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题目大意：给一串构成树的序列，已知该树是完全二叉搜索树，求它的层序遍历的序列
由于是满二叉树，用数组既可以表示
父节点是i，则左孩子是2*i，右孩子是2*i+1
另外根据二分搜索树的性质，中序遍历恰好是从小到大排序
因此先中序遍历填充节点对应的值，然后再层次遍历输出即可。
#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
int n;
vector<int>minorder;
void mintraver(int root)
{
if(root>n) return;
mintraver(2*root);
minorder.push_back(root);
mintraver(2*root+1);
}
int main()
{
cin>>n;
int num[1001],level[1001];
for(int i=0;i<n;i++)
cin>>num[i];
sort(num,num+n);
mintraver(1);
for(int i=0;i<minorder.size();i++)
level[minorder[i]]=num[i];
for(int i=1;i<n;i++)
cout<<level[i]<<" ";
cout<<level[n];
return 0;
}
bfs，本来就是应用层序遍历的思想来扫的
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <string.h>
#include <queue>
using namespace std;
const int maxn=1005;
int a[maxn];
int node[maxn];
int cnt=0;
void build(int root,int n){
if(cnt>n)
return;
if(root>n)
return;
build(root<<1,n);
node[root]=a[++cnt];
//printf("id:%d val:%d\n",root,node[root]);
build((root<<1)|1,n);
}
void BFS(int root,int n){
queue<int> q;
q.push(root);
int v;
bool first=true;
while(!q.empty()){
v=q.front();
q.pop();
if(first){
first=false;
printf("%d",node[v]);
}
else
printf(" %d",node[v]);
if(v*2<=n)
q.push(v*2);
if(v*2+1<=n)
q.push(v*2+1);
}
}
int main()
{
int n;
scanf("%d",&n);
for(int i=1;i<=n;i++)
scanf("%d",&a[i]);
sort(a+1,a+n+1);
build(1,n);
BFS(1,n);
return 0;
}