C++ Strassen算法代碼的實(shí)現(xiàn)
本文僅代碼,無(wú)理論解釋
實(shí)話實(shí)說(shuō),我覺(jué)得這個(gè)算法在C系列的語(yǔ)言下,簡(jiǎn)直垃圾到爆炸……畢竟是一群完全不懂程序數(shù)學(xué)家對(duì)著紙弄出來(lái)的,看起來(lái)好像非常的有用,實(shí)際上耗時(shí)是非常爆炸的。
但是《算法導(dǎo)論》里有啊……然后上課又要求手寫(xiě)一個(gè)
于是我就手寫(xiě)了一個(gè)……我盡可能的減少使用的空間同時(shí)加快速度了,當(dāng) n = 512 的時(shí)候,內(nèi)存使用量峰值沒(méi)有超過(guò) 10mb,而且是通過(guò)遞歸實(shí)現(xiàn) Strassen 算法
其中,in.txt 已經(jīng)預(yù)先準(zhǔn)備了 3000000 個(gè)范圍在 0-100 隨機(jī)數(shù),避免程序在運(yùn)算過(guò)程中爆 int(雖然完全可以取1000)
/** * Created by Mauve on 3/29/2020. * Copyright © 2020 Mauve, All Rights Reserved */ #include <bits/stdc++.h> using namespace std; /** * 矩陣相乘 * 最終結(jié)果耗時(shí)結(jié)果保存至 * https://www.desmos.com/calculator/gl4tm5i1zu */ struct mat { unsigned row, col; mat(unsigned r, unsigned c) : row(r), col(c) {} virtual int &pos_ref(unsigned i, unsigned j) = 0; virtual int pos(unsigned i, unsigned j) const = 0; }; struct base_mat; struct sub_mat; stack<sub_mat *> sub_data; struct base_mat : mat { int *data; base_mat(unsigned r, unsigned c) : mat(r, c), data(new int[row * col]) {} ~base_mat() { delete[] data; } inline int &pos_ref(unsigned i, unsigned j) override { return *(data + i * col + j); } inline int pos(unsigned i, unsigned j) const override { return *(data + i * col + j); } }; unsigned min_mul; struct sub_mat : mat { mat *a, *b; bool is_add; unsigned offset_ai, offset_aj, offset_bi, offset_bj; explicit sub_mat(mat *data) : mat(data->row, data->col), a(data), b(nullptr), is_add(false), offset_ai(0), offset_aj(0), offset_bi(0), offset_bj(0) { sub_data.push(this); } sub_mat(mat *data, bool of_i, bool of_j) : mat(data->row >> 1u, data->col >> 1u), a(data), b(nullptr), is_add(false), offset_ai(of_i ? data->row >> 1u : 0), offset_aj(of_j ? data->col >> 1u : 0), offset_bi(0), offset_bj(0) { sub_data.push(this); } inline int &pos_ref(unsigned i, unsigned j) override { assert(b == nullptr); return a->pos_ref(i + offset_ai, j + offset_aj); } inline int pos(unsigned i, unsigned j) const override { if (b == nullptr) return a->pos(i + offset_ai, j + offset_aj); return a->pos(i + offset_ai, j + offset_aj) + (is_add ? 1 : -1) * b->pos(i + offset_bi, j + offset_bj); } inline sub_mat *operator+(sub_mat &other) { auto res = new sub_mat(this); res->b = &other; res->is_add = true; return res; } inline sub_mat *operator-(sub_mat &other) { auto res = new sub_mat(this); res->b = &other; res->is_add = false; return res; } mat *operator*(sub_mat &other) { assert(col == other.row); auto res = new base_mat(row, other.col); if (col & 1u || row & 1u || col <= min_mul || row <= min_mul || other.col <= min_mul) { memset(res->data, 0, sizeof(int) * res->row * res->col); for (int k = 0; k < col; k++) for (int i = 0; i < row; ++i) for (int j = 0; j < other.col; ++j) res->pos_ref(i, j) += pos(i, k) * other.pos(k, j); } else { size_t sub_data_size = sub_data.size(); #define a(i, j) (*new sub_mat(this, i == 2 , j == 2)) #define b(i, j) (*new sub_mat(&other, i == 2 , j == 2)) auto m1 = *(a(1, 1) + a(2, 2)) * *(b(1, 1) + b (2, 2)); auto m2 = *(a(2, 1) + a(2, 2)) * b(1, 1); auto