1099 Build A Binary Search Tree (30 point(s))

1099 Build A Binary Search Tree (30 point(s))

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.

Given the structure of a binary tree and a sequence of distinct integer keys, there is only one way to fill these keys into the tree so that the resulting tree satisfies the definition of a BST. You are supposed to output the level order traversal sequence of that tree. The sample is illustrated by Figure 1 and 2.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (≤100) which is the total number of nodes in the tree. The next N lines each contains the left and the right children of a node in the format left_index right_index, provided that the nodes are numbered from 0 to N−1, and 0 is always the root. If one child is missing, then −1 will represent the NULL child pointer. Finally N distinct integer keys are given in the last line.

Output Specification:

For each test case, print in one line the level order traversal sequence of that tree. All the numbers must be separated by a space, with no extra space at the end of the line.

Sample Input:

9
1 6
2 3
-1 -1
-1 4
5 -1
-1 -1
7 -1
-1 8
-1 -1
73 45 11 58 82 25 67 38 42

Sample Output:

58 25 82 11 38 67 45 73 42

考察点：

1. 知识点：BST的中序遍历是非递减序列；

2. 静态数组建立二叉树；

3. 利用递归完成树的中序遍历；

4. 利用队列完成树的层次遍历。

思路：

根据题目的图片实例和输入方式，此题适当使用结点静态数组保存二叉树。由于这是一棵二叉搜索树，因此只需要将给出的序列排序后，就可以得到它的中序遍历。因此将树的结构建立起来以后，对整棵树中序遍历（左子树--根--右子树），将按照元素大小排序后的序列依次插入二叉搜索树中。

最后借助队列，输出这棵二叉搜索树的层次遍历。

我的代码：

#include<iostream>
#include<algorithm>
#include<cstring>
#include<vector>
#include<queue>
#define INF 0x3f3f3f3f
using namespace std;
struct Node{
	int data;int left,right;
	Node(){	data = 0;left=right=-1;	}
};
Node node[107];
int a[107];
int idx = 0;
void insert(int root){//中序遍历，同时完成赋值 
	if(node[root].left!=-1){
		insert(node[root].left);
	}
	node[root].data = a[idx];idx++;
	if(node[root].right!=-1){
		insert(node[root].right);
	} 
}
vector<Node> levelOrder(){//利用队列完成层次遍历 
	queue<Node> q;
	vector<Node> ans;
	q.push(node[0]);
	while(!q.empty()){
		Node cur = q.front();
		ans.push_back(cur);
		q.pop();
		if(cur.left!=-1) q.push(node[cur.left]);
		if(cur.right!=-1) q.push(node[cur.right]);
	}
	return ans;
}
int main(void){
	int N;cin>>N;
	for(int i=0;i<N;i++){
		cin>>node[i].left>>node[i].right;
	}
	for(int i=0;i<N;i++) cin>>a[i];
	sort(a,a+N); 
	insert(0);
	vector<Node> order = levelOrder();
	for(int i=0;i<order.size();i++){
		if(i==0) cout<<order[i].data;
		else cout<<" "<<order[i].data;
	}
	return 0;
}

 大神更简洁的代码（思路一致）：

参考链接：https://blog.youkuaiyun.com/richenyunqi/article/details/80150933

#include<bits/stdc++.h>
using namespace std;
struct Node{
    int data,left=-1,right=-1;
};
Node tree[105];
int data[105],N;
void inOrder(int root,int&index){//中根遍历
    if(root==-1)//root==-1,直接返回
        return;
    inOrder(tree[root].left,index);//递归遍历左子树
    tree[root].data=data[index++];//将数据填入根部结点
    inOrder(tree[root].right,index);//递归遍历右子树
}
void levelOrder(){//层次遍历
    queue<int>q;
    q.push(0);
    while(!q.empty()){
        int t=q.front();
        q.pop();
        printf("%s%d",t==0?"":" ",tree[t].data);
        if(tree[t].left!=-1)
            q.push(tree[t].left);
        if(tree[t].right!=-1)
            q.push(tree[t].right);
    }
}
int main(){
    scanf("%d",&N);
    for(int i=0;i<N;++i)
        scanf("%d%d",&tree[i].left,&tree[i].right);
    for(int i=0;i<N;++i)
        scanf("%d",&data[i]);
    sort(data,data+N);//排序
    int index=0;
    inOrder(0,index);
    levelOrder();
    return 0;
}

#include<iostream>
#include<algorithm>
#include<cstring>
#include<vector>
#include<queue>
#define INF 0x3f3f3f3f
using namespace std;
struct Node{
	int data = INF;int left,right;
	Node(){	data = INF;left=right=-1;	}
};
Node node[107];
int a[107];
int idx = 0;
void insert(int root){//中序遍历，同时完成赋值 
	if(node[root].left!=-1){
		insert(node[root].left);
	}
	node[root].data = a[idx];idx++;
	if(node[root].right!=-1){
		insert(node[root].right);
	} 
}
vector<Node> levelOrder(){//利用队列完成层次遍历 
	queue<Node> q;
	vector<Node> ans;
	q.push(node[0]);
	while(!q.empty()){
		Node cur = q.front();
		ans.push_back(cur);
		q.pop();
		if(cur.left!=-1) q.push(node[cur.left]);
		if(cur.right!=-1) q.push(node[cur.right]);
	}
	return ans;
}
int main(void){
	int N;cin>>N;
	for(int i=0;i<N;i++){
		cin>>node[i].left>>node[i].right;
	}
	for(int i=0;i<N;i++) cin>>a[i];
	sort(a,a+N); 
	insert(0);
	vector<Node> order = levelOrder();
	for(int i=0;i<order.size();i++){
		if(i==0) cout<<order[i].data;
		else cout<<" "<<order[i].data;
	}
	return 0;
}