# 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:

1. Build the BST (Binary Search Tree) with empty value nodes
2. Sort the values,
3. Insert the values into the empty nodes BST following in order traversal in order to fit the values into their correct position
4. 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.

Written on June 6, 2015