动态规划之最优二叉搜索树

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/* * 最优二叉搜索树 */public class OptimalBST {private final int MAX=10000;private final int SCALE = 5;//树的规模private double[][]  e= null;//e[i][j]表示树ki..kj的期望代价private double[][]  w= null;//子树期望代价增加值private int[][]  root=null;//记录子树的根private double[] p = {0,0.15,0.10,0.05,0.10,0.20};//k1..k5的概率private double[] q = {0.05,0.10,0.05,0.05,0.05,0.10};//d1..d5的概率public static void main(String[] args) {OptimalBST obst = new OptimalBST();obst.compute();//最优二叉搜索树obst.print(1, obst.SCALE, 0);}public OptimalBST() {e = new double[SCALE+2][SCALE+1];w = new double[SCALE+2][SCALE+1];root = new int[SCALE+2][SCALE+1];}//计算得到最优二叉搜索树期望代价private void compute() {for(int i=1;i<=SCALE+1;i++) {e[i][i-1] = q[i-1];w[i][i-1] = q[i-1];}for(int len=1;len<=SCALE;len++) {for(int i=1;i<=SCALE-len+1;i++) {int j=i+len-1;e[i][j] = MAX;w[i][j] = w[i][j-1] + p[j] + q[j];for(int r=i;r<=j;r++) {double 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;}}}}}//打印最优二叉查找树的结构void print(int i,int j,int r){int rootChild = root[i][j];//子树根节点if (rootChild == root[1][SCALE]) {//输出整棵树的根System.out.println("k" + rootChild + "是根");print(i,rootChild - 1,rootChild);print(rootChild + 1,j,rootChild);return;}if (j < i - 1) {return;}else if (j == i - 1) { //遇到虚拟键if (j < r) {System.out.println("d" + j + "是k" + r + "的左孩子");}elseSystem.out.println("d" + j + "是k" + r + "的右孩子");return;}else {      //遇到内部结点if (rootChild < r) {System.out.println("k" + j + "是k" + r + "的左孩子");}else {System.out.println("k" + j + "是k" + r + "的右孩子");}}print(i,rootChild - 1,rootChild);print(rootChild + 1,j,rootChild);}}

运行结果与算法导论上一致：

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

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