【算法】重建二叉树并进行后序遍历的Java实现

import java.util.HashMap;
import java.util.Map;

class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;
    TreeNode(int x) { val = x; }
}

public class BinaryTree {
    private int preIndex = 0;
    private Map<Integer, Integer> inorderIndexMap = new HashMap<>();

    public TreeNode buildTree(int[] preorder, int[] inorder) {
        for (int i = 0; i < inorder.length; i++) {
            inorderIndexMap.put(inorder[i], i);
        }
        return buildTreeHelper(preorder, 0, inorder.length - 1);
    }

    private TreeNode buildTreeHelper(int[] preorder, int inorderStart, int inorderEnd) {
        if (inorderStart > inorderEnd) {
            return null;
        }
        
        int rootVal = preorder[preIndex++];
        TreeNode root = new TreeNode(rootVal);
        int inorderIndex = inorderIndexMap.get(rootVal);
        
        root.left = buildTreeHelper(preorder, inorderStart, inorderIndex - 1);
        root.right = buildTreeHelper(preorder, inorderIndex + 1, inorderEnd);
        
        return root;
    }

    public void postorderTraversal(TreeNode root) {
        if (root == null) {
            return;
        }
        postorderTraversal(root.left);
        postorderTraversal(root.right);
        System.out.print(root.val + " ");
    }

    public static void main(String[] args) {
        int[] preorder = {3, 9, 20, 15, 7};
        int[] inorder = {9, 3, 15, 20, 7};
        
        BinaryTree binaryTree = new BinaryTree();
        TreeNode root = binaryTree.buildTree(preorder, inorder);
        
        System.out.println("Postorder traversal:");
        binaryTree.postorderTraversal(root);
    }
}

代码解释

TreeNode类：定义二叉树节点的数据结构。

java 复制代码

class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;
    TreeNode(int x) { val = x; }
}

BinaryTree类：包含重建二叉树和后序遍历的方法。
- buildTree 方法：接受前序遍历和中序遍历数组，构建并返回二叉树的根节点。
- buildTreeHelper 方法：递归地构建二叉树。
- postorderTraversal 方法：递归地进行后序遍历，并输出节点值。

buildTreeHelper方法：通过前序遍历的当前节点值和中序遍历的索引，递归地构建左右子树。

java 复制代码

private TreeNode buildTreeHelper(int[] preorder, int inorderStart, int inorderEnd) {
    if (inorderStart > inorderEnd) {
        return null; // Base case: no elements to construct the tree
    }

    int rootVal = preorder[preIndex++]; // Get the current root value from preorder traversal
    TreeNode root = new TreeNode(rootVal); // Create the root node
    int inorderIndex = inorderIndexMap.get(rootVal); // Find the index of the root in inorder traversal

    // Recursively build the left subtree
    root.left = buildTreeHelper(preorder, inorderStart, inorderIndex - 1);
    // Recursively build the right subtree
    root.right = buildTreeHelper(preorder, inorderIndex + 1, inorderEnd);

    return root;
}

后序遍历：通过递归方法进行后序遍历，按照左子树 -> 右子树 -> 根节点的顺序输出节点值。

java 复制代码

public void postorderTraversal(TreeNode root) {
    if (root == null) {
        return;
    }
    postorderTraversal(root.left);
    postorderTraversal(root.right);
    System.out.print(root.val + " ");
}

main方法 ：创建前序遍历和中序遍历数组，调用buildTree方法构建二叉树，然后调用postorderTraversal方法输出后序遍历结果。

java 复制代码

public static void main(String[] args) {
    int[] preorder = {3, 9, 20, 15, 7};
    int[] inorder = {9, 3, 15, 20, 7};
    
    BinaryTree binaryTree = new BinaryTree();
    TreeNode root = binaryTree.buildTree(preorder, inorder);
    
    System.out.println("Postorder traversal:");
    binaryTree.postorderTraversal(root);
}