// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
 This simple example shows how to call dlib's optimal linear assignment problem solver.
 It is an implementation of the famous Hungarian algorithm and is quite fast, operating in
 O(N^3) time.


#include <dlib/optimization/max_cost_assignment.h>
#include <iostream>

using namespace std;
using namespace dlib;

int main ()
    // Let's imagine you need to assign N people to N jobs.  Additionally, each person will make
    // your company a certain amount of money at each job, but each person has different skills
    // so they are better at some jobs and worse at others.  You would like to find the best way
    // to assign people to these jobs.  In particular, you would like to maximize the amount of
    // money the group makes as a whole.  This is an example of an assignment problem and is
    // what is solved by the max_cost_assignment() routine.
    // So in this example, let's imagine we have 3 people and 3 jobs.  We represent the amount of
    // money each person will produce at each job with a cost matrix.  Each row corresponds to a
    // person and each column corresponds to a job.  So for example, below we are saying that
    // person 0 will make $1 at job 0, $2 at job 1, and $6 at job 2.  
    matrix<int> cost(3,3);
    cost = 1, 2, 6,
           5, 3, 6,
           4, 5, 0;

    // To find out the best assignment of people to jobs we just need to call this function.
    std::vector<long> assignment = max_cost_assignment(cost);

    // This prints optimal assignments:  [2, 0, 1] which indicates that we should assign
    // the person from the first row of the cost matrix to job 2, the middle row person to
    // job 0, and the bottom row person to job 1.
    for (unsigned int i = 0; i < assignment.size(); i++)
        cout << assignment[i] << std::endl;

    // This prints optimal cost:  16.0
    // which is correct since our optimal assignment is 6+5+5.
    cout << "optimal cost: " << assignment_cost(cost, assignment) << endl;