Binary Tree Vertical Order Traversal

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Questions and Answers

In the provided C++ code for vertical order traversal of a binary tree, what data structure is primarily used to maintain the order of nodes at each level during traversal?

  • Linked List
  • Stack
  • Priority Queue
  • Queue (correct)

The provided C++ code for vertical order traversal uses a depth-first search (DFS) approach to traverse the binary tree.

False (B)

In the context of the provided C++ code, explain the significance of using a map data structure with column indices as keys.

The map ensures that the column indices are naturally sorted, allowing for easy collection of nodes in the correct vertical order.

In the given C++ code, the column index for a left child node is determined by ______ the column index of its parent node.

<p>decrementing</p> Signup and view all the answers

Match each described action with the part of the provided C++ code that performs it:

<p>Initializes the tree node. = <code>TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}</code> Adds a node and its column to the queue for processing. = <code>q.push({root, 0});</code> Retrieves the node and column index from the queue. = <code>auto front = q.front();</code> Stores the node values by column index. = <code>cols[col].push_back(node-&gt;val);</code></p> Signup and view all the answers

What is the purpose of the if (!root) return result; statement at the beginning of the verticalOrder function?

<p>To handle the base case of an empty tree. (C)</p> Signup and view all the answers

The provided C++ code will produce incorrect output if the binary tree contains duplicate values.

<p>False (B)</p> Signup and view all the answers

Explain how the provided BFS approach ensures that nodes in the same column are processed from top to bottom.

<p>BFS processes nodes level by level, ensuring that nodes closer to the root (higher levels) are visited before nodes farther from the root (lower levels) within the same column.</p> Signup and view all the answers

The verticalOrder function returns a vector of vectors of int, where each inner vector represents a ______ in the vertical order.

<p>column</p> Signup and view all the answers

What would be the impact of replacing the map with an unordered_map in the provided C++ code?

<p>The code would run faster, but the output order would be unpredictable. (C)</p> Signup and view all the answers

If the root node has a column index of 0, then all nodes in the left subtree will have negative column indices, and all nodes in the right subtree will have positive column indices.

<p>True (A)</p> Signup and view all the answers

In the given C++ code, what is the role of the auto &entry : cols loop?

<p>It iterates through the stored columns in the <code>cols</code> map, appending the list of node values for each column to the final <code>result</code> vector.</p> Signup and view all the answers

Inside the while loop, the TreeNode* node = front.first; line extracts the ______ from the front of the queue.

<p>node</p> Signup and view all the answers

Suppose you modify the given code to use a stack instead of a queue. What would be the most significant consequence of this change?

<p>The tree would be traversed in a depth-first manner instead of breadth-first. (B)</p> Signup and view all the answers

The provided verticalOrder function modifies the structure of the input binary tree.

<p>False (B)</p> Signup and view all the answers

Explain why the column indices can be integers (positive, negative, or zero) in this implementation.

<p>The column indices represent relative horizontal positions of nodes with respect to the root, allowing for negative indices for nodes to the left and positive indices for nodes to the right.</p> Signup and view all the answers

The statement cols[col].push_back(node->val); is responsible for ______ the value of the current node into the vector associated with its column index.

<p>appending</p> Signup and view all the answers

What is the time complexity of the provided verticalOrder function, assuming a balanced binary tree with n nodes?

<p>$O(n \log n)$ (A)</p> Signup and view all the answers

The TreeNode struct provided includes a constructor that initializes a node with a value and sets its left and right children to nullptr by default.

<p>True (A)</p> Signup and view all the answers

Explain how the example tree is constructed in the main function of the C++ code.

<p>A root node with value 3 is created, then its left child is set to a node with value 9, and its right child is set to a node with value 20, which in turn has left and right children of 15 and 7, respectively.</p> Signup and view all the answers

Flashcards

Level-Order Traversal (BFS)

A tree traversal algorithm that visits nodes level by level, from top to bottom and left to right.

Vertical Order Traversal

A method of traversing a binary tree where nodes are grouped by their column position, from left to right.

Map data structure

A data structure that organizes data into key-value pairs, with unique keys and their associated values.

Queue

A data structure that follows the First-In-First-Out (FIFO) principle.

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Column Indexing in Tree Traversal

A node’s column index decrements when moving to its left child and increments when moving to its right child.

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Root Column Position

The root node is at the center column. Nodes to the left have decreasing column indices, and nodes to the right have increasing indices.

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Collecting Nodes by Column

Nodes are collected into a map using column indices as keys to maintain vertical order.

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Processing Columns for Output

Iterate through each column (key) in sorted order, and gather the node values from top to bottom.

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Initial Queue State

The first element in the queue contains the root of the tree and column index 0.

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Child Node Existence Check

Check if the current node has a left or right child before pushing them onto the queue.

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Study Notes

  • A level-order traversal (BFS) is used to achieve vertical order traversal.
  • Nodes are processed from top to bottom.
  • If nodes share the same row and column, they are processed from left to right.
  • A queue is used to traverse the tree level by level.
  • Each node’s column index is tracked, decrementing for a left child and incrementing for a right child.
  • Nodes’ values are stored in a map where keys are column indices.
  • The insertion order in each column is correct due to BFS processing nodes level-wise and left to right.
  • The map is iterated in order of keys (columns) to form the final result.

Code Explanation

  • The verticalOrder function takes the root of a binary tree as input.
  • It returns a vector of vectors of integers, representing the vertical order traversal of the tree.
  • If the root is null, it returns an empty vector.
  • A map cols is used to hold the nodes for each column.
  • The keys of the map are the column indices, and the values are vectors of integers representing the node values in that column.
  • A queue q is used for BFS; each element is a pair of TreeNode* and column index.
  • The root node and its column index (0) are pushed onto the queue.
  • While the queue is not empty:
    • The front element is retrieved and removed from the queue.
    • The node and column index are extracted from the front element.
    • The node's value is added to the vector of values for the corresponding column in the cols map.
    • If the node has a left child, the left child and its column index (col - 1) are pushed onto the queue.
    • If the node has a right child, the right child and its column index (col + 1) are pushed onto the queue.
  • The function iterates through the cols map and collects the results column by column into the result vector.
  • The result vector is returned.

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