題目

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.

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

題目大意

創(chuàng)建二叉搜索樹，且該樹同時為完全二叉樹。

思路

創(chuàng)建BST一般方法是鏈表插入，但注意到是完全二叉樹，其特殊性質(zhì)是在數(shù)組中，若根節(jié)點下標為i，則2i為左子樹根節(jié)點下標，2i+1為右子樹根結(jié)點下標（兩下標皆不超過節(jié)點數(shù)n），所以可以考慮使用數(shù)組進行創(chuàng)建比較簡便。
　　顯然BST的中序遍歷是有序的，在構(gòu)造完全二叉樹的時候按中序構(gòu)造即可（注意要先進行排序）。
　　
代碼實現(xiàn)

#include <stdio.h>
#include <stdlib.h>
#define maxSize 1001

int tree[maxSize];      // 存放完全二叉搜索樹
int node[maxSize];      // 存放節(jié)點信息
int root, pos;          // 樹中根節(jié)點下標，存儲節(jié)點下標
int n;

 /*qsort比較函數(shù)*/
int cmp(const void *a, const void *b)
{
    return *(int *)a - *(int *)b; 
}

/*tree數(shù)組輸出，即為層次遍歷輸出*/
void print(int a[], int n)
{
    int flag = 0;
    int i;
    for (i = 1; i <= n; ++i)
    {
        if(!flag)
        {
            flag = 1;
            printf("%d", a[i]);
        }
        else
            printf(" %d", a[i]);
    } 
}

/*創(chuàng)建CBST*/
void build(int root)
{
    if (root > n)
        return;
    int lchild = root * 2;
    int rchild = root * 2 + 1;
    
    /*關(guān)鍵步驟，中序遍歷建樹*/
    build(lchild);              
    tree[root] = node[pos++];       // 按序?qū)⒋鎯Φ慕Y(jié)點插入樹中
    build(rchild);
}

int main(void)
{
    int i;
    scanf("%d", &n);
    for(i = 1; i <= n; ++i)
        scanf("%d", &node[i]);
    qsort(&node[1], n, sizeof(int), cmp);
    pos = 1;
    build(1);
    print(tree, n);
    return 0;
}

參考

CSDN博客 - 凌風