当元素数 > 1000 时，如何制作向量的笛卡尔积？

Question

我有 1,2,...,n 个向量。每个向量都有超过 10000 个元素，我必须得到这些向量的笛卡尔积。我有一个有效的代码，但只有不到 1000 个元素和 4 个向量。我想将笛卡尔积写入文件，但如果输出文件大于 1GB，我会得到："terminate called after throwing an instance of 'std::bad_alloc' what(): std::bad_alloc".

我的主要问题是，如何修复此内存分配错误？

这是我的一段可运行代码：

#include <iostream>
#include <vector>
#include <algorithm>
#include <time.h>
#include <fstream>
#include <math.h>

using namespace std;

vector<double> makeVectorByRange(double min, double max, double step){
    vector<double> out = {};
    for( ; min <= max; min+=step){
        out.push_back(min);
    }
    return out;
} 


void cart_product_solve_and_write_to_file (const vector<vector<double>>& inpV) {
    vector<vector<double>> out = {{}};

    std::ofstream outputFile;
    std::fixed;

    for (auto& u : inpV) {
        vector<vector<double>> r;
        r.clear();
        for (auto& x : out) {

            //make/open file, append
            outputFile.open ("out.csv", std::ofstream::out | std::ofstream::app);
            outputFile.precision(8);

            for (auto y : u) {
                r.push_back(x);
                r.back().push_back(y);

                if( r.back().size() == inpV.size() ){

                    // write the input parameters of griewank to file
                    for(double asd : r.back()){
                        outputFile << asd << ";";
                    }

                    outputFile << "; \n";
                    outputFile << std::flush;

                    r.back().clear();
                }
            }
            //close file
            outputFile.close();
        }
        out.swap(r);
    }  
}

// Pure cartesian product. This function returns the cartesian product as a vector, but if the input vectors are too big, it has an error
/*
vector < vector<double> > cartesian_product (const vector< vector<double> >& inpV) {
    vector< vector<double> > out = {{}};
    for (auto& u : inpV) {
        vector< vector<double> > r;
        for (auto& x : out) {
            for (auto y : u) {
                r.push_back(x);
                r.back().push_back(y);
            }
        }
        out.swap(r);
    }
    return out;
}
*/

int main(){

    clock_t tStart = clock();

    // it works
    // const vector<vector<int> > test ={ {0,1,2,3,4}, {5,6,7}, {8,9,10,11,12,13} };
    // vector<vector<int> > cart_prod = cartesian_product(test);

    vector <vector<double> > test = {};
    test.push_back( makeVectorByRange( 0, 0.5, 0.001) );
    test.push_back( makeVectorByRange( 0, 0.5, 0.001) );
    test.push_back( makeVectorByRange( 0, 0.5, 0.001) );

    cart_product_solve_and_write_to_file(test);

    printf("Time taken: %.6fs\n", (double)(clock() - tStart)/CLOCKS_PER_SEC);

    return 0;
}

Answer 1

您需要迭代生成的笛卡尔积的所有组合。这通常通过递归来实现。然后在每个递归级别中迭代一个输入向量的元素。

这是将结果组合打印到 std::cout 的示例解决方案。您可以通过向递归函数提供一个打开的 std::ofstream 对象的附加参考参数来轻松修改它以打印到文件。

#include <iostream>
#include <vector>

template <typename T>
void vector_cartesian_product_helper(
  const std::vector<std::vector<T>>& v, std::vector<T>& combination, size_t level)
{
  if (level == v.size()) {
    for (auto elem : combination)
      std::cout << elem << ";";
    std::cout << "\n";
  }
  else {
    for (const auto& elem : v[level]) {
      combination[level] = elem;
      vector_cartesian_product_helper(v, combination, level + 1);
    }
  }
}

template <typename T>
void vector_cartesian_product(const std::vector<std::vector<T>>& v)
{
  std::vector<T> combination(v.size());
  vector_cartesian_product_helper(v, combination, 0);
}

int main(){
  std::vector<std::vector<int>> test = {{0,1,2,3,4}, {5,6,7}, {8,9,10,11,12,13}};
  vector_cartesian_product(test);
}

现场演示：https://wandbox.org/permlink/PoyEviWGDtEpvN1z

它适用于任何大小的向量，并且仅使用 O(N) 的额外内存，其中 N 是向量的数量.

当元素数 > 1000 时，如何制作向量的笛卡尔积？

How to make the cartesian products of vectors, when the number of elements > 1000?

c++

cartesian-product

bad-alloc

c++11