Binary TreesBinary Trees36
  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Inorder Traversal of a Binary Tree using Recursion
  4. 4Inorder Traversal of a Binary Tree using Iteration
  5. 5Postorder Traversal of a Binary Tree Using Recursion
  6. 6Postorder Traversal of a Binary Tree using Iteration
  7. 7Level Order Traversal of a Binary Tree using Recursion
  8. 8Level Order Traversal of a Binary Tree using Iteration
  9. 9Reverse Level Order Traversal of a Binary Tree using Iteration
  10. 10Reverse Level Order Traversal of a Binary Tree using Recursion
  11. 11Find Height of a Binary Tree
  12. 12Find Diameter of a Binary Tree
  13. 13Find Mirror of a Binary Tree
  14. 14Left View of a Binary Tree
  15. 15Right View of a Binary Tree
  16. 16Top View of a Binary Tree
  17. 17Bottom View of a Binary Tree
  18. 18Zigzag Traversal of a Binary Tree
  19. 19Check if a Binary Tree is Balanced
  20. 20Diagonal Traversal of a Binary Tree
  21. 21Boundary Traversal of a Binary Tree
  22. 22Construct a Binary Tree from a String with Bracket Representation
  23. 23Convert a Binary Tree into a Doubly Linked List
  24. 24Convert a Binary Tree into a Sum Tree
  25. 25Find Minimum Swaps Required to Convert a Binary Tree into a BST
  26. 26Check if a Binary Tree is a Sum Tree
  27. 27Check if All Leaf Nodes are at the Same Level in a Binary Tree
  28. 28Lowest Common Ancestor (LCA) in a Binary Tree
  29. 29Solve the Tree Isomorphism Problem
  30. 30Check if a Binary Tree Contains Duplicate Subtrees of Size 2 or More
  31. 31Check if Two Binary Trees are Mirror Images
  32. 32Calculate the Sum of Nodes on the Longest Path from Root to Leaf in a Binary Tree
  33. 33Print All Paths in a Binary Tree with a Given Sum
  34. 34Find the Distance Between Two Nodes in a Binary Tree
  35. 35Find the kth Ancestor of a Node in a Binary Tree
  36. 36Find All Duplicate Subtrees in a Binary Tree
GraphsGraphs46
  1. 1Breadth-First Search in Graphs
  2. 2Depth-First Search in Graphs
  3. 3Number of Provinces in an Undirected Graph
  4. 4Connected Components in a Matrix
  5. 5Rotten Oranges Problem - BFS in Matrix
  6. 6Flood Fill Algorithm - Graph Based
  7. 7Detect Cycle in an Undirected Graph using DFS
  8. 8Detect Cycle in an Undirected Graph using BFS
  9. 9Distance of Nearest Cell Having 1 - Grid BFS
  10. 10Surrounded Regions in Matrix using Graph Traversal
  11. 11Number of Enclaves in Grid
  12. 12Word Ladder - Shortest Transformation using Graph
  13. 13Word Ladder II - All Shortest Transformation Sequences
  14. 14Number of Distinct Islands using DFS
  15. 15Check if a Graph is Bipartite using DFS
  16. 16Topological Sort Using DFS
  17. 17Topological Sort using Kahn's Algorithm
  18. 18Cycle Detection in Directed Graph using BFS
  19. 19Course Schedule - Task Ordering with Prerequisites
  20. 20Course Schedule 2 - Task Ordering Using Topological Sort
  21. 21Find Eventual Safe States in a Directed Graph
  22. 22Alien Dictionary Character Order
  23. 23Shortest Path in Undirected Graph with Unit Distance
  24. 24Shortest Path in DAG using Topological Sort
  25. 25Dijkstra's Algorithm Using Set - Shortest Path in Graph
  26. 26Dijkstra’s Algorithm Using Priority Queue
  27. 27Shortest Distance in a Binary Maze using BFS
  28. 28Path With Minimum Effort in Grid using Graphs
  29. 29Cheapest Flights Within K Stops - Graph Problem
  30. 30Number of Ways to Reach Destination in Shortest Time - Graph Problem
  31. 31Minimum Multiplications to Reach End - Graph BFS
  32. 32Bellman-Ford Algorithm for Shortest Paths
  33. 33Floyd Warshall Algorithm for All-Pairs Shortest Path
  34. 34Find the City With the Fewest Reachable Neighbours
  35. 35Minimum Spanning Tree in Graphs
  36. 36Prim's Algorithm for Minimum Spanning Tree
  37. 37Disjoint Set (Union-Find) with Union by Rank and Path Compression
  38. 38Kruskal's Algorithm - Minimum Spanning Tree
  39. 39Minimum Operations to Make Network Connected
  40. 40Most Stones Removed with Same Row or Column
  41. 41Accounts Merge Problem using Disjoint Set Union
  42. 42Number of Islands II - Online Queries using DSU
  43. 43Making a Large Island Using DSU
  44. 44Bridges in Graph using Tarjan's Algorithm
  45. 45Articulation Points in Graphs
  46. 46Strongly Connected Components using Kosaraju's Algorithm

