PAT甲级练习1064. Complete Binary Search Tree (30)

最新推荐文章于 2019-09-06 15:00:37 发布

最新推荐文章于 2019-09-06 15:00:37 发布 · 270 阅读

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本文介绍如何通过给定的一组非负整数构造一个既为二叉搜索树又为完全二叉树的数据结构，并输出该树的层次遍历序列。文章提供了完整的代码实现，包括DFS构建树和BFS进行层次遍历。

1064. Complete Binary Search Tree (30)

时间限制

100 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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

完全搜索二叉树的中序遍历就是一个序列的递增排序，反推可以用dfs把值放到对应的位置上，层次遍历用bfs，参考http://blog.youkuaiyun.com/jtjy568805874/article/details/50917474

#include <iostream>  
#include <cstdio>  
#include <algorithm>  
#include <vector>  
#include <map>  
#include <set>  
#include <stack>  
#include <queue>  
#include <string>  
#include <string.h> 
using namespace std;

const int MAX = 1e3+10;
int n, a[MAX], b[MAX], cnt;

void dfs(int x){
	if(x>n) return;
	dfs(x<<1);
	b[x] = a[cnt++];
	dfs(x<<1|1);
}

void bfs(int x){
	queue<int> p; p.push(x);
	while(!p.empty()){
		int q = p.front();p.pop();
		printf("%d%s", b[q], q == n ? "\n" : " ");
		if((q<<1)<=n) p.push(q<<1);
		if((q<<1|1)<=n) p.push(q<<1|1);
	}
}

int main() {

	scanf("%d", &n);
	for(int i=0; i<n; i++){
		scanf("%d", &a[i]);
	}
	sort(a, a+n);

	dfs(1);
	bfs(1);

	scanf("%d",&n);
    return 0;
}