# include <math.h>
# include <stdio.h>
# include <stdlib.h>

# include "tsp_nearest.h"

/******************************************************************************/

void tsp_nearest ( int n, double *x, int *order_best, double *cost_best )

/******************************************************************************/
/*
  Purpose:

    tsp_nearest() seeks an optimal traveling salesperson path by the nearest neighbor method.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    02 June 2026

  Author:

    John Burkardt

  Input:

    int n: the number of cities.

    double *x[n*2]: the coordinates of the cities.

  Output:

    int order_best[n]: a list of the order in which the N cities should be visited.

    double cost_best: the length of the round trip.
*/
{
  double cost;
  int i;
  int *order;
  int start;
/*
  Initialize:
    the best cost so far is Infinity;
    the best tour so far is 1, 2, ..., n.
*/
  *cost_best = HUGE_VAL;
  for ( i = 0; i < n; i++ )
  {
    order_best[i] = i;
  }
/*
  Try starting at city START and moving to the nearest unvisited city.
*/
  for ( start = 0; start < n; start++ )
  {
    order = tsp_tour_nearest ( n, x, start );
    cost = tsp_tour_cost ( n, x, order );

    if ( cost < *cost_best )
    {
      for ( i = 0; i < n; i++ )
      {
        order_best[i] = order[i];
      }
      *cost_best = cost;
      printf ( "  Route starting at city %d has cost = %g\n", start, *cost_best );
    } 
    free ( order );
  }

  return;
}
/******************************************************************************/

double tsp_tour_cost ( int n, double *x, int *order )

/******************************************************************************/
/*
  Purpose:

    tsp_tour_cost() evaluates the cost of a round trip.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    18 June 2026

  Author:

    John Burkardt

  Input:

    int n: the number of cities.

    double x[n,2]: the city locations.

    int order[n]: the order in which the cities are visited.

  Output:

    double cost: the cost of the route.
*/
{
  double cost;
  int from;
  int to;

  cost = 0.0;
  from = n - 1;
  for ( to = 0; to < n; to++ )
  {
    cost = cost + sqrt ( pow ( x[order[from]*2]   - x[order[to]*2],   2 )
                       + pow ( x[order[from]*2+1] - x[order[to]*2+1], 2 ) );
    from = to;
  }

  return cost;
}
/******************************************************************************/

int *tsp_tour_nearest ( int n, double *x, int start )

/******************************************************************************/
/*
  Purpose:

    tsp_path_nearest() finds a nearest neighbor route for a given start.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    07 July 2026

  Author:

    John Burkardt

  Input:

    int n: the number of cities.

    double x[n*2]: the city to city distance table.

    int start: the starting city.

  Output:

    int order[n]: the route that starts at START.
*/
{
  double *d;
  double dmin;
  int from;
  int i;
  int j;
  int k;
  int *order;
  int to;
/*
  Create the distance table.
*/
  d = ( double * ) malloc ( n * n * sizeof ( double ) );

  for ( i = 0; i < n; i++ )
  {
    for ( j = 0; j < n; j++ )
    {
      d[i+j*n] = sqrt ( pow ( x[i*2]   - x[j*2],   2 )
                      + pow ( x[i*2+1] - x[j*2+1], 2 ) );
    }
  }
  for ( i = 0; i < n; i++ )
  {
    d[i+i*n] = HUGE_VAL;
  }
/*
  At FROM, find nearest unvisited city TO.
*/
  order = ( int * ) malloc ( n * sizeof ( int ) );

  for ( j = 0; j < n; j++ )
  {
    if ( j == 0 )
    {
      to = start;
    }
    else
    {
      to = 0;
      dmin = d[from+to*n];
      for ( k = 1; k < n; k++ )
      {
        if ( d[from+k*n] < dmin )
        {
          to = k;
          dmin = d[from+to*n];
        }
      }
    }
/*
  Add TO to path, and move there.
*/
    order[j] = to;
    from = to;
/*
  Reset D so we can't revisit city TO.
*/
    for ( i = 0; i < n; i++ )
    {
      d[i+to*n] = HUGE_VAL;
    }
  }
  
  free ( d );

  return order;
}