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

Postorder Traversal of a Binary Tree Using Recursion - Algorithm, Visualization, Examples

Problem Statement

Given a binary tree, perform a postorder traversal using recursion. In a postorder traversal, the nodes are visited in the order: left subtree, right subtree, then the current node. You need to return a list containing the values of the nodes in postorder.

Examples

Input Tree Postorder Output Description
[1, null, 2, null, null, null, 3]
[3, 2, 1] Right-skewed tree with nodes processed left to right and then root.
[1, 2, 3]
[2, 3, 1] Balanced tree with left and right children.
[1]
[1] Single node tree, output is just the root.
[] [] Empty tree, no nodes to process.
[1, 2, null, 3]
[3, 2, 1] Left-skewed tree with nodes deeply nested on left.

Visualization Player

Solution

Understanding the Problem

In this problem, we are asked to perform a postorder traversal on a binary tree using recursion. Postorder traversal is one of the depth-first traversal techniques in binary trees, and it follows a specific order:

  • Traverse the left subtree
  • Traverse the right subtree
  • Visit the root node

In other words, for each node, we visit all its children before we visit the node itself. This order is especially useful when you want to delete or evaluate trees from the bottom-up.

Step-by-Step Solution with Example

Step 1: Understand the Tree Structure

Let’s take a sample binary tree:


      1
     /     2   3

Here, the root is 1, the left child is 2, and the right child is 3.

Step 2: Apply Postorder Traversal Definition

We follow the left → right → root order. So we:

  • First traverse the left subtree rooted at 2
  • Then traverse the right subtree rooted at 3
  • Then visit the root node, which is 1

This gives the output: [2, 3, 1]

Step 3: Write the Recursive Code


function postorderTraversal(root) {
  if (root === null) return [];
  const left = postorderTraversal(root.left);
  const right = postorderTraversal(root.right);
  return [...left, ...right, root.val];
}

This code breaks down the problem into smaller subproblems, solving the postorder traversal for each subtree and then combining the results.

Step 4: Recap the Recursive Flow

For a node, we call the function recursively on the left child, then the right child, and finally add the current node's value to the result list. This ensures all children are processed before the parent node, just like postorder requires.

Edge Cases

Case 1: Empty Tree

If the tree is empty (null), the output should be an empty array []. The function handles this gracefully with the base case check.

Case 2: Single Node Tree

For a tree with only one node (e.g., [1]), the traversal returns just [1] since there are no children.

Case 3: Left-skewed Tree

Consider a tree like [1, 2, null, 3]. It looks like:


    1
   /
  2
 /
3

We go left down to 3, then back up: [3, 2, 1]

Case 4: Right-skewed Tree

For [1, null, 2, null, 3]:


1
   2
       3

The output will be [3, 2, 1]

Case 5: Balanced Tree

Our initial example [1, 2, 3] is a good case of a balanced tree, resulting in [2, 3, 1].

Finally

Postorder traversal is a fundamental recursive algorithm for binary trees. It emphasizes processing children before parents, and it’s useful in many scenarios like expression tree evaluation, directory cleanup, and more.

By breaking the problem down recursively and understanding the order clearly, even beginners can master this traversal. Always consider edge cases like empty trees or skewed trees while designing and testing your solution.

Algorithm Steps

  1. Start at the root of the binary tree.
  2. Recursively traverse the left subtree.
  3. Recursively traverse the right subtree.
  4. Visit (process) the current node.

Code

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

def postorder(root):
    if root is not None:
        postorder(root.left)
        postorder(root.right)
        print(root.value, end=' ')

# Example usage:
if __name__ == '__main__':
    root = Node(1)
    root.left = Node(2)
    root.right = Node(3)
    root.left.left = Node(4)
    root.left.right = Node(5)
    postorder(root)

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