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#include <stdlib.h>
#ifdef MYDIR
#else
#include "TwoDView.h"
#include "TwoDTSP.h"
#include <appkit/graphics.h>
#endif
#include <math.h>
#include <limits.h>
#include <stdio.h>
#include "tspheaders.h"
#include "prototypes.h"
/************************************************************************/
/* This function implements the Cheapest Insertion Algorithm for the
Travelling Salesperson Algorithm. It provides an approximate optimal
value rather than the optimal value.
Reference: Salkin & Mathur, Foundations Of Integer Programming, 1989
North-Holland, p 683.
*/
/************************************************************************/
/* Parameters: TwoDView *self: Ye Old Drawing Object
float *Data: Pointer to the list of points.
Used to draw intermediate graph.
float *Distance: Pointer to area that contains the
Distances Between Each Pair of Cities
int *Tour: Pointer to area that will contain the
indices of the n arcs that are selected
to be a part of the tour
int NumberOfCities: Number of cities in the problem
*/
/************************************************************************/
/************************************************************************/
#ifdef MYDIR
float CheapestInsertion(float *Distance,int *Tour,int NumberOfCities) {
#else
float CheapestInsertion(TwoDView *self,float *data,float *Distance,int *Tour,
int NumberOfCities) {
#endif
int i,j,k,l,m,x,y,I,J,Arc,From,To,CurrentCity,SubTourEnd,NewCity,FromIndex;
int *OnTour;
float MinDistance,OldDistance,ThisDistance,NewDistance,OptimalValue;
char msg[256];
/* allocate space for OnTour */
OnTour = (int *)malloc(NumberOfCities*sizeof(int));
if (OnTour == (int *) 0)
printf("Malloc for OnTour failed. \n");
for (i=0;i<NumberOfCities;i++) {
OnTour[i] = 0;
}
#ifdef DEBUGMYDIR
for (i=0;i<(NumberOfCities-1)*NumberOfCities/2;i++) {
printf("Distance[%d] = %f; \n",i,Distance[i]);
}
#endif
/* find the two cities with the minimum distance */
/* these two cities make up the initial subtour */
MinDistance = ClosestCities(Distance,&From,&To,NumberOfCities);
/* if MinDistance doesn't change, there is a problem ... */
if (MinDistance == INT_MAX) {
printf("Error no initial subtour found. \n");
#ifdef DEBUGMYDIR
#else
STATUS("No initial subtour found.");
#endif
}
#ifdef DEBUGMYDIR
else {
printf("initial subtour \n");
printf("from %d to %d distance %f \n",From,To,MinDistance);
}
#endif
/* given a subtour of m cities, add city k with minimum insertion cost */
/* cost of inserting city k between cities i and j =
Distance(i,k) + Distance(k,j) - Distance(i,j) */
/* OnTour indicates status of city
1 -- city is on tour 0 -- city is not yet on the tour */
Tour[0] = Tour[3] = From;
Tour[1] = Tour[2] = To;
OnTour[From] = OnTour[To] = 1;
/* FromIndex is the number of the city currently being tested */
FromIndex = 0;
NewDistance = INT_MAX;
OptimalValue = 2*MinDistance;
SubTourEnd = 1;
CurrentCity = -1;
NewCity = NumberOfCities;
/* keep adding cities until you include all NumberOfCities of them */
while (SubTourEnd < NumberOfCities-1) {
#ifdef DEBUGMYDIR
printf("Start of Iteration with %d cities in tour \n",SubTourEnd+1);
printf("From is %d \n",From);
printf("To is %d \n",To);
printf("FromIndex is %d \n",FromIndex);
#else
sprintf(msg,"From %d To %d",From, To); //added wgr
STATUS(msg);// wgr
#endif
/* at the end of this while loop, there will be a new city to insert */
while (CurrentCity < SubTourEnd) {
/* look at the next city already on the tour */
