1099 Build A Binary Search Tree

发布时间：2020-12-14 03:48:47 所属栏目：大数据来源：网络整理

导读：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 ri

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:

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;
const int N=105;
struct Node{
    int val;
    int left,right;
}Tree[N];
int data[N];
int n;

void inOrderTraversal(int root)
{
    static int idx=0;
    if(root!=-1){
        inOrderTraversal(Tree[root].left);
        Tree[root].val=data[idx++];
        inOrderTraversal(Tree[root].right);
    }
}

void layerOrderTraversal(int root)
{
    int idx=0;
    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(" ");
        if(Tree[top].left!=-1) q.push(Tree[top].left);
        if(Tree[top].right!=-1) q.push(Tree[top].right);
    }
}

int main()
{
    scanf("%d",&n);
    int u,v;
    for(int i=0;i<n;i++){
        scanf("%d%d",&u,&v);
        Tree[i].left=u;
        Tree[i].right=v;
    }
    for(int i=0;i<n;i++)
        scanf("%d",&data[i]);
    sort(data,data+n);
    inOrderTraversal(0);//中序遍历，填入数据
    layerOrderTraversal(0);
    return 0;
}

（编辑：李大同）

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