树的遍历_构造后序

通过前序遍历和后序遍历来构造出后序遍历/树

思路：由前序遍历可以看出树根是A，对应中序遍历，可以看出左子树有4个元素为DBGE，再把这四个元素对应到前序遍历中可以得知B是左子树的树跟……

左子树前序：BDEG

左子树中序：DBGE

由此可见，规模不断缩小，可用递归推出这棵树。

 思考算法时：只要减小问题规模即可

初始值的确定：根据递归函数定义

代码示例：

package com.sise.recursion;
/*
 * 遍历
 */
public class TreeTraversal {
	/*
	 * 前序遍历
	 */
	public void preOrder(TreeNode root) {
		if(root==null){
			return;
		}
		System.out.print(root.getValue());
		preOrder(root.getLeft());
		preOrder(root.getRighe());
	}
	
	/*
	 * 中序遍历
	 */
	public void inOrder(TreeNode root) {
		if(root==null){
			return;
		}
		inOrder(root.getLeft());
		System.out.print(root.getValue());
		inOrder(root.getRighe());
	}
	
	/*
	 * 后序遍历
	 */
	public void postOrder(TreeNode root) {
		if(root==null){
			return;
		}
		postOrder(root.getLeft());
		postOrder(root.getRighe());
		System.out.print(root.getValue());
	}
	
	/*
	 * 直接返回后序遍历，不建树
	 */
	public String postOrder(String preOrder,String inOrder) {
		if(preOrder.isEmpty()){//判断特殊情况
//			return null;返回的应该是字符串
			return "";
		}
		
		char rootValue=preOrder.charAt(0);
		int rootIndex=inOrder.indexOf(rootValue);
		
		return
		postOrder(
						preOrder.substring(1,1+rootIndex), 
						inOrder.substring(0,rootIndex))+
		postOrder(
						preOrder.substring(1+rootIndex),
						inOrder.substring(1+rootIndex))+
		rootValue;
	}
	
	
	public static void main(String[] args) {
		TreeCreator creator=new TreeCreator();
		TreeTraversal traversal=new TreeTraversal();
		
//		TreeNode sampleTree=creator.createSampleTree();
//		System.out.print("前序：");
//		traversal.preOrder(sampleTree);
//		System.out.println();
//		System.out.print("中序：");
//		traversal.inOrder(sampleTree);
//		System.out.println();
//		System.out.print("后序：");
//		traversal.postOrder(sampleTree);
//		System.out.println();
		
		System.out.println("-----构造树再遍历出后序--------");
		TreeNode tree=creator.creataTree("ABDEGCF", "DBGEACF");
		traversal.postOrder(tree);
		System.out.println();
		traversal.postOrder(creator.creataTree("", ""));
		System.out.println();
		traversal.postOrder(creator.creataTree("A", "A"));
		System.out.println();
		traversal.postOrder(creator.creataTree("AB", "BA"));
		System.out.println();
		
		System.out.println("-----直接构造后序--------");
		System.out.println(
				traversal.postOrder("ABDEGCF", "DBGEACF"));
		System.out.println(
				traversal.postOrder("", ""));
		System.out.println(		
			traversal.postOrder("A", "A"));
		System.out.println(
				traversal.postOrder("AB", "BA"));
	}
}

package com.sise.recursion;

/*
 * 建树
 */
public class TreeCreator {
//	public TreeNode createSampleTree() {
//	TreeNode root=new TreeNode('A');
//	root.setLeft(new TreeNode('B'));
//	root.getLeft().setLeft(new TreeNode('D'));
//	root.getLeft().setRighe(new TreeNode('E'));
//	root.getLeft().getRighe().setLeft(new TreeNode('G'));
//	root.setRighe(new TreeNode('C'));
//	root.getRighe().setRighe(new TreeNode('F'));
//	return root;
//	}
	
	public TreeNode creataTree(String preOrder,String inOrder) {
		if(preOrder.isEmpty()){//判断特殊情况
			return null;
		}
		char rootValue=preOrder.charAt(0);
		int rootIndex=inOrder.indexOf(rootValue);
		
		TreeNode root=new TreeNode(rootValue);
		root.setLeft(
				creataTree(
						preOrder.substring(1,1+rootIndex), 
						inOrder.substring(0,rootIndex)));
		root.setRighe(
				creataTree(
						preOrder.substring(1+rootIndex),
						inOrder.substring(1+rootIndex)));
		return root;
		
	}
}

package com.sise.recursion;

public class TreeNode {
	private final char value;
	private TreeNode left;
	private TreeNode righe;
	
	public TreeNode (char value) {
		this.value=value;
		this.left=null;
		this.righe=null;
	}

	public TreeNode getLeft() {
		return left;
	}

	public void setLeft(TreeNode left) {
		this.left = left;
	}

	public TreeNode getRighe() {
		return righe;
	}

	public void setRighe(TreeNode righe) {
		this.righe = righe;
	}

	public char getValue() {
		return value;
	}
	
	
}

运行结果：