1064 Complete Binary Search Tree （BST+CBT）

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

　　

这道题十分巧妙，当BST是完全二叉树时，它的数组存储即满足层序遍历。

思路为对数组表示的二叉树进行中序遍历，并按从小到大的顺序填入数组，最后顺序输出即为层序遍历。

#include<cstdio>
#include<algorithm>
using namespace std;
int n,index=0;
int a[1010];
int b[1010];

void inorder(int x){
    if(x>n) return;
    inorder(2*x);
    b[x]=a[index++];
    inorder(2*x+1);
}

int main(){
    scanf("%d",&n);
    for(int i=0;i<n;i++)
        scanf("%d",&a[i]);
    sort(a,a+n);
    inorder(1);
    for(int i=1;i<=n;i++){
        printf("%d",b[i]);
        if(i<n) printf(" ");
    }    
    return 0;
}

最后附上我之前自己写的递归，代码存在死循环问题，但vs过期了，没有调试排错，留到以后解决

#include<cstdio>
#include<algorithm>
#include<queue> 
#include<cmath>
using namespace std;
int a[1010];
int b[15];
int n;

struct node{
    int data;
    node *left,*right;
}*Node;

node* change(int num,int l,int r){
    sort(a+l,a+r+1);
    if(num==0) return NULL;
    node *root=new node;
    int t=0,now=num-1;
    if(now==0){
        root->data=a[l];
        root->left=root->right=NULL;
        return root;
    }
    while(now>2*b[t]) t++;
    if(now>=b[t]+b[t-1]){//zuoman
        root->data=a[l+b[t]];
        root->left=change(b[t],l,l+b[t]-1);
        root->right=change(num-b[t]-1,l+b[t]+1,r);
        printf("%d
",root->data);
        return root;
    }else{//zuoweiman
        root->data=a[r-b[t-1]];
        root->left=change(num-b[t-1]-1,l,r-b[t-1]-1);
        root->right=change(b[t-1],r-b[t-1]+1,r);
        return root;
    }
}

void bfsprint(node *r){
    queue<node*> q;
    q.push(r);
    int tt=0;
    while(!q.empty()){
        node *f=q.front();
        q.pop();
        printf("%d",f->data);
        if(++tt<n) printf(" ");
        if(r->left!=NULL) q.push(r->left);
        if(r->right!=NULL) q.push(r->right);
    }
}

int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d",&a[i]);
    for(int i=0;i<=15;i++)
        b[i]=pow(2,i)-1;
    Node=change(n,1,n);
    //bfsprint(Node);
    return 0;
}