1099 Build A Binary Search Tree (30 分) BST 中序遍历构造树然后输出层次遍历

柔光的暖阳◎ 2021-10-29 17:16 227阅读 0赞

1099 Build A Binary Search Tree (30 分)

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.

![figBST.jpg][]

### 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 Nlines 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

给定一棵固定位置的BST，然后插入一组序列。

因为BST的中序遍历就是从小到大的排序，所以借此可以还原这棵树。

然后输出层次遍历。

#include <stdio.h>
    #include <string.h>
    #include <string>
    #include <map>
    #include <queue>
    #include <math.h>
    #include <algorithm>
    #include <iostream>
    #define INF 0x3f3f3f3f
    using namespace std;
    struct Node
    {
    	int val;
    	int l,r;
    }tree[105];
    int a[105],p;
    void Inorder(int x)
    {//中序遍历建立BST 
    	if(tree[x].l!=-1) Inorder(tree[x].l);
    	tree[x].val=a[p++];
    	if(tree[x].r!=-1) Inorder(tree[x].r);
    }	
    int main()
    {
    	int n,i,j;
    	scanf("%d",&n);
    	for(i=0;i<n;i++)
    	scanf("%d%d",&tree[i].l,&tree[i].r);
    	for(i=0;i<n;i++)
    	scanf("%d",&a[i]);
    	sort(a,a+n);
    	p=0;
    	Inorder(0);
    	//层次遍历 
    	vector<int> v;
    	queue<Node> q;
    	q.push(tree[0]);
    	while(!q.empty())
     	{
     		Node u=q.front();
     		q.pop();
     		v.push_back(u.val);
     		if(u.l!=-1)
     		q.push(tree[u.l]);
     		if(u.r!=-1)
     		q.push(tree[u.r]);
     	}
     	for(i=0;i<v.size()-1;i++)
     	printf("%d ",v[i]);
     	printf("%d\n",v[v.size()-1]);
    }

[figBST.jpg]: /images/20211029/d8c824f819ee4cee9541b0baf70d3a99.png