PAT 1099 Build A Binary Search Tree(30分)

1099Build 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.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integerN(≤100) which is the total number of nodes in the tree. The nextNlines each contains the left and the right children of a node in the formatleft_index right_index, provided that the nodes are numbered from 0 toN−1, and 0 is always the root. If one child is missing, then−1will represent the NULL child pointer. FinallyNdistinct 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

思路

• 对于一棵二叉树中序序列是递增的，因此将给定的序列从小到大排序，之后按照进行中序遍历，将排好序的序列插入到二叉排序树中，最后进行层次遍历即可。

代码

#include <cstdio>
#include <queue>
#include <algorithm>

using namespace std;

const int maxn = 110;
int data[maxn];

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

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

void layer_order(int root)
{
    queue<int> q;
    q.push(root);
    int num = 0;
    while (!q.empty())
    {
        int now = q.front();
        q.pop();
        num ++;
        printf("%d", Node[now].data);
        if (num < n)
        {
            printf(" ");
        }
        if (Node[now].lchild != -1) q.push(Node[now].lchild);
        if (Node[now].rchild != -1) q.push(Node[now].rchild);
    }
}

int main()
{
    //freopen("test.txt","r", stdin);
    scanf("%d", &n);
    int lchild, rchild;
    for (int i = 0; i < n; i ++)
    {
        scanf("%d %d", &lchild, &rchild);
        Node[i].lchild = lchild;
        Node[i].rchild = rchild;
    }

    for (int i = 0; i < n; i ++)
    {
        scanf("%d", &data[i]);    
    }
    sort(data, data + n);
    in_create(0);
    
    layer_order(0);
    
    return 0;
}