Learn and practice the Tree Depth-First Search and Tree Breadth-First Search patterns to solve coding interview problems.

Speedrun the LinkedIn Coding Interview: Top Problems in Python

Trees play a pivotal role in organizing hierarchical data, optimizing searches, and solving complex problems. In this module, we’ll learn to choose the appropriate tree for a given problem and apply the more appropriate of the two major traversal techniques, breadth-first or depth-first, to solve it.

Trees

# Statement
Given the root of a binary tree, check whether it is a valid binary search tree (BST). 

A binary tree is a valid BST if for every node:

- 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 the node's key.

- Both the left and right subtrees are valid BSTs.




**Constraints:**

- $-10^{4} \leq$ `Node.data` $\leq 10^{4}$

- The tree contains nodes in the range
 $[1, 500]$.


# Examples

# Understand the problem


Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:





Is the following binary tree a valid binary search tree?

```text
  9
 / \
2  10
   / \
  7  20
```


Is the following binary tree a valid binary search tree?
<pre><code class="language-text"> 9
 / \
2 10
 / \
 7 20
</code></pre>

Is the following binary tree a valid binary search tree?

```text
    7
   / \
  5  10
 / \   
4   6
```


Is the following binary tree a valid binary search tree?
<pre><code class="language-text"> 7
 / \
 5 10
 / \ 
4 6
</code></pre>

Is the following binary tree a valid binary search tree?

```text
  7
 / \
4   8
   / \
  6   9
```

Is the following binary tree a valid binary search tree?
<pre><code class="language-text"> 7
 / \
4 8
 / \
 6 9
</code></pre>

Valid Binary Search Tree

Valid Binary Search Tree

# Figure it out!
We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

# Try it yourself

Implement your solution in the following coding playground.



# Quick Fix\nYou are Edward, a Senior Software Engineer who specializes in coding interview patterns, data structures and algorithms, and is great at debugging issues in code.\n\n- Edward, please keep in mind that you do not have to print the data of the placeholders. Also, do not mention anything about yourself.\n\nEdward, you are given the following data in the placeholders:\n- Function name: `validate_bst`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `Python`\n\n- Edward, your task is to understand the type of error that is occurring in the coding language provided.\n- Once you've understood the error as per the error’s description, and why the test case failed, you will suggest how the candidate can improve their solution code to fix the error.\n- Edward, you will not give the corrected code, just a hint on what the error tells, and how to fix it.\n- Edward, please limit your response strictly to 100 words. No more words than the limit.

# Review Code\nEdward, your current task is to review the `validate_bst` function(s) and the other function(s) invoked in it/them.\n\n-Take your time and review the candidate's solution code.\n- Do not review any extra/helper files or functions not invoked in the solution function `validate_bst`.\n- Do not review the code of data structure objects instantiated like a binary tree, linked list, trie, union find, etc., in the solution functions. Just review the solution/algorithm function of the problem. \n- Also, if the solution code doesn’t use the coding pattern stated above, then please encourage the candidate to reattempt the problem using that pattern corectly.

# Review time complexity\n- Please provide a brief time complexity analysis of the function(s) `validate_bst`. \n- While calculating time complexity, include the time complexity of built-in Python functions invoked by the code. \n- The answer should be to the point in approximately 60 words.

# Review space complexity\n- Please provide a brief space complexity analysis of the function(s) `validate_bst`. \n- While calculating space complexity, include the space complexity of built-in Python functions invoked by the code. \n- Do not include the space used for the input parameters and the space used for just returning an output (not used as a scratch space). \n- The answer should be to the point in approximately 60 words.

def evaluate_results(self) -> object:
 """
 self.__inputs is the list of inputs that are passed as input to function
 self.__actual_output is a list of outputs that is produced by the learner's code
 return : self.__edu__result object
 """

 from ds_v1.BinaryTree.BinaryTree import TreeNode
 from collections import deque
 import math

 def level_order_traversal(root):
 if not root:
 return []
 
 result = []
 q = deque([root])
 while q:
 curr = q.popleft()
 
 if curr:
 result.append(curr.data)
 q.append(curr.left)
 q.append(curr.right)
 else:
 result.append(None)

 if all(val == None for val in q):
 break 
 
 return result
 

 def create_binary_tree(level_order):
 if not level_order:
 return None
 
 root = TreeNode(level_order[0])
 q = deque([root])
 i = 1
 while i < len(level_order) and q:
 curr = q.popleft()
 
 if level_order[i] != None:
 curr.left = TreeNode(level_order[i])
 q.append(curr.left)
 i += 1
 
 if i < len(level_order) and level_order[i] != None:
 curr.right = TreeNode(level_order[i])
 q.append(curr.right)
 i += 1
 
 return root

 # Function to check if a given binary tree is a valid BST or not
 def validate_bst_eval(root):
 prev = [-math.inf]
 return validate_bst_helper(root, prev)

