Question

1. Suppose you have a set of coins of various denominations, with values v₁, v₂, …, v_n. Some of the coins may have the same value as other of the coins (or maybe not, for the purpose of this problem it doesn’t matter). I want to use these to buy an item that costs exactly M. That is, I want to find out if there is some subset of the coins whose values will sum to exactly M. (Note that I don’t care about minimizing the number of coins used, or finding out how many different sets of coins might have values that sum to M, I just want to find out if I have the exact cost of the item.)
   1. [5 pts] Write the recursion equation for this problem.

2. [5 pts] Write short pseudocode that converts this equation into a dynamic program.

Answer 1

SOLUTION :-

#include<stdio.h>
#include<stdlib.h>
struct node{
   int data;
   struct node *next;
};
void printlist(struct node *h){
   while(h != NULL){
       printf("%d ",h->data);
       h = h->next;
   }
}

int main(){
   struct node *start=NULL;
   int a,i;
   printf("Enter the no.of Nodes:");
   scanf("%d",&a);
   for(i=0;i<a;i++){
       struct node *newNode = (struct node *)malloc(sizeof(struct node));
       printf("Enter the data:");
       scanf("%d",&newNode->data);
       newNode->next = NULL;
       if(start==NULL)
           start = newNode;
       else{
           struct node *ptr = start;
           while(ptr->next!=NULL)
               ptr = ptr->next;
           ptr->next = newNode;
       }
   }
   printf("Linked List is:\n");
   printlist(start);
   printf("\nAfter sorting the list is:\n");
   struct node *s = start,*st = start;
   for(;s!=NULL;s = s->next){
       st = start;
       for(;st->next!=NULL;st = st->next){
           if(st->data>st->next->data){
               int te;
               te = st->data;
               st->data = st->next->data;
               st->next->data = te;
           }
       }
   }
   printlist(start);
}