# PAT Advanced 1099 Build A Binary Search Tree: DFS + BFS + Sort

## Overview

PAT Advanced 1099 Build A Binary Search Tree: Sort the values, DFS (inorder travels) to insert the values into correct nodes, BFS to print in level order.

## PAT Advanced 1099 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

## Solution Analysis: DFS + BFS + Sort

The solution is very straightforward, and it takes the following steps to tackle this problem:

- Build the BST (Binary Search Tree) with empty value nodes
- Sort the values,
- Insert the values into the empty nodes BST following in order traversal in order to fit the values into their correct position
- breadth first search (BFS) to print the values in level order.

The following C++ source code could be accepted by PAT OJ to pass this PAT Advanced 1099 Build A Binary Search Tree problem:

#include <cstdio> #include <queue> #include <algorithm> using std::sort; using std::queue; struct TreeNode{ int value; TreeNode *left; TreeNode *right; public: TreeNode(int v) : value(v), left(NULL), right(NULL) {} TreeNode() : value(0), left(NULL), right(NULL) {} }; int values[105]; TreeNode nodes[105]; int n; TreeNode *build() { int l, r; for (int i = 0; i < n; ++i) { scanf("%d %d", &l, &r); if (l != -1) nodes[i].left = &nodes[l]; if (r != -1) nodes[i].right = &nodes[r]; } return &nodes[0]; } int valPos = 0; void dfs(TreeNode *root) { if (NULL == root) return ; dfs(root->left); root->value = values[valPos++]; dfs(root->right); } void fill(TreeNode *root) { for (int i = 0; i < n; ++i) { scanf("%d", &values[i]); } sort(values, values + n); dfs(root); } void bfs(TreeNode *root) { printf("%d", root->value); queue<TreeNode *> q; if (root->left) q.push(root->left); if (root->right) q.push(root->right); while (!q.empty()) { TreeNode *curr = q.front(); q.pop(); printf(" %d", curr->value); if (curr->left) q.push(curr->left); if (curr->right) q.push(curr->right); } } int main() { scanf("%d", &n); TreeNode *root = build(); fill(root); bfs(root); return 0; }

## Summary

PAT Advanced 1099 Build A Binary Search Tree: Sort the values, DFS (inorder travels) to insert the values into correct nodes, BFS to print in level order.