1064 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 (≤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

代码: 

#include<iostream>
#include<queue>
#include<algorithm>
#include<cmath>
using namespace std;
int N,count1=0;
vector<int > keys;
struct node
{
    int data;
    node* lchild;
    node* rchild;
};
node* creat(int L,int R)
{
    if(L>R)
        return NULL;
    int n=R-L+1;
    int h=ceil(log(n+1)/log(2));
    int bottom=n-pow(2,h-1)+1,BL;
    if(bottom>pow(2,h-1)/2)
        BL=pow(2,h-1)/2;
    else
        BL=bottom;
    int SL=(pow(2,h-1)-2)/2+BL;
    node *root=new node;
    root->data=keys[L+SL];
    root->lchild=creat(L,L+SL-1);
    root->rchild=creat(L+SL+1,R);
    return root;
}
void levelorder(node* root)
{
    queue<node *> Q;
    if(root==NULL)
        return;
    Q.push(root);
    while(!Q.empty())
    {
        node *p=Q.front();
        Q.pop();
        count1++;
        if(count1==1)
             printf("%d",p->data);
        else
            printf(" %d",p->data);
        if(p->lchild!=NULL)
            Q.push(p->lchild);
        if(p->rchild!=NULL)
            Q.push(p->rchild);
    }
}
int main()
{
    scanf("%d",&N);
    int temp;
    for(int i=0;i<N;i++)
    {
        scanf("%d",&temp);
        keys.push_back(temp);
    }
    sort(keys.begin(),keys.end());
    node* root=creat(0,N-1);
    levelorder(root);
    return 0;
}

 

原文地址：https://blog.csdn.net/fairylyt/article/details/123168270