BST：有序数组构建成二叉搜索树

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有序数组构建成二叉搜索树,使用x=change(x)模式

降序储存和顺序储存都会得到退化树。最有效保持树平衡的是，取数组中值（对于无重复元素的有序数组，中值就是数组中间元素）作为树根的值，将数组分为左右两个子数组，左子数组的数值均小于根节点，右子数组的值均大于根节点。将左子数组的中间元素作为根节点的左子树，将右子树的中间元素作为根节点的右子树，由此，形成递归关系，就能得到平衡的二叉搜索树。

package cc.binarytree;/* * 二叉查找树 Int  *  */import java.util.*;public class IntSearchTree {private IntTreeNode overallRoot;//根节点public IntSearchTree(){overallRoot=null;//空树}//构建二叉搜索树：//输入：有序数组 //返回值: 无public IntSearchTree(int[] a){overallRoot=buildTree(overallRoot,a,0,a.length-1);}//函数：构建二叉搜索树//输入：树根引用，数组，数组索引 0到a.length-1//返回值：节点引用private IntTreeNode buildTree(IntTreeNode root,int[] a,int start,int end){if(start>end){return null;//数组索引交叉，说明已经反问完该数组，退出递归}else{int m=(start+end)/2;root=new IntTreeNode(a[m]);root.left=buildTree(root.left,a,start,m-1);root.right=buildTree(root.right,a,m+1,end);}return root;}//添加元素public void add(int value){overallRoot=add(overallRoot,value);}private IntTreeNode add(IntTreeNode root,int value){if(root==null){root=new IntTreeNode(value);}else if(value<=root.data){root.left=add(root.left,value);}else{root.right=add(root.right,value);}return root;}//搜索元素 返回值类型boolean true：存在 false：不存在public boolean contain(int element){return contain(overallRoot,element);}private boolean contain(IntTreeNode root,int element){if(root==null){return false;}else if(root.data==element){return true;}else if(root.data>element){return contain(root.left,element);}else{return contain(root.right,element);}}//中序遍历二叉树public void printInOrder(){System.out.println("InOrder:  ");printInOrder(overallRoot);System.out.println();}private void printInOrder(IntTreeNode root){if(root!=null){printInOrder(root.left);System.out.print(root.data+" ");printInOrder(root.right);}}//打印出二叉树结构public void printSideWays(){System.out.println("BinaryTree Structure: ");printSideWays(0,overallRoot);}private void printSideWays(int level,IntTreeNode root){if(root!=null){printSideWays(level+1,root.right);for(int i=0;i<level;i++){System.out.print("     ");}System.out.print(root.data+"\n");printSideWays(level+1,root.left);}}public static void main(String[] args) {int[] a=new int[63];for(int i=0;i<63;i++){a[i]=2*i+1;}IntSearchTree tree=new IntSearchTree(a);//输入有序数组构建二叉树tree.printSideWays();tree.printInOrder();System.out.println("numbers contian 30?: "+tree.contain(30));System.out.println("numbers contian 99?: "+tree.contain(99));}}

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