CurrentCity+=1;
From = Tour[2*CurrentCity];
To = Tour[2*CurrentCity+1];
OldDistance = Distance[kfrom(From,To,NumberOfCities)];
/* look at all arcs starting at From */
I = ArcIndex(From,NumberOfCities);
J = ArcIndex((From+1),NumberOfCities);
for (Arc=I;Arc<J;Arc++) {
/* j = terminating end of this arc */
j = Arc-I+From+1;
/* if the city at the other end isn't already on the tour ...*/
if (!OnTour[j]) {
/* Is the arc a new candidate for insertion? */
if ((j != From) && (j != To)) {
k = kfrom(From,j,NumberOfCities);
l = kfrom(j,To,NumberOfCities);
ThisDistance = Distance[k] + Distance[l] - OldDistance;
if (ThisDistance < 0) {
printf("Error: ThisDistance = %f for From %f To %f j %f \n",
From,To,j);
}
if (ThisDistance < NewDistance) {
#ifdef DEBUGMYDIR
printf("Changing cities from %d to %d \n",NewCity,j);
printf("From, To, j, %d %d %d \n",From,To,j);
#else
sprintf(msg,"Change from %d to %d",From,To);
STATUS(msg);
#endif
NewDistance = ThisDistance;
NewCity = j;
FromIndex = CurrentCity;
}
}
}
}
/* look at all arcs ending at From */
for (m=0;m<From;m++) {
/* if the starting city isn't already on the tour ...*/
if (!OnTour[m]) {
/* Is this arc a new candidate for insertion? */
if ((m != From) && (m != To)) {
k = kfrom(m,From,NumberOfCities);
l = kfrom(m,To,NumberOfCities);
ThisDistance = Distance[k] + Distance[l] - OldDistance;
if (ThisDistance < 0) {
printf("Error: ThisDistance = %f for From %f To %f m %f \n",
From,To,m);
}
if (ThisDistance < NewDistance) {
#ifdef DEBUGMYDIR
printf("Changing cities from %d to %d \n",NewCity,m);
printf("From, To, J, %d %d %d \n",From,To,m);
#else
sprintf(msg,"change from %d to %d",NewCity,m);
STATUS(msg);
#endif
NewDistance = ThisDistance;
NewCity = m;
FromIndex = CurrentCity;
}
}
}
}
}
if (NewCity >= NumberOfCities) {
printf("Error: new city has not been found for tour. \n");
CurrentCity = SubTourEnd = NumberOfCities;
OptimalValue = -1;
}
else {
/* add the new arc going from j to FromIndex+1 Tour */
#ifdef DEBUGMYDIR
printf("adding arc from %d to %d \n",NewCity,Tour[2*FromIndex+1]);
#else
sprintf(msg,"add arc %d to %d \n",NewCity,Tour[2*FromIndex+1]);
STATUS(msg);
#endif
SubTourEnd+=1;
Tour[2*SubTourEnd] = NewCity;
Tour[2*SubTourEnd+1] = Tour[2*FromIndex+1];
OnTour[NewCity] = 1;
/* replace arc indexed by FromIndex in Tour with new arc going from
old From to NewCity */
#ifdef DEBUGMYDIR
printf("replacing arc from %d to %d with %d to %d \n",
Tour[2*FromIndex],Tour[2*FromIndex+1],Tour[2*FromIndex],NewCity);
#else
sprintf(msg,"replace %d %d with %d %d",
Tour[2*FromIndex],Tour[2*FromIndex+1],Tour[2*FromIndex],NewCity);
STATUS(msg);
#endif
Tour[2*FromIndex] = Tour[2*FromIndex];
Tour[2*FromIndex+1] = NewCity;
/* update the Optimal Value */
OptimalValue+=NewDistance;
#ifdef DEBUGMYDIR
printf("addding %f to Opval to get %f \n",NewDistance,OptimalValue);
#endif
/* get ready to start at the top of the list again */
FromIndex = 0;
CurrentCity = -1;
NewDistance = INT_MAX;
NewCity = NumberOfCities;
#ifdef DEBUGMYDIR
/* print out current subtour */
for (i=0;i<2*(SubTourEnd+1);i++) {
printf("i tour %d %d \n",i,Tour[i]);
}
#endif
#ifdef MYDIR
#else
/* draw the intermediate tour */
PSnewinstance();
for(i=0;i<2*(SubTourEnd+1);i+=2) {
x = Tour[i];
y = Tour[i+1];
[self drawEdge:X(x):Y(x):X(y):Y(y)];
}
NXPing();
[self->optimalValueField setFloatValue: OptimalValue at: 0];
usleep(self->drawTime);
#endif
}
}
/* clean up */
free(OnTour);
/* return the optimal value */
return(OptimalValue);
}
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.