题目
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:
10
1 2 3 4 5 6 7 8 9 0
Sample Output:
6 3 8 1 5 7 9 0 2 4
解题思路
题目大意: 题目要求对给定的序列建立完全二叉搜索树,所谓完全二叉搜索树就是要满足完全二叉树的搜索树。 。
解题思路: 我们知道,完全二叉树的结点i如果从1开始编号,那么左儿子为2* i,右儿子为2*i+1;而二叉搜索树的中序遍历为升序,因此只需要对输入序列按照升序排序,然后对完全二叉树进行中序遍历,填入相应的元素即可。。
#include <iostream>
#include <vector>
#include <stdio.h>
#include <algorithm>
using namespace std;
vector<int> tree;
vector<int> nodes;
int N;
void buildTree(int root){
static int index = 1;
if(root > N) return;
buildTree(root * 2);
tree[root] = nodes[index++];
buildTree(root * 2 + 1);
}
int main()
{
cin >> N;
nodes.resize(N+1);
tree.resize(N+1);
for(int i = 1; i <= N; i++){
scanf("%d",&nodes[i]);
}
sort(nodes.begin(),nodes.end());
buildTree(1);
printf("%d",tree[1]);
for(int i = 2; i <= N; i++)
printf(" %d",tree[i]);
cout << endl;
return 0;
}