pat 甲级 1064. Complete Binary Search Tree (30)

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

先按照定义构建完全二叉树的框架，接下来就是把数字分别填到这颗二叉树的节点中，使得其满足二叉搜索树的定义。其实填入节点可以直接中序遍历这颗二叉树框架即可。
AC代码：

#define _CRT_SECURE_NO_DEPRECATE
#pragma warning(disable:4996)
#include<iostream>
#include<string>
#include<algorithm>
#include<map>
#include<cctype>
#include<cmath>
#include<cstring>
#include<vector>
#include<set>
#include<queue>
#include<limits.h>
using namespace std;
typedef long long ll;
#define N_MAX 1000+5
#define INF 0x3f3f3f3f
int n, a[N_MAX];
struct Node {
    int key;
    int l_child, r_child;
    Node(int key=INF,int l_child=INF,int r_child=INF):key(key),l_child(l_child),r_child(r_child) {}
}node[N_MAX];
void init(int n) {//建立完全二叉树的框架
    n--;
    int cur = 0;
    int flag = 0;
    while (n--) {
        if (!(flag & 1))node[cur].l_child = 2 * cur + 1;
        else {
            node[cur].r_child = 2*cur+2;
            cur++;
        }
        flag++;
    }
}

int cnt = 0;
void inorder(int n) {
    if(node[n].l_child!=INF)inorder(node[n].l_child);
    node[n].key = a[cnt++];
    if(node[n].r_child!=INF)inorder(node[n].r_child);
}
vector<int>vec;
void bfs() {
    queue<int>que;
    que.push(0);
    while (!que.empty()) {
        int p = que.front(); que.pop();
        vec.push_back(node[p].key);
        if (node[p].l_child != INF)que.push(node[p].l_child);
        if (node[p].r_child != INF)que.push(node[p].r_child);
    }
}
int main() {
    while (scanf("%d", &n) != EOF) {
        for (int i = 0; i < n; i++) {
            scanf("%d", &a[i]);
        }
        sort(a,a+n);
        init(n);
        cnt = 0;
        inorder(0);
        bfs();
        for (int i = 0; i < vec.size();i++) {
            printf("%d%c",vec[i],i+1==vec.size()?'\n':' ');
        }
    }
    return 0;
}