, 0.21, 0.12, 0.23, 0.68}; + auto startBucket = chrono::high_resolution_clock::now(); + bucketSort(bucketArr); + auto endBucket = chrono::high_resolution_clock::now(); + for (double num : bucketArr) { + cout << num << " "; + } + cout << "\nВремя выполнения Bucket Sort: " + << chrono::duration_cast(endBucket - startBucket).count() << " микросекунд\n"; + + // Пример для Heap Sort + vector heapArr = {4, 10, 3, 5, 1}; + auto startHeap = chrono::high_resolution_clock::now(); + heapSort(heapArr); + auto endHeap = chrono::high_resolution_clock::now(); + for (int num : heapArr) { + cout << num << " "; + } + cout << "\nВремя выполнения Heap Sort: " + << chrono::duration_cast(endHeap - startHeap).count() << " микросекунд\n"; + + // Пример для Shaker Sort + vector shakerArr = {5, 3, 8, 6, 2, 7, 4, 1}; + auto startShaker = chrono::high_resolution_clock::now(); + shakerSort(shakerArr); + auto endShaker = chrono::high_resolution_clock::now(); + for (int num : shakerArr) { + cout << num << " "; + } + cout << "\nВремя выполнения Shaker Sort: " + << chrono::duration_cast(endShaker - startShaker).count() << " микросекунд\n"; + + return 0; +} From d295e71d2d492a492b28f35e501bd60ac06b30dc Mon Sep 17 00:00:00 2001 From: gghxq Date: Fri, 17 Jan 2025 19:57:22 +0300 Subject: [PATCH 07/12] =?UTF-8?q?=D0=BE=D1=82=D1=87=D0=B5=D1=82=205=20?= =?UTF-8?q?=D0=BB=D0=B0=D0=B1=D0=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...265\321\202 \320\273\320\260\320\2615.docx" | Bin 0 -> 238967 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 "\320\236\321\202\321\207\320\265\321\202 \320\273\320\260\320\2615.docx" diff --git "a/\320\236\321\202\321\207\320\265\321\202 \320\273\320\260\320\2615.docx" "b/\320\236\321\202\321\207\320\265\321\202 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zr}~G_Iv#rwZI)kUtGRFduyCY63dNHYRiz1I(6Dd$R%?_0ow~u;8?wExT;7#muEy=( zOuoENY!%H}mGw)UQSR~Y#w%44quqOID-yp2Sr2j|u{D3Dn3XEWdW91th8B+KVz62p z=xCUhj~vFo&Jh~cTiM)GKfWmN`8oCSposXI0!~Q-eiZl1CiCZ(T#mAy9CMMsyxwGPKe3LRgr@-LN-x#pVj zFAk^&P2b1SE~X*Ies3d`lKj$=i6(vlmCv$LgVON)1?Q^sRQ)rKgpk(V&nHfEW{k&+ zbl(4`W4MIM3PJh5o3~El_fmu4H9eqTUjJ`KUrP+aBx4&VJry@QV@Dli^C-&v*Aq}h zkXLTPf$|Vx0a5cme!ju>({nJka%5*ie*a$&%)xa?ZYD=T`MmrO5B`4~IS0*Tf9t*A zr<|?f?f+-*JJ|G`6qzI31Ak2UKaPb*gEap-{GT`f&y)O5KggaA)BmxBw}Gw?gSHP5 zh9#;%O-jqpFUiXjOfvTs!{bpbQVN@fw15*t+B9M$Q!e)eAhgkKTV2;_Yh=-ScO8Y8q Date: Thu, 20 Feb 2025 08:58:33 +0300 Subject: [PATCH 08/12] Create lab6.cpp --- lab6.cpp | 30 ++++++++++++++++++++++++++++++ 1 file changed, 30 insertions(+) create mode 100644 lab6.cpp diff --git a/lab6.cpp b/lab6.cpp new file mode 100644 index 00000000..bc58c4d8 --- /dev/null +++ b/lab6.cpp @@ -0,0 +1,30 @@ +class Solution { +public: + int uniquePaths(int m, int n) { + // подсчет памяти: + // - используем одномерный вектор dp размером n. + // - память: O(n), так как храним только одну строку таблицы DP. + + // асимптотика: + // - временная сложность: O(m * n), так как заполняем таблицу DP. + // - пространственная сложность: O(n), так как используем одномерный массив. + + // инициализация вектора dp: + // - dp[j] хранит количество путей до клетки (текущая строка, j). + // - изначально все элементы равны 1, так как в первой строке только один путь (вправо). + vector dp(n, 1); + + // заполнение таблицы DP: + // - для каждой строки (начиная со второй) обновляем значения dp[j]. + // - dp[j] = dp[j] (количество путей сверху) + dp[j - 1] (количество путей слева). + for (int i = 1; i < m; ++i) { + for (int j = 1; j < n; ++j) { + dp[j] += dp[j - 1]; + } + } + + // возвращаем количество путей до конечной клетки (m-1, n-1): + // - dp[n - 1] содержит результат для последней клетки. + return dp[n - 1]; + } +}; From ae3f063ab084b978c6a5dbf27e275aab8342e169 Mon Sep 17 00:00:00 2001 From: gghxq Date: Thu, 20 Feb 2025 09:27:22 +0300 Subject: [PATCH 09/12] Create lab7.cpp --- lab7.cpp | 34 ++++++++++++++++++++++++++++++++++ 1 file changed, 34 insertions(+) create mode 100644 lab7.cpp diff --git a/lab7.cpp b/lab7.cpp new file mode 100644 index 00000000..bd83ab06 --- /dev/null +++ b/lab7.cpp @@ -0,0 +1,34 @@ +class Solution { +public: + int minPatches(vector& nums, int n) { + // подсчет памяти: + // - используем несколько переменных: ans, i, miss. + // - память: O(1), так как не используем дополнительных структур данных. + + // асимптотика: + // - временная сложность: O(m + log n), где m — длина nums. + // - проходим по nums один раз (O(m)). + // - каждое удвоение miss занимает O(log n) шагов. + // - пространственная сложность: O(1). + + int ans = 0; // количество добавленных патчей + int i = 0; // индекс для обхода nums + long miss = 1; // минимальное число, которое мы не можем покрыть + + // пока miss <= n, продолжаем искать числа, которые нужно добавить + while (miss <= n) { + if (i < nums.size() && nums[i] <= miss) { + // если текущее число nums[i] <= miss, добавляем его к диапазону + // теперь мы можем покрыть все числа до miss + nums[i] - 1 + miss += nums[i++]; + } else { + // если nums[i] > miss или nums закончились, добавляем miss + // это увеличивает диапазон покрытия до 2 * miss + miss += miss; + ++ans; // увеличиваем счетчик добавленных патчей + } + } + + return ans; + } +}; From 3c303fc219eefe603400a98e5cc6505fa2b0ba85 Mon Sep 17 00:00:00 2001 From: gghxq Date: Thu, 20 Feb 2025 12:51:34 +0300 Subject: [PATCH 10/12] Update C3100_tregubov_vadim_lab4.cpp --- C3100_tregubov_vadim_lab4.cpp | 109 +++++++++++++++++----------------- 1 file changed, 54 insertions(+), 55 deletions(-) diff --git a/C3100_tregubov_vadim_lab4.cpp b/C3100_tregubov_vadim_lab4.cpp index 55d89156..65505f77 100644 --- a/C3100_tregubov_vadim_lab4.cpp +++ b/C3100_tregubov_vadim_lab4.cpp @@ -6,87 +6,86 @@ using namespace std; -// Функция для подсчета суммы отклонений в кластере +// функция для подсчета суммы отклонений в кластере double calculateClusterCost(const vector& arr, int start, int end) { double mean = 0; for (int i = start; i <= end; ++i) { mean += arr[i]; } - mean /= (end - start + 1); // Среднее значение кластера + mean /= (end - start + 1); // среднее значение кластера double cost = 0; for (int i = start; i <= end; ++i) { - cost += abs(arr[i] - mean); // Сумма модулей отклонений + cost += abs(arr[i] - mean); // сумма модулей отклонений } return cost; } -// Рекурсивная функция для полного перебора кластеров -double findOptimalClustering(const vector& arr, int k, int start, vector>& memo) { +// рекурсивная функция для поиска оптимального разбиения +void findOptimalClustering(const vector& arr, int k, int start, vector& currentCluster, vector>& bestClusters, double& minCost) { if (k == 1) { - // Базовый случай: один кластер от start до конца массива - return calculateClusterCost(arr, start, arr.size() - 1); + // базовый случай: один кластер от start до конца массива + double cost = calculateClusterCost(arr, start, arr.size() - 1); + if (cost < minCost) { + minCost = cost; + bestClusters.clear(); + bestClusters.push_back(vector(arr.begin() + start, arr.end())); + } + return; } - if (memo[start][k] != -1) { - // Используем мемоизацию для предотвращения повторных вычислений - return memo[start][k]; - } - - double minCost = numeric_limits::max(); // Инициализируем минимальную стоимость большим значением - // Перебираем все возможные позиции разделения кластера + // перебираем все возможные позиции разделения кластера for (int i = start; i < arr.size() - (k - 1); ++i) { - double currentCost = calculateClusterCost(arr, start, i) + - findOptimalClustering(arr, k - 1, i + 1, memo); - minCost = min(minCost, currentCost); - } + // добавляем текущий кластер + for (int j = start; j <= i; ++j) { + currentCluster.push_back(arr[j]); + } - return memo[start][k] = minCost; // Сохраняем результат в таблицу мемоизации -} + // рекурсивно ищем разбиение для оставшихся кластеров + vector nextCluster; + findOptimalClustering(arr, k - 1, i + 1, nextCluster, bestClusters, minCost); -// Основная функция кластеризации -// Параметры: -// arr - массив чисел, k - количество кластеров -// Возвращает минимальную сумму отклонений + // удаляем текущий кластер + currentCluster.clear(); + } +} -double clusterArray(const vector& arr, int k) { - int n = arr.size(); +// основная функция кластеризации +vector> clusterArray(const vector& arr, int k) { + vector> bestClusters; + double minCost = numeric_limits::max(); + vector currentCluster; - // Таблица мемоизации размером O(N * K) - vector> memo(n, vector(k + 1, -1)); + findOptimalClustering(arr, k, 0, currentCluster, bestClusters, minCost); - return findOptimalClustering(arr, k, 0, memo); + return bestClusters; } int main() { - // Пример ввода - vector arr = {1, -2, 3, 4, -5, 6}; // Массив чисел - int k = 3; // Количество кластеров + vector arr = {1, -2, 3, 4, -5, 6}; + int k = 3; + + vector> clusters = clusterArray(arr, k); + + cout << "Кластеры:" << endl; + for (size_t i = 0; i < clusters.size(); ++i) { + cout << "Кластер " << i + 1 << ": "; + for (int num : clusters[i]) { + cout << num << " "; + } + cout << endl; + } - // Вызов алгоритма кластеризации - double result = clusterArray(arr, k); + /* + Время: + calculateClusterCost: O(n) для вычисления среднего и суммы отклонений. + findOptimalClustering: O(n * k) из-за перебора всех возможных разбиений. + Итого: O(n^2 * k) в худшем случае из-за рекурсивного перебора. - // Вывод результата - cout << "Минимальная сумма отклонений: " << result << endl; + Память: + Используется O(n) для хранения текущего кластера и O(n) для хранения лучших кластеров. + Итого: O(n). + */ return 0; } - -/* -Память: -1. memo (N * (K + 1)): каждый double занимает 8 байт. Пример: N = 6, K = 3 -> 6 * 4 * 8 = 192 байта. -2. Локальные переменные (на вызов): 36 байт (4 double и int). - -В сумме: -- memo: 192 байта. -- Переменные: 36 байт. -Итого: ~228 байт. - -Время: -1. Перебор всех разбиений O(2^N). -2. Мемоизация ускоряет, но не убирает O(2^N). - -Ограничения: -1. Максимум 25 элементов в массиве. -2. K намного меньше N. -*/ From e92c230f2d0441c9524c1c2453eec80778874717 Mon Sep 17 00:00:00 2001 From: gghxq Date: Thu, 20 Feb 2025 14:25:25 +0300 Subject: [PATCH 11/12] Update2 C3100_tregubov_vadim_lab4.cpp --- C3100_tregubov_vadim_lab4.cpp | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/C3100_tregubov_vadim_lab4.cpp b/C3100_tregubov_vadim_lab4.cpp index 65505f77..090dc5c3 100644 --- a/C3100_tregubov_vadim_lab4.cpp +++ b/C3100_tregubov_vadim_lab4.cpp @@ -85,7 +85,14 @@ int main() { Память: Используется O(n) для хранения текущего кластера и O(n) для хранения лучших кластеров. Итого: O(n). + + Итоговая асимптотика: + - calculateClusterCost: O(n) на каждое вычисление + - заполнение dp: O(k * n^2), так как перебираем все разбиения + - восстановление разбиения: O(k), так как идем по split + Итого: O(k * n^2), что гораздо быстрее рекурсивного O(n^k) */ return 0; } + From bd2e9fad36e01907345c4f579fb99a0ce1086076 Mon Sep 17 00:00:00 2001 From: gghxq Date: Thu, 6 Mar 2025 06:20:55 +0300 Subject: [PATCH 12/12] Create lab6no2.cpp --- lab6no2.cpp | 35 +++++++++++++++++++++++++++++++++++ 1 file changed, 35 insertions(+) create mode 100644 lab6no2.cpp diff --git a/lab6no2.cpp b/lab6no2.cpp new file mode 100644 index 00000000..44328b77 --- /dev/null +++ b/lab6no2.cpp @@ -0,0 +1,35 @@ +class Solution { +public: + int minDistance(string word1, string word2) { + const int m = word1.length(); // длина первой строки + const int n = word2.length(); // длина второй строки + + // создаем двумерный вектор dp размером (m + 1) * (n + 1) + // он займет O(m * n) памяти + vector> dp(m + 1, vector(n + 1)); + + for (int i = 1; i <= m; ++i) + dp[i][0] = i; // для преобразования word1[0..i) в пустую строку нужно i операций удаления + + for (int j = 1; j <= n; ++j) + dp[0][j] = j; // для преобразования пустой строки в word2[0..j) нужно j операций вставки + + // Заполнение таблицы dp + for (int i = 1; i <= m; ++i) { + for (int j = 1; j <= n; ++j) { + if (word1[i - 1] == word2[j - 1]) { + // если буквы совпадают, берем значение из диагонали + dp[i][j] = dp[i - 1][j - 1]; // Ничего не нужно делать + } else { + // если буквы разные, берем минимум из трех операций + dp[i][j] = min({dp[i - 1][j - 1], dp[i - 1][j], dp[i][j - 1]}) + 1; + } + } + } + + // возвращаем минимальное количество операций для преобразования word1 в word2 + return dp[m][n]; + } +}; + +// асимптотика и память O(m * n)