1064. Complete Binary Search Tree

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

基本思路是：先对输入的数进行非递减排序，排序之后，创建一棵空的完全二叉树，按中序遍历填充依次将数组中的元素填充到树中，因为二叉搜索树的中序遍历就是按元素值从小到大的排序。完成后再层序遍历一次。
程序代码：

#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<queue>
#define MAX 1001
using namespace std;
typedef struct node
{
    int data;
    struct node* left;
    struct node* right;
}node;
node* creat(node a[],int n);
int m=1;
void InOrderSet(node* s,int num[],int* i);
void InOrderVisit(node* s);
void levelTravel(node* root);
int comp(const void* a,const void* b);
int main()
{
    node a[MAX];
    int num[MAX];
    int n;
    scanf("%d",&n);
    int i=0;
    for(i=1;i<=n;i++)
    {
        scanf("%d",&num[i]);
    }
    qsort(&num[1],n,sizeof(int),comp);//排序
    creat(a,n);//创建空树
    InOrderSet(&a[1],num,&m);//中序遍历填充树
    levelTravel(&a[1]);//层序遍历树
    return 0;
}
node* creat(node a[],int n)//创建n个节点的空完全二叉树
{
    int i=1;
    if(n%2==0)
    {
        while((i*2+1)<=n)
        {
            a[i].left = &a[i*2];
            a[i].right = &a[i*2+1];
            i++;
        }
        a[i].left=&a[i*2];
        a[i].right=NULL;
        i++;
        while(i<=n)
        {
            a[i].left = NULL;
            a[i].right = NULL;
            i++;
        }
    }
    else
    {
                while((i*2)<=n)
                {
                        a[i].left = &a[i*2];
                        a[i].right = &a[i*2+1];
                        i++;
                }
                while(i<=n)
                {
                        a[i].left = NULL;
                        a[i].right = NULL;
                        i++;
                }

    }
    return &a[1];
}
void InOrderSet(node* s,int num[],int* i)//按中序遍历顺序填充完全二叉树
{

    if(s==NULL)
        return;
    else
        {
            InOrderSet(s->left,num,&m);
            s->data = num[m++];
        InOrderSet(s->right,num,&m);
        }  
}
/*void InOrderVisit(node* s) { if(s==NULL) return; else { InOrderVisit(s->left); printf("%d ",s->data); InOrderVisit(s->right); } }*/
void levelTravel(node* root) //层序遍历
{
    queue<node> s;
    s.push(*root);
    node p;
    while(!s.empty())
    {
        p = s.front();
        s.pop();
        cout<<p.data;
        if(p.left!=NULL)
            s.push(*(p.left));
        if(p.right!=NULL)
            s.push(*(p.right));
        if(!s.empty())
            cout<<' ';//避免在行末添加空格

    }   
}
int comp(const void* a,const void* b)//供qsort函数使用的比较函数
{
    return *(int*)a-*(int*)b;
}