1099. Build A Binary Search Tree

Build A Binary Search Tree

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

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题意

给定一个空二叉查找树以及一串数字，要求将数字按照BST的性质填入二叉树中(只有唯一填法)，并输出BST的层序序列。

思路

由二叉查找树的性质可得，其中序序列必然是有序的(递增)，所以只要对空树进行中序遍历，在遍历过程中将排好序的整数依次填入空结点，即可重建二叉树。再来进行层序遍历输出即可。

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代码实现

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

const int maxn = 100;
int value[maxn];
int index = 0;      // 记录已使用的整数的个数

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

void inOrder(int root)
{
    if (root == -1)
        return;

    inOrder(node[root].lchild);
    node[root].data = value[index++];       // 中序遍历填入整数
    inOrder(node[root].rchild);
}

void levelOrder(int root, bool flag)        // 层序输出，flag用来控制空格输出
{
    queue<int> q;
    q.push(root);
    while (!q.empty())
    {
        int now = q.front();
        q.pop();
        if (flag)
            flag = false;
        else
            printf(" ");
        printf("%d", node[now].data);
        if (node[now].lchild != -1)
            q.push(node[now].lchild);
        if (node[now].rchild != -1)
            q.push(node[now].rchild);
    }
}

int main()
{
    int n;
    int l, r;

    scanf("%d", &n);
    for (int i = 0; i < n; i++)
    {
        scanf("%d %d", &l, &r);
        node[i].lchild = l;
        node[i].rchild = r;
    }
    for (int i = 0; i < n; i++)
        scanf("%d", &value[i]);
    sort(value, value + n);         // 对整数序列进行排序

    inOrder(0);
    levelOrder(0, true);

    return 0;
}