完全二叉搜索樹Complete Binary Search Tree

問題描述

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

思路分析

先將輸入排個序，然後最小的結點放在樹中的最左下的結點，次小的放在上個結點的根結點，再次小的放在根結點的右子樹上，遞歸放置，最後層序輸出即可。

C語言代碼

#include <stdio.h>
#include <stdlib.h>

int b[2048];
int pos = 0;

void sort(int *arr, int num)
{
    int i, j;
    int temp;

    for(i=0;i<num;i++) {
        for(j=i;j<num;j++) {
            if(arr[i]>arr[j]) {
                temp = arr[j];
                arr[j] = arr[i];
                arr[i] = temp;
            }
        }
    }
}

void mid_tree(int root, int N, int a[])
{
    if(root<=N) {
        mid_tree(2*root, N, a);
        b[root] =  a[pos++];
        mid_tree(2*root+1, N, a);
    }
}

int main()
{
    int N, i;
    int data[2048];
    scanf("%d\n", &N);
    for(i=0;i<N;i++) {
        scanf("%d", &data[i]);        
    }
    sort(data, N);
    mid_tree(1, N, data);
    for(i=1;i<=N;i++) {
        if(i==1) {
            printf("%d", b[i]);
        } else {
            printf(" %d", b[i]);
        }
    }

    return 0;
}