Question

Problem: Implement (in C) the dynamic program algorithm for the coin-change algorithm, discussed in class. Assume that the coins with which you make change are quarters, dimes, nickels and pennies. Thus you are going to set n = 4 in your program. The amount k for which you have to make change will be provided by the user and your program will return the minimum number of coins needed and also the break-up of the change in terms of the different denominations used. Thus if the input is 31, the output for the minimum number of coins needed would be 3 and the break-up 25 + 5 + 1. (10 points)

Answer 1

CODE

#include<stdio.h>

#include <limits.h>

// m is size of coins array (number of different coins)

int minCoins(int coins[], int m, int V)

{

// base case

if (V == 0) return 0;

// Initialize result

int res = INT_MAX;

// Try every coin that has smaller value than V

for (int i=0; i<m; i++)

{

if (coins[i] <= V)

{

int sub_res = minCoins(coins, m, V-coins[i]);

// Check for INT_MAX to avoid overflow and see if

// result can minimized

if (sub_res != INT_MAX && sub_res + 1 < res)

res = sub_res + 1;

}

}

return res;

}

// Driver program to test above function

int main()

{

  int i, j;

  int arr[] = {1, 5, 10, 25};

  int n = 4;

int k;

printf("Enter the amount: ");

scanf("%d", &k);

  printf("%d ", minCoins(arr, n, k));

  getchar();

  return 0;

}