Implement Program for “Making Change” using Dynamic Programming.


#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
int min(int a,int b)
{
            if(a<b)
            {
                        return a;
            }
            else
            {
                        return b;
            }
}

void main()
{
            int ncoins,change,i,j,**c;
            int denom[10];
            clrscr();
            printf("enter no.of coins:");
            scanf("%d",&ncoins);
            printf("enter the value of ncoins:\n");
            for(i=0;i<ncoins;i++)
            {
                        scanf("%d",&denom[i]);
            }
            printf("enter the amount to get the change:");
            scanf("%d",&change);

            *c=(int *)malloc(ncoins*sizeof(int));
            for(i=0;i<change;i++)
            {
                        *(c+i)=(int *)malloc((change+1)*sizeof(int));
            }
            for(i=0;i<ncoins;i++)
            {
                        c[i][0]=0;
            }

            for(i=0;i<ncoins;i++)
            {
                        for(j=1;j<=change;j++)
                        {

                                    if(i==0 && j<denom[0])
                                    {
                                                c[i][j]=infinite;
                                    }
                                    else if(i==0)
                                    {
                                                if(c[i][j-denom[0]]==infinite)
                                                {
                                                            c[i][j]=infinite;
                                                }
                                                else
                                                {
                                                            c[i][j]=1+c[i][j-denom[0]];
                                                }
                                    }
                                    else if(j<denom[i])
                                    {
                                                c[i][j]=c[i-1][j];
                                    }
                                    else
                                    {
                                                c[i][j]=min(c[i-1][j],1+c[i][j-denom[i]]);
                                    }
                        }
            }
            printf("Table:\n");
            for(i=0;i<ncoins;i++)
            {
                        for(j=1;j<=change;j++)
                        {
                                    printf("\t%d",c[i][j]);
                        }
                        printf("\n");
            }

            getch();
}

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