首页 > 试题广场 >

Complete Binary Search Tree (3

[编程题]Complete Binary Search Tree (3

热度指数：2458 时间限制：C/C++ 1秒，其他语言2秒空间限制：C/C++ 64M，其他语言128M
算法知识视频讲解

A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

The left subtree of a node contains only nodes with keys less than the node's key.
The right subtree of a node contains only nodes with keys greater than or equal to the node's key.
Both the left and right subtrees must also be binary search trees.
A Complete Binary Tree (CBT) is a tree that is completely filled, with the possible exception of the bottom level, which is filled from left to right.
Now given a sequence of distinct non-negative integer keys, a unique BST can be constructed if it is required that the tree must also be a CBT. You are supposed to output the level order traversal sequence of this BST.

输入描述:

Each input file contains one test case.  For each case, the first line contains a positive integer N (<=1000).  Then N distinct non-negative integer keys are given in the next line.  All the numbers in a line are separated by a space and are no greater than 2000.

输出描述:

For each test case, print in one line the level order traversal sequence of the corresponding complete binary search tree.  All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.

示例1

输入

10
1 2 3 4 5 6 7 8 9 0

输出

6 3 8 1 5 7 9 0 2 4

算法知识视频讲解

Java

Jingmin

我的方法：

（引用方式/非数组）按层次建树，中序遍历写值，层次遍历输出

package com.jingmin.advanced2;

import java.util.*;

/**
 * @author : wangjm
 * @date : 2020/6/9 21:21
 * @discription : https://www.nowcoder.com/pat/5/problem/4115
 * 建立二叉搜索树，且要求为完全二叉树（唯一），然后层次遍历输出
 * <p>
 * 按层次建树，中序遍历写值，再层次遍历取值
 */
public class Advanced1022 {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
        }
        scanner.close();

        Arrays.sort(a);
        Node1022 root = setupCompleteBinaryTree(n);
        ArrayList<Node1022> inOrdrList = inOrderTraversal(root);
        for (int i = 0; i < n; i++) {
            inOrdrList.get(i).value = a[i];
        }
        ArrayList<Node1022> levelOrderList = bfs(root);
        StringBuilder sb = new StringBuilder();
        for (Node1022 node : levelOrderList) {
            sb.append(node.value).append(" ");
        }
        sb.setLength(sb.length() - 1);
        System.out.println(sb);
    }

    /**
     * 层次建树，初始化一个n个节点的完全二叉树(n>=1)
     * 注意，这个二叉树只建立起结构，没有存入值
     */
    private static Node1022 setupCompleteBinaryTree(int n) {
        int count = 0;
        Node1022 root = new Node1022();
        Queue<Node1022> queue = new LinkedList<>();
        queue.add(root);
        count++;
        while (!queue.isEmpty() && count < n) {
            Node1022 node = queue.poll();
            if (count < n) {
                node.lChild = new Node1022();
                queue.add(node.lChild);
                count++;
            }
            if (count < n) {
                node.rChild = new Node1022();
                queue.add(node.rChild);
                count++;
            }
        }
        return root;
    }

    /**
     * 中序遍历
     */
    private static ArrayList<Node1022> inOrderTraversal(Node1022 node) {
        ArrayList<Node1022> list = new ArrayList<>();
        Stack<Node1022> stack = new Stack<>();
        while (!stack.isEmpty() || node != null) {
            while (node != null) {
                stack.push(node);
                node = node.lChild;
            }
            node = stack.pop();
            list.add(node);
            node = node.rChild;
        }
        return list;
    }

    private static ArrayList<Node1022> bfs(Node1022 root) {
        ArrayList<Node1022> list = new ArrayList<>();
        Queue<Node1022> queue = new LinkedList<>();
        queue.add(root);
        while (!queue.isEmpty()) {
            Node1022 node = queue.poll();
            list.add(node);
            if (node.lChild != null) {
                queue.add(node.lChild);
            }
            if (node.rChild != null) {
                queue.add(node.rChild);
            }
        }
        return list;
    }
}

class Node1022 {
    int value;
    Node1022 lChild, rChild;
}

发表于 2020-06-09 23:07:58 回复(0)