The minimum number of coins the sum of which is S

Question

Given a list of N coins, their values (V1, V2, ... , VN), and the total sum S. Find the minimum number of coins the sum of which is S (we can use as many coins of one type a

Answer 1

int getMinCoins(int arr[],int sum,int index){

        int INFINITY=1000000;
        if(sum==0) return 0;
        else if(sum!=0 && index<0) return INFINITY;

        if(arr[index]>sum) return getMinCoins(arr, sum, index-1);

        return Math.min(getMinCoins(arr, sum, index-1), getMinCoins(arr, sum-arr[index], index-1)+1);
    }

Consider i-th coin. Either it will be included or not. If it is included, then the value sum is decreased by the coin value and the number of used coins increases by 1. If it is not included, then we need to explore the remaining coins similarly. We take the minimum of two cases.