/* 算法导论  15.5-1 打印最优二叉查找树
 * 最优二叉查找树 
 * e[i,j] = q[i-1](j = i-1)  e[i,j] = min{e[i,r-1] + r[r+1,j] + w[i,j] | i=<r<=j} 
 * w[i,j] = w[i,j-1] + p[j] + q[j]    
 * root[i,j]为k[r]的下标  k[r]是包含关键字的一棵最优二叉树的根
 * */

public class OptimalBest {
    public static final int N = 5;
    public int count = 0;

    public static void main(String[] args) {
        OptimalBest ob = new OptimalBest();
        int[] p = new int[] { 0, 15, 10, 5, 10, 20 };
        int[] q = new int[] { 5, 10, 5, 5, 5, 10 };
        int[][] e = new int[N + 2][N + 1];
        int[][] w = new int[N + 2][N + 1];
        int[][] root = new int[N + 1][N + 1];

        for (int i = 1; i <= N + 1; i++)
            w[i][i - 1] = e[i][i - 1] = q[i - 1];
        for (int l = 1; l <= N; l++) {
            for (int i = 1; i <= N - l + 1; i++) {
                int j = i + l - 1;
                e[i][j] = Integer.MAX_VALUE;
                w[i][j] = w[i][j - 1] + p[j] + q[j];
                for (int r = i; r <= j; r++) {
                    int t = e[i][r - 1] + e[r + 1][j] + w[i][j];
                    if (t < e[i][j]) {
                        e[i][j] = t;
                        root[i][j] = r;
                    }
                }
            }
        }
        ob.construct_optimal_bst(root);
    }

    private void construct_optimal_bst(int[][] root) {
        int r = root[1][N];
        System.out.println("k" + r + "是根");
        construct_opt_subtree(1, r - 1, r, "左", root);
        construct_opt_subtree(r + 1, N, r, "右", root);
    }

    private void construct_opt_subtree(int i, int j, int r, String dir,
            int[][] root) {
        if (i <= j) {
            int t = root[i][j];
            System.out.println("k" + t + "是k" + r + "的" + dir + "孩子");
            construct_opt_subtree(i, t - 1, t, "左", root);
            construct_opt_subtree(t + 1, j, t, "右", root);
        } else {
            System.out.println("d" + (count++) + "是k" + r + "的" + dir + "孩子");
        }
    }
}

输出结果

k2是根
k1是k2的左孩子
d0是k1的左孩子
d1是k1的右孩子
k5是k2的右孩子
k4是k5的左孩子
k3是k4的左孩子
d2是k3的左孩子
d3是k3的右孩子
d4是k4的右孩子
d5是k5的右孩子