Java数据结构——根据遍历结果构造二叉树

一、已知前序、中序、后序遍历结果的其中两种，还原二叉树。

①已知前序遍历结果：1，2，4，5，3，6，7
中序遍历结果：4，2，5，1，6，3，7
还原二叉树后BFS出结果。

TreeNode.java

public class TreeNode {
private TreeNode leftChild;
private TreeNode rightChild;
private Object data;

public TreeNode getLeftChild() {
return leftChild;
}

public void setLeftChild(TreeNode leftChild) {
this.leftChild = leftChild;
}

public TreeNode getRightChild() {
return rightChild;
}

public void setRightChild(TreeNode rightChild) {
this.rightChild = rightChild;
}

public Object getData() {
return data;
}

public void setData(Object data) {
this.data = data;
}

public TreeNode(Object data) {
super();
this.data = data;
}
}

CreateTree.java:

import java.util.LinkedList;
import java.util.Queue;

public class CreateTree {
public static TreeNode genenateTree(int[] pre, int[] in) {
if (pre.length == 0 || in.length == 0) {
return null;
}
TreeNode root = new TreeNode(pre[0]);
int i = 0;
while (in[i] != pre[0]) {
i++;
}
int[] preLeftChild = new int[i];
int[] preRightChild = new int[pre.length - 1 - i];
int[] inLeftChild = new int[i];
int[] inRightChild = new int[pre.length - 1 - i];
for (int j = 0; j < in.length; j++) {
if (j < i) {
preLeftChild[j] = pre[j + 1];
inLeftChild[j] = in[j];
} else if (j > i) {
preRightChild[j - i - 1] = pre[j];
inRightChild[j - i - 1] = in[j];
}
}
root.setLeftChild(genenateTree(preLeftChild, inLeftChild));
root.setRightChild(genenateTree(preRightChild, inRightChild));
return root;
}

public static void visited(TreeNode node) {
System.out.print(node.getData() + " ");
}

public static void LevenOrder(TreeNode root) {
if (root == null) {
return;
}
Queue<TreeNode> queue = new LinkedList<>();
queue.add(root);
TreeNode temp = null;
while (!queue.isEmpty()) {
temp = queue.poll();
visited(temp);
if (temp.getLeftChild() != null) {
queue.add(temp.getLeftChild());
}
if (temp.getRightChild() != null) {
queue.add(temp.getRightChild());
}
}
}

public static void main(String[] args) {
int[] pre = { 1, 2, 4, 5, 3, 6, 7 };
int[] in = { 4, 2, 5, 1, 6, 3, 7 };
LevenOrder(genenateTree(pre, in));
}
}

　　

②已知前序遍历结果：1，2，4，5，3，6，7
后序遍历结果：4，5，2，6，7，3，1
这种情况不能确定唯一的二叉树（即根据前序、后序结果不能确定唯一二叉树）

③已知 中序遍历结果：4，2，5，1，6，3，7
后序遍历结果：4，5，2，6，7，3，1
还原二叉树后BFS出结果。

//这里只写出核心代码，其他部分可以参考第一种情况
public class CreateTree {
public static TreeNode genenateTree(int[] in, int[] post) {
if (post.length == 0 || in.length == 0) {
return null;
}
TreeNode root = new TreeNode(post[post.length - 1]);
int i = 0;
while (in[i] != post[post.length - 1]) {
i++;
}
int[] postLeftChild = new int[i];
int[] postRightChild = new int[post.length - 1 - i];
int[] inLeftChild = new int[i];
int[] inRightChild = new int[post.length - 1 - i];
for (int j = 0; j < in.length; j++) {
if (j < i) {
postLeftChild[j] = post[j];
inLeftChild[j] = in[j];
} else if (j > i) {
postRightChild[j - i - 1] = post[j - 1];
inRightChild[j - i - 1] = in[j];
}
}
root.setLeftChild(genenateTree(inLeftChild, postLeftChild));
root.setRightChild(genenateTree(inRightChild, postRightChild));
return root;
}

　　

二、如果已知的前序、中序、后序的结果中包含占位符#，此时，只需知道其中一种遍历结果就能还原二叉树，且结果是唯一的。

 

①已知前序遍历结果是 ："1", "2", "4", "#", "#", "5", "#", "#", "3", "6", "#", "#", "7", "#", "#"，还原二叉树后BFS出结果。

import java.util.LinkedList;
import java.util.Queue;

public class CreateTree {
static int count = 0;

public static TreeNode genenateTree(String[] data) {
TreeNode root = null;
if (count >= data.length || data[count++].equals("#")) {
root = null;
} else {
root = new TreeNode(data[count - 1]);
root.setLeftChild(genenateTree(data));
root.setRightChild(genenateTree(data));
}
return root;
}

public static void visited(TreeNode node) {
System.out.print(node.getData() + " ");
}

public static void LevenOrder(TreeNode root) {
if (root == null) {
return;
}
Queue<TreeNode> queue = new LinkedList<>();
queue.add(root);
TreeNode temp = null;
while (!queue.isEmpty()) {
temp = queue.poll();
visited(temp);
if (temp.getLeftChild() != null) {
queue.add(temp.getLeftChild());
}
if (temp.getRightChild() != null) {
queue.add(temp.getRightChild());
}
}
}

public static void main(String[] args) {
String[] dataStr = { "1", "2", "4", "#", "#", "5", "#", "#", "3", "6", "#", "#", "7", "#", "#" };
LevenOrder(genenateTree(dataStr));
}
}