打印最优二叉查找树

/* 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