java - Coin change DP解决方案来跟踪硬币

Question

尝试为一般硬币找零问题编写 DP 解决方案，同时跟踪使用了哪些硬币。到目前为止，我一直在努力为我提供所需的最少硬币数量，但无法弄清楚如何获得使用了哪些硬币以及使用了多少次。如果使用硬币，我尝试用值设置另一个表( boolean 值)，但这似乎无法正常工作。有什么想法吗？

public static int minChange(int[] denom, int changeAmount) 
{   
    int m = denom.length;
    int n = changeAmount + 1;

    int[][] table = new int[m][n];
    boolean[][] used = new boolean[m][n];
    for (int j = 0; j < n; j++)
        table[m - 1][j] = j;
    for (int i = 0; i < m; i++)
        table[i][0] = 0;

    for (int i = m-2; i >= 0; i--) //i denotes denominationIndex
    {
        for (int j = 1; j < n; j++) //j denotes current Amount
        {
            if (denom[i] > j)
            {
                table[i][j] = table[i+1][j];
                //used[i][j] = false;
            }
            else
            {
                table[i][j] = Math.min(1 + table[i][j-denom[i]], table[i+1][j]);
                /*Trying table for used coins
                if (1 + table[i][j-denom[i]] < table[i+1][j]) 
                    used[i][j] = true;
                else
                    used[i][j] = false;
                */
            }
        }
    }
}

Answer 1

试试这个解决方案，它只使用 O(M) 内存并且具有 O(N*M) 复杂度:

   public static int[] minChange(int[] denom, int changeAmount)
    {
        int n = denom.length;
        int[] count = new int[changeAmount + 1];
        int[] from = new int[changeAmount + 1];

        count[0] = 1;
        for (int i = 0 ; i < changeAmount; i++)
            if (count[i] > 0)
                for (int j = 0; j < n; j++)
                {
                    int p = i + denom[j];
                    if (p <= changeAmount)
                    {
                        if (count[p] == 0 || count[p] > count[i] + 1)
                        {
                            count[p] = count[i] + 1;
                            from[p] = j;
                        }
                    }
                }

        // No solutions:
        if (count[changeAmount] == 0)
            return null;

        // Build answer.
        int[] result = new int[count[changeAmount] - 1];
        int k = changeAmount;
        while (k > 0)
        {
            result[count[k] - 2] = denom[from[k]];
            k = k - denom[from[k]];
        }

        return result;
    }