Knapsack Using Backtracking in C Programming

#include < stdio.h>
#include < conio.h>
#define MAX 20
float final_profit;
int w[MAX];
int p[MAX];
int n,m;
int temp[MAX],x[MAX];
float final_wt;

float Bound_Calculation(int,int,int);
void BackTracking(int,int,int);

void main()
{
 int i;
 clrscr();
 printf("\n-------------------------------------------------------");
 printf("\n     KNAPSACK PROBLEM USING BACKTRACKING");
 printf("\n-------------------------------------------------------");
 printf("\n Enter number of Objects you want:");
 scanf("%d",&n);
 printf("\n-------------------------------------------------------");
 for(i=1;i < =n;i++)
 {
  printf("\n Enter Weight and value for object%d:",i);
  scanf("%3d %3d",&w[i],&p[i]);
 }
 printf("\n Enter Capacity of Knapsack:");
 scanf("%d",&m);
 getch();
 printf("\n-------------------------------------------------------");
 printf("\n Weight\tProfit");
 printf("\n-------------------------------------------------------");

 for(i=1;i < =n;i++)
 {
  printf("\n %d \t %d",w[i],p[i]); 
 }
 
 BackTracking(1,0,0);
 
 printf("\n-------------------------------------------------------");
 printf("\n Following Objects are included:");
 printf("\n-------------------------------------------------------");
 for(i=1;i < =n;i++)
 {
  if(x[i]==1)
   printf("\n%d",i);
 }
 printf("\n-------------------------------------------------------");
 printf("\n Final Weight:%0.2f",final_wt);
 printf("\n Final Profit:%0.2f",final_profit);
getch();
}
float Bound_Calculation(int cp,int cw,int k)
{
 int ub,c,i;
 ub=cp;
 c=cw;
 for(i=k+1;i < =n;i++)
 {
  c=c+w[i];
  if(c < m)
   ub=ub+p[i];
  else
   return (ub+(1-(c-m)/w[i])*p[i]);
 }
 return ub;
}
void BackTracking(int k,int cp,int cw)
{
 int new_k,new_cp,new_cw,j;
 if(cw+w[k] < =m)
 {
  temp[k]=1;
  if(k < n)
  {
   new_k=k+1;
   new_cp=cp+p[k];
   new_cw=cw+w[k];
   BackTracking(new_k,new_cp,new_cw);
  }
  if((new_cp>final_profit)&&(k==n))
  {
   final_profit=new_cp;
   final_wt=new_cw;
   for(j=1;j < =k;j++)
   {
    x[j]=temp[j];
   }
  }
 }
 
 if(Bound_Calculation(cp,cw,k)>=final_profit)
 {
  temp[k]=0;
  if(k < n)
   BackTracking(k+1,cp,cw);
  if((cp>final_profit)&&(k==n))
  {
   final_profit=cp;
   final_wt=cw;
   for(j=1;j < =n;j++)
    x[j]=temp[j];
  }
 }
}

OUTPUT

-------------------------------------------------------
     KNAPSACK PROBLEM USING BACKTRACKING
-------------------------------------------------------
 Enter number of Objects you want:4

-------------------------------------------------------
 Enter Weight and value for object1:5 6

 Enter Weight and value for object2:6 8

 Enter Weight and value for object3:7 12

 Enter Weight and value for object4:8 15

 Enter Capacity of Knapsack:13

-------------------------------------------------------
 Weight Profit
-------------------------------------------------------
 5       6
 6       8
 7       12
 8       15
-------------------------------------------------------
 Following Objects are included:
-------------------------------------------------------
2
3
-------------------------------------------------------
 Final Weight:13.00
 Final Profit:20.00