1064 Complete Binary Search Tree （30 分)

2019-03-31

1064 Complete Binary Search Tree （30 分)

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 (≤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.

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:

1 2	10 1 2 3 4 5 6 7 8 9 0

Sample Output:

1	6 3 8 1 5 7 9 0 2 4

作者: CHEN, Yue

单位: 浙江大学

时间限制: 400 ms

内存限制: 64 MB

代码长度限制: 16 KB

题目大意

给出一组序列，要求建立完全二叉树，并输出层序遍历

分析

因为是完全二叉树，已知根结点编号i(从1开始)，可知左儿子编号2i，右儿子编号2i+1。且中序遍历结果为输入序列的递增序列。从根结点开始中序遍历，又已知中序遍历结果，那么就可以知道各结点上的值。然后从1-N遍历即是层序遍历结果。

代码

#include <iostream>
#include <vector>
#include <algorithm>
#include <deque>
#include <map>
#include <set>
#include <cstring>
#include <cmath>
#include<sstream>

using namespace std;
vector<int> tree;
vector<int> nodes;
int n,indexx=1;

void buildtree(int root){
    if(root>n)
        return;
    int left=root*2;
    int right=left+1;
    buildtree(left);
    tree[root]=nodes[indexx++];
    buildtree(right);
}

int main() {
    cin >> n;
    tree.resize(n+1);
    nodes.resize(n+1);
    for(int i=1;i<=n;i++)
        cin>>nodes[i];
    sort(nodes.begin(),nodes.end());
    buildtree(1);
    cout<<tree[1];
    for(int i=2;i<=n;i++)
        cout<<" "<<tree[i];
    return 0;
}