```// 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;
}

```