1064 Complete Binary Search Tree

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.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (≤). 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.

Output Specification:

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.

Sample Input:

10
1 2 3 4 5 6 7 8 9 0

 

Sample Output:

6 3 8 1 5 7 9 0 2 4

 

题意：

　　给出一组数字，用这组数字构成一棵完全二叉搜索树。

思路：

　　完全二叉搜索树中序遍历的结果，就是升序排序的结果。所以我们可以根据结点的个数，构造出一棵完全二叉搜索树的框架，然后再中序遍历这棵树，将所给的数组排序后依次插入即可。

Code：　　

#include <bits/stdc++.h>

using namespace std;

typedef struct Node* node;

struct Node {
    int val;
    node left;
    node right;
    Node(int v) {
        val = v;
        left = NULL;
        right = NULL;
    }
};

void buildTree(node& root, int num) {
    queue<node> que;
    que.push(root);
    int count = 1;
    while (count < num) {
        node temp = que.front();
        que.pop();
        temp->left = new Node(-1);
        que.push(temp->left);
        count++;
        if (count < num) {
            temp->right = new Node(-1);
            que.push(temp->right);
            count++;
        }
    }
};

int tempIndex = 0;
void inorderTraveral(node& root, vector<int>& keys) {
    if (root == NULL) return;
    inorderTraveral(root->left, keys);
    root->val = keys[tempIndex++];
    inorderTraveral(root->right, keys);
}

void levelTraveral(node& root) {
    queue<node> que;
    que.push(root);
    bool isFirst = true;
    while (!que.empty()) {
        node temp = que.front();
        que.pop();
        if (isFirst) {
            cout << temp->val;
            isFirst = false;
        } else {
            cout << " " << temp->val;
        }
        if (temp->left != NULL) que.push(temp->left);
        if (temp->right != NULL) que.push(temp->right);
    }
}

int main() {
    int n;
    cin >> n;
    vector<int> keys(n);
    for (int i = 0; i < n; ++i) cin >> keys[i];
    sort(keys.begin(), keys.end());
    node root = new Node(-1);
    buildTree(root, n);
    inorderTraveral(root, keys);
    levelTraveral(root);
    return 0;
}