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

Bottom View of a Binary Tree - Iterative Approach

Problem Statement

Given a binary tree, return the bottom view of the tree. The bottom view consists of the nodes that are visible when the tree is viewed from the bottom. For each horizontal distance from the root, the node that is at the lowest level (deepest) will be visible. Your task is to determine these visible nodes using an iterative approach.

Examples

Input Tree Bottom View Output Description
[20, 8, 22, 5, 3, null, 25, null, null, 10, 14]
[5, 10, 3, 14, 25] Standard binary tree showing nodes visible from the bottom across horizontal distances
[1]
[1] Single node tree; only the root is visible from the bottom
[] [] Empty tree; no nodes to display in bottom view
[1, 2, null, 3, null, 4]
[4, 2, 1] Left-skewed tree; last node at each horizontal distance is shown
[1, null, 2, null, null, null, 3]
[1, 2, 3] Right-skewed tree; all nodes fall on unique horizontal distances
[1, 2, 3, 4, 5, 6, 7]
[4, 2, 6, 3, 7] Complete binary tree; bottom-most nodes overwrite top ones at each horizontal distance

Visualization Player

Solution

Understanding the Problem

We are given a binary tree, and our task is to find its bottom view. Imagine standing below the binary tree and looking up — the nodes that are visible from that viewpoint form the bottom view. In other words, for each vertical line (or horizontal distance from the root), we want the bottommost node visible in that column.

This means we need to process nodes based on their horizontal distances and pick the last node (deepest node) at each distance level as seen in a level-order (breadth-first) traversal.

Step-by-Step Solution with Example

step 1: Use a Queue for Level Order Traversal

To process nodes level by level, we use a queue. Each element in the queue will be a pair of the node and its horizontal distance (HD) from the root.

step 2: Track Horizontal Distances in a Map

We maintain a map or dictionary that maps each horizontal distance to the latest node value we see at that distance. Since we are doing level-order traversal, nodes at lower levels naturally overwrite those at higher levels for the same horizontal distance.

step 3: Traverse the Tree and Fill the Map

For every node, we:

  • Dequeue it and update the map with its value for its horizontal distance
  • Enqueue its left child with HD - 1
  • Enqueue its right child with HD + 1
This ensures that for each column (HD), the bottommost node is the one last seen in traversal.

step 4: Sort the Map by Horizontal Distance

Finally, we collect the node values from the map, sorted by the horizontal distance (from leftmost to rightmost), to form our bottom view.

step 5: Apply the Steps to an Example

Let’s consider this binary tree:


       20
      /       8    22
    /         5   3     25
      /      10 14

Horizontal distances (HD) from root (20 at HD = 0):

  • 5 → HD = -2
  • 8 → HD = -1
  • 10 → HD = 0
  • 14 → HD = 1
  • 25 → HD = 2

During traversal, we keep updating values at each HD. At the end, the bottom view map (sorted by HD) is:

  • -2 → 5
  • -1 → 8
  • 0 → 10
  • 1 → 14
  • 2 → 25

Bottom view: [5, 8, 10, 14, 25]

Edge Cases

Empty Tree

If the tree is empty (root is null), we simply return an empty list as there are no nodes to show.

Single Node Tree

If there is only one node, the bottom view will contain just that node.

Left-Skewed Tree

Every node has a unique horizontal distance, so all will be visible in the bottom view. For example:


    1
   /
  2
 /
3

Bottom view: [3, 2, 1]

Right-Skewed Tree

Same as left-skewed but horizontal distances increase:


1
   2
       3
Bottom view: [1, 2, 3]

Nodes Overlapping at Same HD

When multiple nodes have the same horizontal distance, only the bottommost (deepest and latest in level order) is retained.

Finally

The key to solving the bottom view problem is combining level-order traversal with horizontal distance tracking. This ensures we always get the bottommost node for each vertical column. By thinking in terms of vertical slices and processing depth, we make the logic intuitive and beginner-friendly.

Always test with skewed trees and overlapping nodes to make sure your solution handles all edge cases.

Algorithm Steps

  1. If the binary tree is empty, return an empty result.
  2. Initialize a queue and enqueue the root node along with its horizontal distance (hd = 0).
  3. Initialize an empty map (hdMap) to store the latest node value at each horizontal distance.
  4. While the queue is not empty, dequeue an element (node, hd).
  5. Update hdMap[hd] with the node's value (this ensures the bottom-most node at that hd is recorded).
  6. If the node has a left child, enqueue it with hd - 1; if it has a right child, enqueue it with hd + 1.
  7. After processing all nodes, sort the keys of hdMap and record their corresponding values. The ordered values form the bottom view of the binary tree.

Code

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

from collections import deque

def bottomView(root):
    if not root:
        return []
    q = deque([(root, 0)])
    hdMap = {}
    while q:
        node, hd = q.popleft()
        hdMap[hd] = node.val
        if node.left:
            q.append((node.left, hd - 1))
        if node.right:
            q.append((node.right, hd + 1))
    result = [hdMap[hd] for hd in sorted(hdMap)]
    return result

if __name__ == '__main__':
    # Construct binary tree:
    #         20
    #        /  \
    #       8    22
    #      / \     \
    #     5   3     25
    #        / \
    #       10  14
    root = TreeNode(20,
                    TreeNode(8, TreeNode(5), TreeNode(3, TreeNode(10), TreeNode(14))),
                    TreeNode(22, None, TreeNode(25)))
    print(bottomView(root))

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