动态规划之最优二叉搜索树

/*
* 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");
}
else
System.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);
}
}