C dynamic programming with caching

Question

I need to create a program that computes change, using dynamic programming with caching. The program is to return an array with the coins adding up to the change.

I have consulted this page for pseudocode regarding dynamic programming, but the output is only the number of coins, and I am unsure whether the below line actually implements caching.

if ((values[j] <=a)&& (1+coins[a-values[j]]<coins[a]))

Below is all the working code which still needs modification.

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


/**
  @param amt value of change
  @param values[] array of coin values
  @param n number of available coins (length of values array)
*/
float  DynamicMakeChange(int amt,int values[],int n){
    int coins[amt];  //array of number of coins needed up to amt
    coins[0]=0;
    int a; //the current change to compute

    // put number of coins in coins array at index a
    for (a=1;a<=amt;a++){
        int array[a];
        int counter=0;
        coins[a]=(int)INFINITY;
        int j;

        //loops all values of coins
        for (j=0;j<n;j++){


            // if current coin value is smaller or equal than a (the current change value)
            // and if the number of coins at the current amount-the currently looped value of a coin
            // is less than the number of coins at the current amount.
            if ((values[j] <=a)&& (1+coins[a-values[j]]<coins[a])){
                //array[counter++]=values[j];
                coins[a]=1+coins[a-values[j]];

            }


        }
    }
    return coins[amt];

}

int main()
{
    int choice;
    int array[] = { 1,2,5,10,20,50,100,200};
    printf("Please enter change to turn to coins:\n");
    scanf("%d",&choice);
    int n= sizeof(array)/sizeof(array[0]);
    float jasdkas=DynamicMakeChange(choice,array,n);
    printf("Number of coins: %.0f",jasdkas);
    return 0;
}

Answer 1

This, as stated in the link you provided should be solved using recursion . Your solution is not recursive. You´re program should recur, eg call itself. I am unsure what you needed to return but if it was the addition of the values in the int array then there should be something like:

inside DynamicMakeChange():

if (n>0)
 return (array[n] + DynamicMakeChange(choice,array[n-1],n-1));
return 0;