PAT甲级1064. Complete Binary Search Tree (30)

A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

1. The left subtree of a node contains only nodes with keys less than the node’s key.

2. The right subtree of a node contains only nodes with keys greater than or equal to the node’s key.

3. 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

利用BST的中序遍历序列是有序的这一性质，
先给题目中给出的序列排序，
然后进行中序遍历，按顺序填数。
又因为是完全二叉树，所以结点i的左子是(2*i+1)，右子是(2*i+2) ，所以很容易进行各种遍历。

#include <cstdio>using namespace std;#include <vector>#include <algorithm>#include <queue>const int MAX=1000+10;int num[MAX],value[MAX];int N;int cnt=0;void FillNums(int root){  if((2*root+1)<N) FillNums(2*root+1);  value[root]=num[cnt];  cnt++;  if(2*root+2<N) FillNums(2*root+2);}void LevelOrder(int root){  queue<int> Q;  Q.push(root);  int flag=0;  while(!Q.empty()){    int tmp=Q.front();    Q.pop();    if(!flag) {      printf("%d",value[tmp]);      flag=1;    }    else printf(" %d",value[tmp]);    if((2*tmp+1)<N) Q.push(2*tmp+1);    if((2*tmp+2)<N) Q.push(2*tmp+2);  }}int main(){  scanf("%d",&N);  for(int i=0;i<N;i++) scanf("%d",&num[i]);  sort(num,num+N);  FillNums(0);  LevelOrder(0);  return 0;}