PAT 甲级 1064 Complete Binary Search Tree

发布时间：2020-12-14 05:12:37 所属栏目：大数据来源：网络整理

导读：https://pintia.cn/problem-sets/994805342720868352/problems/994805407749357568 ? 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

https://pintia.cn/problem-sets/994805342720868352/problems/994805407749357568

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?

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 <bits/stdc++.h>
using namespace std;

const int maxn = 1e5 + 10;
int N;
int a[maxn];
vector<int> level;

void levelorder(int st,int en,int index) {
    if(st > en) return ;
    int n = en - st + 1;
    int l = log(n + 1) / log(2);
    int leave = n - (pow(2,l) - 1);
    int root = st + (pow(2,l - 1) - 1) + min((int)pow(2,l - 1),leave);
    level[index] = a[root];
    levelorder(st,root - 1,2 * index + 1);
    levelorder(root + 1,en,2 * index + 2);
}

int main() {
    scanf("%d",&N);
    level.resize(N);
    for(int i = 0; i < N; i ++)
        scanf("%d",&a[i]);

    sort(a,a + N);
    levelorder(0,N - 1,0);
    for(int i = 0; i < N; i ++) {
        printf("%d",level[i]);
        printf("%s",i != N - 1 ? " " : "n");
    }
    return 0;
}

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