04-树6 Complete Binary Search Tree（30 分）

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

#include <cstdio>#include <algorithm>//#define LOCAL#define MAXSIZE 1010int cbt[MAXSIZE];int num[MAXSIZE];int N, index = 0;void inOrder(int root) {    if(root > N) return;    inOrder(root*2);    cbt[root] = num[index++];    inOrder(root*2+1);}int main(){#ifdef LOCAL    freopen("test.txt", "r", stdin);#endif    scanf("%d", &N);    for(int i=0; i<N; ++i){        int tmp;        scanf("%d", &tmp);        num[i]=tmp;    }    std::sort(num, num+N);    inOrder(1);    for(int i=1; i<=N; ++i) {        if(i!=1) putchar(' ');        printf("%d", cbt[i]);    }    return 0;}

想了想，还是很困难，看了下晴神笔记，卧槽，豁然开朗，也很简洁。