A1099. Build A Binary Search Tree (30)

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

Code

#include <stdio.h>
#include <stdlib.h>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;
const int maxn = 1010;
int n, data[maxn], left, right, index = 0;
vector<int> vnode[maxn], result;
typedef struct node{int data, right, left;
}node;
node nodes[maxn];
void inorder(int root){if (nodes[root].left != -1)inorder(nodes[root].left);nodes[root].data = data[index++];if (nodes[root].right != -1)inorder(nodes[root].right);
}
void levelorder(int root){queue<int> qi;qi.push(root);while (!qi.empty()){int now = qi.front();qi.pop();result.push_back(nodes[now].data);if (nodes[now].left != -1)    qi.push(nodes[now].left);if (nodes[now].right != -1)   qi.push(nodes[now].right);}
}
int main(){scanf("%d", &n);for (int i = 0; i < n; i++){scanf("%d %d", &left, &right);nodes[i].left = left;nodes[i].right = right;}for (int i = 0; i < n; i++)scanf("%d", &data[i]);sort(data, data + n);inorder(0);levelorder(0);for (int i = 0; i < n; i++){if (i)  printf(" ");printf("%d", result[i]);}printf("\n");return 0;
}

Analysis

-已知一颗二叉排序树的树型，并且给出n个key值。要求将这n个key值放入给出的树型中，且满足二叉排序树的要求。最后输出其层序遍历。

-使用中序遍历的思想，按照中序遍历的顺序向对应位置，按按序添入key值（先将key值按升序排列）。

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【PAT】A1099. Build A Binary Search Tree (30)