C++ Strassen算法代码的实现

本文仅代码，无理论解释

实话实说，我觉得这个算法在C系列的语言下，简直垃圾到爆炸……毕竟是一群完全不懂程序数学家对着纸弄出来的，看起来好像非常的有用，实际上耗时是非常爆炸的。

但是《算法导论》里有啊……然后上课又要求手写一个

于是我就手写了一个……我尽可能的减少使用的空间同时加快速度了，当 n = 512 的时候，内存使用量峰值没有超过 10mb，而且是通过递归实现 Strassen 算法

其中，in.txt 已经预先准备了 3000000 个范围在 0-100 随机数，避免程序在运算过程中爆 int（虽然完全可以取1000）

/**
 * Created by Mauve on 3/29/2020.
 * Copyright © 2020 Mauve, All Rights Reserved
 */

#include <bits/stdc++.h>

using namespace std;

/**
 * 矩阵相乘
 * 最终结果耗时结果保存至
 * 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;
}

到此这篇关于C++ Strassen算法代码的实现的文章就介绍到这了,更多相关C++ Strassen算法 内容请搜索自由互联以前的文章或继续浏览下面的相关文章希望大家以后多多支持自由互联！