C - Remove Duplicate Results in Recursive Function - c

Question

I have to create a recursive function that tells you the number of ways a number of cents can be made into change. (Using quarters, dimes nickels, and pennies).
So far, I have a recursive function that does that, however it counts the same combination more than once, so the number is too big. How do I remove the duplicate combinations?
Code:
#include <stdio.h>
//Prototypes
int coins(int);
int main(void){
//Declarations
int num;
//Get user input
printf("Enter an amount of change in cents: ");
scanf("%d", &num); //Change to fgets
//Call function
printf("There are %d ways to make change for %d cents.\n", (coins(num)), num);
}
int coins(int amt){
//Declarations
int ways=0;
//Base Case
if(amt == 0){
return 1;
}
//int ways=0; More efficient after base case.
if(amt >= 1){
ways+=coins(amt-1);
}
if(amt >= 5){
ways+=coins(amt-5);
}
if(amt >= 10){
ways+=coins(amt-10);
}
if(amt >= 25){
ways+=coins(amt-25);
}
return ways;
}
Example:
Input: 17 (cents)
Output: 80 ways
**Output should be 6

Answer 1

#include <stdio.h>
int coins(int, int);
int main(void){
int num;
printf("Enter an amount of change in cents: ");
scanf("%d", &num);
printf("There are %d ways to make change for %d cents.\n", coins(num, 0), num);
return 0;
}
int coins(int amt, int kind){
static int kinds[4] = {25, 10, 5, 1};
int ways=0, i, n;
if(kinds[kind] == 1)//always divisible
return 1;
n = amt / kinds[kind];
for(i = 0; i <= n; ++i)
ways+=coins(amt-kinds[kind]*i, kind + 1);
return ways;
}