m3 = a(1, 1) * *(b(1, 2) - b(2, 2)); auto m4 = a(2, 2) * *(b(2, 1) - b(1, 1)); auto m5 = *(a(1, 1) + a(1, 2)) * b(2, 2); auto m6 = *(a(2, 1) - a(1, 1)) * *(b(1, 1) + b(1, 2)); auto m7 = *(a(1, 2) - a(2, 2)) * *(b(2, 1) + b(2, 2)); #undef a #undef b unsigned half_row = row >> 1u, half_col = col >> 1u; #define m(t) (m##t->pos(i, j)) // C11 for (unsigned i = 0; i < half_row; ++i) for (unsigned j = 0; j < half_col; ++j) res->pos_ref(i, j) = m(1) + m(4) - m(5) + m(7); // C12 for (unsigned i = 0; i < half_row; ++i) for (unsigned j = 0; j < half_col; ++j) res->pos_ref(i, j + half_col) = m(3) + m(5); // C21 for (unsigned i = 0; i < half_row; ++i) for (unsigned j = 0; j < half_col; ++j) res->pos_ref(i + half_row, j) = m(2) + m(4); // C22 for (unsigned i = 0; i < half_row; ++i) for (unsigned j = 0; j < half_col; ++j) res->pos_ref(i + half_row, j + half_col) = m(1) - m(2) + m(3) + m(6); #undef m delete dynamic_cast<base_mat *>(m1); delete dynamic_cast<base_mat *>(m2); delete dynamic_cast<base_mat *>(m3); delete dynamic_cast<base_mat *>(m4); delete dynamic_cast<base_mat *>(m5); delete dynamic_cast<base_mat *>(m6); delete dynamic_cast<base_mat *>(m7); while (sub_data.size() > sub_data_size) { delete sub_data.top(); sub_data.pop(); } } return res; } }; unsigned N = 2; void solve() { cerr << "N = " << N << endl; base_mat a(N, N), b(N, N); for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) cin >> a.pos_ref(i, j); for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) cin >> b.pos_ref(i, j); for (int t = 1; t < min(10u, N); t += 3) { auto x = new sub_mat(&a), y = new sub_mat(&b); min_mul = t; auto time_1 = clock(); auto z = *x * *y; auto time_2 = clock(); cerr << "t = " << t << " time: " << double(time_2 - time_1) / CLOCKS_PER_SEC << endl; delete dynamic_cast<base_mat *>(z); while (!sub_data.empty()) { delete sub_data.top(); sub_data.pop(); } } auto x = new sub_mat(&a), y = new sub_mat(&b); min_mul = 10000; auto time_1 = clock(); auto z = *x * *y; auto time_2 = clock(); cerr << "tradition: " << double(time_2 - time_1) / CLOCKS_PER_SEC << endl; delete dynamic_cast<base_mat *>(z); while (!sub_data.empty()) { delete sub_data.top(); sub_data.pop(); } N *= 2; if (N >= 1000) exit(0); } signed main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); #ifdef ACM_LOCAL freopen("in.txt", "r", stdin); freopen("out.txt", "w", stdout); long long test_index_for_debug = 1; char acm_local_for_debug; while (cin >> acm_local_for_debug && acm_local_for_debug != '~') { cin.putback(acm_local_for_debug); if (test_index_for_debug > 20) { throw runtime_error("Check the stdin!!!"); } auto start_clock_for_debug = clock(); solve(); auto end_clock_for_debug = clock(); cout << "Test " << test_index_for_debug << " successful" << endl; cerr << "Test " << test_index_for_debug++ << " Run Time: " << double(end_clock_for_debug - start_clock_for_debug) / CLOCKS_PER_SEC << "s" << endl; cout << "--------------------------------------------------" << endl; } #else solve(); #endif return 0; }
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