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

题目大意

题目给定一个二叉树和一个数字序列，要求将数字填入数中使其成为一个二叉查找树，并输出其层序遍历。

解题思路

1. 读入二叉树和数字序列，并将数字序列排序；
2. 中序遍历二叉树并将排好序的数字按照遍历序列填入节点中；
3. 用层序遍历按照题目要求的格式输出结果；
4. 返回零值。

代码

#include<cstdio>
#include<algorithm>
using namespace std;

#define maxn 110

struct Node{
    int lchild,rchild,data;
}BST[maxn];

int N,num[maxn],seq=0;

void Init(){
    int i;
    scanf("%d",&N);
    for(i=0;i<N;i++){
        scanf("%d%d",&BST[i].lchild,&BST[i].rchild);
    }
    for(i=0;i<N;i++){
        scanf("%d",&num[i]);
    }
    sort(num,num+N);
}

void InOrder(int root){
    if(root==-1){
        return;
    }
    InOrder(BST[root].lchild);
    BST[root].data=num[seq++];
    InOrder(BST[root].rchild);
}

void LayerOrder(){
    int Queue[maxn];
    int top,front=0,rear=0;
    Queue[rear++]=0;
    while(rear>front){
        top=Queue[front++];
        printf("%d",BST[top].data);
        N--;
        if(N>0){
            printf(" ");
        }else{
            printf("\n");
        }
        if(BST[top].lchild!=-1){
            Queue[rear++]=BST[top].lchild;
        }
        if(BST[top].rchild!=-1){
            Queue[rear++]=BST[top].rchild;
        }
    }
}

int main(){
    Init();
    InOrder(0);
    LayerOrder();
    return 0;
}

运行结果