求解赋值问题的分枝定界算法

Question

我开始在C ++中为分配问题做分支定界算法，但我找不到合适的解决方案。首先是分配问题的例子： Assignment problem

好的，所以每个人都可以被分配到一个工作，并且想法是将每个工作分配给一个人，以便所有工作以最快的方式完成。

到目前为止，这是我的代码：

#include "Matrix.h"
// Program to solve Job Assignment problem
// using Branch and Bound

#include <limits.h>
#include <vector>
#include <algorithm>



using namespace std;

template<class T>

NUM getCost(Matrix& matrix, size_t x, size_t y, vector<bool>& colUsed);

void run(Matrix& matrix, vector<size_t>& assignedJobs);



int main()
{
    Matrix matrix;
    matrix.setMatrix(N);
    matrix.print();

    vector<size_t> assignedJobs;

    run(matrix, assignedJobs);
    cout << assignedJobs[0];
    /*
    cout << "size:E " << v.size() << endl;
    for (vector<NUM>::iterator i = v.begin(); i != v.end(); i++)
    {
        cout << *i << endl;
    }
    */
    return 0;
}

// remember to use x only LOCALLY!!!
NUM getCost(Matrix& matrix, size_t x, size_t y, vector<bool>& colUsed)
{
    // pathCost
    NUM pathCost = matrix.matrix[x++][y];

    for (size_t col = 0; col < matrix.size(); col++)
    {
        if (!colUsed.at(col))
        {
            NUM min =
            #if defined NUM_INT
                        INT_MAX;
            #endif
            #if defined NUM_DBL
                        DBL_MAX;
            #endif
            size_t row = x;
            for (; row < matrix.size(); row++)
            {
                if (min > matrix.matrix[row][col])
                {
                    min = matrix.matrix[row][col];
                }
            }
            pathCost += min;
        }

    }
    return pathCost;
}

void run(Matrix& matrix, vector<size_t>& assignedJobs)
{
    // array of used columns
    vector<bool> colUsed;
    for (size_t i = 0; i < matrix.size(); i++)
    {
        colUsed.push_back(false);
    }

    for (size_t row = 0; row < matrix.size(); row++)
    {
        size_t col = 0;
        // bombona
        while (colUsed.at(col++)); col--;
        // choose the best job for the current worker
        vector<NUM> jobs;
        // get all the job costs from which to choose the smallest
        // row++
        jobs.push_back(getCost(matrix, col, row, colUsed));
        // iterator at the position of the smallest element of jobs
        vector<NUM>::iterator i_min = min_element(jobs.begin(), jobs.end());
        // index of the smallest element in jobs
        size_t index = (size_t)distance(jobs.begin(), i_min);

        colUsed.at(index) = true;
        assignedJobs.push_back(index);
    }
}

我知道我可能会失控。我在开始时没有使用下限，我实际上有点混淆这个算法是如何工作的。因此，即使一步一步地通过算法也很有帮助。