Java Program for Coin Change

Given a value N, if we want to make change for N cents, and we have infinite supply of each of S = { S1, S2, .. , Sm} valued coins, how many ways can we make the change? The order of coins doesn\’t matter.

For example, for N = 4 and S = {1,2,3}, there are four solutions: {1,1,1,1},{1,1,2},{2,2},{1,3}. So output should be 4. For N = 10 and S = {2, 5, 3, 6}, there are five solutions: {2,2,2,2,2}, {2,2,3,3}, {2,2,6}, {2,3,5} and {5,5}. So the output should be 5.

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/* Dynamic Programming Java implementation of Coin
   Change problem */
import java.util.Arrays;
  
class CoinChange
{
    static long countWays(int S[], int m, int n)
    {
        // Time complexity of this function: O(mn)
  
        // table[i] will be storing the number of solutions
        // for value i. We need n+1 rows as the table is
        // constructed in bottom up manner using the base
        // case (n = 0)
        long[] table = new long[n+1];
  
        // Initialize all table values as 0
        Arrays.fill(table, 0);   //O(n)
  
        // Base case (If given value is 0)
        table[0] = 1;
  
        // Pick all coins one by one and update the table[]
        // values after the index greater than or equal to
        // the value of the picked coin
        for (int i=0; i<m; i++)
            for (int j=S[i]; j<=n; j++)
                table[j] += table[j-S[i]];
  
        return table[n];
    }
  
    // Driver Function to test above function
    public static void main(String args[])
    {
        int arr[] = {1, 2, 3};
        int m = arr.length;
        int n = 4;
        System.out.println(countWays(arr, m, n));
    }
}
// This code is contributed by Pankaj Kumar

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Please refer complete article on Dynamic Programming | Set 7 (Coin Change) for more details!




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