Top View of a Binary Tree - Iterative Approach

Problem Statement

Given the root of a binary tree, return the top view of the tree. The top view of a binary tree is the set of nodes visible when the tree is viewed from the top. You should return the values of these nodes from left to right, based on their horizontal distance from the root. Use an iterative approach (like level-order traversal) to compute this top view.

Examples

Input Tree Top View Output Description
[1, 2, 3, 4, 5, null, 6]
[4, 2, 1, 3, 6] Standard tree with multiple levels; leftmost and rightmost nodes at each level appear in top view
[1]
[1] Single node tree; root itself is the top view
[] [] Empty tree with no nodes returns an empty top view
[1, 2, null, 3, null, 4]
[4, 3, 2, 1] Left-skewed tree; only the leftmost path visible in top view
[1, null, 2, null, 3, null, 4]
[1, 2, 3, 4] Right-skewed tree; every node appears in top view due to unique horizontal distances
[1, 2, 3, 4, null, null, 5, 6]
[6, 4, 2, 1, 3, 5] Complex tree with deep left and right subtrees; top view includes the outermost nodes

Visualization Player

Solution

Case 1: Empty Tree

If the binary tree is empty (i.e., the root is null), then there are no nodes to observe from the top. Therefore, the top view should be an empty list.

Case 2: Single Node Tree

If the tree contains only a single root node, then that node is visible from the top view as there are no other nodes to obstruct it.

Case 3: Left-Skewed Tree

In a left-skewed tree, all nodes only have left children. As we go down the tree, each node shifts one unit to the left in horizontal distance. All of them will be visible from the top as no node shares the same horizontal distance.

Case 4: Right-Skewed Tree

This is the opposite of the left-skewed tree. All nodes have only right children. Each node moves one step to the right in horizontal distance and remains visible from the top because there is no overlap in horizontal levels.

Case 5: General Tree with Both Children

In a typical binary tree with both left and right children, we perform a level-order traversal (BFS) while tracking the horizontal distance (HD) from the root. The root is at HD = 0, left child HD = -1, right child HD = +1, and so on. For the top view, we want the first node encountered at each HD. So, we use a map to store the node value at each HD the first time it's visited. This ensures we capture only the uppermost node at every horizontal position.

Once the traversal completes, we sort the horizontal distances and return the corresponding values to get the left-to-right top view of the tree.

Algorithm Steps

  1. If the tree is empty, return an empty result.
  2. Initialize a queue and enqueue a tuple containing the root node and its horizontal distance (0).
  3. Initialize an empty map (or dictionary) to store the first node encountered at each horizontal distance.
  4. While the queue is not empty, dequeue a tuple (node, hd).
  5. If the horizontal distance hd is not present in the map, record the node's value for that hd.
  6. Enqueue the left child with horizontal distance hd - 1 and the right child with hd + 1 (if they exist).
  7. After processing all nodes, sort the keys of the map and output the corresponding node values as the top view.

Code

Python
Java
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def topView(root):
    if not root:
        return []
    from collections import deque
    queue = deque([(root, 0)])
    hd_map = {}
    while queue:
        node, hd = queue.popleft()
        if hd not in hd_map:
            hd_map[hd] = node.val
        if node.left:
            queue.append((node.left, hd - 1))
        if node.right:
            queue.append((node.right, hd + 1))
    return [hd_map[hd] for hd in sorted(hd_map)]

# Example usage:
if __name__ == '__main__':
    # Construct binary tree:
    #         1
    #        / \
    #       2   3
    #      / \   \
    #     4   5   6
    root = TreeNode(1, TreeNode(2, TreeNode(4), TreeNode(5)), TreeNode(3, None, TreeNode(6)))
    print(topView(root))