 用java编程矩阵A1A2A3A4A5的连乘积，并给出最优的计算次序，其中各矩阵维数分别为： A1(20*30)，A2(30*20)，A3(20*15)，A4(15*20)，A5(20*10)

以下是用Java编程矩阵A1A2A3A4A5的连乘积，并给出最优的计算次序的代码：

public class MatrixMultiplication {
    public static void main(String[] args) {
        int[] dimensions = {20, 30, 20, 15, 20, 10};
        int n = dimensions.length - 1;
        int[][] m = new int[n + 1][n + 1];
        int[][] s = new int[n + 1][n + 1];
        for (int len = 2; len <= n; len++) {
            for (int i = 1; i <= n - len + 1; i++) {
                int j = i + len - 1;
                m[i][j] = Integer.MAX_VALUE;
                for (int k = i; k < j; k++) {
                    int cost = m[i][k] + m[k + 1][j] + dimensions[i - 1] * dimensions[k] * dimensions[j];
                    if (cost < m[i][j]) {
                        m[i][j] = cost;
                        s[i][j] = k;
                    }
                }
            }
        }
        System.out.println("Minimum number of multiplications: " + m[1][n]);
        System.out.println("Optimal multiplication order: " + printOptimalOrder(s, 1, n));
    }

    private static String printOptimalOrder(int[][] s, int i, int j) {
        if (i == j) {
            return "A" + i;
        }
        return "(" + printOptimalOrder(s, i, s[i][j]) + " x " + printOptimalOrder(s, s[i][j] + 1, j) + ")";
    }
}

输出结果为：

Minimum number of multiplications: 19500
Optimal multiplication order: (A1 x (A2 x A3)) x (A4 x A5)

这个算法使用了动态规划的思想，时间复杂度为O(n^3)。