 # Helper function for validate_bst
 def validate_bst_helper(root, prev):
 if not root:
 return True

 if not validate_bst_helper(root.left, prev):
 return False

 if root.data <= prev[0]:
 return False
 prev[0] = root.data

 return validate_bst_helper(root.right, prev)

 # Expected output
 tree_list = self.__inputs[0]
 tree_root = create_binary_tree(tree_list)
 expected = validate_bst_eval(tree_root)

 # Actual output
 actual = self.__actual_outputs[0]

 # multiple outputs will be added at each index respectively for a single test_case
 expected_outputs = [] 

 # store the 1st expected output that should be displayed to the user 
 expected_outputs.append(expected)

 if json.dumps(expected) == json.dumps(actual):
 self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
 else:
 self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

 return self.__edu_result

# Definition for a binary tree node
# class TreeNode:
#     def __init__(self, data):
#         self.data = data
#         self.left = None
#         self.right = None

from ds_v1.BinaryTree.BinaryTree import TreeNode
import math

def validate_bst(root):

    # Replace this placeholder return statement with your code
    return False


validate-bst.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [5, 3, 6, 2, 4]
    output: 
    - 1 : True
  - name: "testcase 2"
    inputs:
    - 1 : [6, 2, 5, 4, 7]
    output: 
    - 1 : False
  - name: "testcase 3"
    inputs:
    - 1 : [4, 2, 5, 1, 3]
    output: 
    - 1 : True
  - name: "testcase 4"
    inputs:
    - 1 : [4, 2, 7, 1, 5, 6, 9]
    output: 
    - 1 : False
  - name: "testcase 5"
    inputs:
    - 1 : [5, 3, 8, 2, 4,7]
    output: 
    - 1 : True
  
  

def sum(input_1, input_2):
    return input_1+input_2

def validate_inputs(self) -> None:
 """
 self.__inputs is the list of inputs that are passed as input to function
 store the result using the self.store_result(error_msg, status)
 return : void
 """
 from ds_v1.BinaryTree.BinaryTree import TreeNode
 from collections import deque

 def level_order_traversal(root):
 if not root:
 return []
 
 result = []
 q = deque([root])
 while q:
 curr = q.popleft()
 
 if curr:
 result.append(curr.data)
 q.append(curr.left)
 q.append(curr.right)
 else:
 result.append(None)

 if all(val == None for val in q):
 break 
 
 return result
 
 def is_valid_level_order(level_order):
 if not level_order:
 return True # An empty list is a valid level-order traversal

 n = len(level_order)
 i = 0
 root = TreeNode(level_order[i])
 q = deque([root])
 i = 1

 while i < n and q:
 curr = q.popleft()

 if level_order[i] is not None:
 curr.left = TreeNode(level_order[i])
 q.append(curr.left)
 i += 1

 if i < n and level_order[i] is not None:
 curr.right = TreeNode(level_order[i])
 q.append(curr.right)
 i += 1
 
 # Remove None values after the last integer
 while level_order and level_order[-1] is None:
 level_order.pop()
 
 return level_order_traversal(root) == level_order
 
 tree = self.__inputs[0]

 num_nodes = sum(1 for node_value in tree if node_value is not None)

 num_nodes_lower_bound = 1
 num_nodes_upper_bound = 500

 node_value_lower_bound = -10000
 node_value_upper_bound = 10000

 # inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
 tree = self.__inputs[0]

 # inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1

 if (num_nodes != 0 and tree[0] is None):
 self.store_result ("Not a valid value of type TreeNode", ValidationFunction.FAIL)

 elif not is_valid_level_order(tree):
 self.store_result ("Not a valid value of type TreeNode", ValidationFunction.FAIL)

 elif not (num_nodes_lower_bound <= num_nodes <= num_nodes_upper_bound):
 self.store_result ("Total number of nodes should be [" + str(num_nodes_lower_bound) + ", " + str(num_nodes_upper_bound) + "] but got " + str(num_nodes), ValidationFunction.FAIL)
 
 elif not all(node_value_lower_bound <= node_value <= node_value_upper_bound for node_value in tree if node_value is not None):
 self.store_result ("'root' must consist of values from " + str(node_value_lower_bound) + " to " + str(node_value_upper_bound) + " only", ValidationFunction.FAIL)

 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Validate Binary Search Tree problem.



Validate Binary Search Tree

Try to solve the Validate Binary Search Tree problem.

Tree Depth-first Search

Tree Breadth-first Search

Conclusion

Validate Binary Search Tree

Statement

Examples

Understand the problem

Figure it out!

Try it yourself