04-树6 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 $N$ ($\le 1000$). 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:

101 2 3 4 5 6 7 8 9 0

Sample Output:

6 3 8 1 5 7 9 0 2 4

/*  输出CBT（complete BST）的层序 */#include "iostream"#include "algorithm"using namespace std;int k = 1;int n;int *a;int tree[1001];void build(int root) {if (root >n)return;int l = root << 1;int r = (root << 1) + 1;build(l);tree[root] = a[k++];build(r);}int main(){cin >> n;    a = new int[n+1];for (int i = 1; i <= n; i++)cin >> a[i];sort(a + 1, a + n +1);  /* 得到CBT的中序 */build(1);for (int i = 1; i <= n; i++)if (i == 1)cout << tree[i];elsecout << " " << tree[i];cout << endl;return 0;}