1099 Build A Binary Search Tree (30)（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.
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
题意：
给出二叉树的结构和数字序列，把该序列填入二叉树中，使其该树成为一棵BST。输出层序序列。
思路：
1、根据给出的树的结构构建二叉树。（静态写法，root题目规定为0）
2、将输入的序列从小到大排序。
3、中序遍历二叉树，把序列中的元素逐个填入（利用BST中序序列是有序序列的性质）
4、层序遍历
代码：
#include <cstdio>
#include <queue>
#include <algorithm>
using namespace std;
;
struct Node{
int val;
int left,right;
}Tree[N];
int data[N];
int n;
void inOrderTraversal(int root)
{
;
){
inOrderTraversal(Tree[root].left);
Tree[root].val=data[idx++];
inOrderTraversal(Tree[root].right);
}
}
void layerOrderTraversal(int root)
{
;
queue<int> q;
q.push(root);
while(!q.empty()){
int top=q.front();
q.pop();
printf("%d",Tree[top].val);
idx++;
if(idx<n) printf(" ");
) q.push(Tree[top].left);
) q.push(Tree[top].right);
}
}
int main()
{
scanf("%d",&n);
int u,v;
;i<n;i++){
scanf("%d%d",&u,&v);
Tree[i].left=u;
Tree[i].right=v;
}
;i<n;i++)
scanf("%d",&data[i]);
sort(data,data+n);
inOrderTraversal();//中序遍历，填入数据
layerOrderTraversal();
;
}