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

Bubble Sort - Algorithm, Visualization, Examples

Sorting

Contents

ProblemExamplesVisualizationSolutionAlgorithmCodeTimeSpace Detailed Exmpl

Problem Statement❯

Given an array of integers, your task is to sort the array in ascending order using the Bubble Sort algorithm.

Bubble Sort works by repeatedly stepping through the list, comparing adjacent elements, and swapping them if they are in the wrong order. The largest unsorted element 'bubbles up' to its correct position after each pass.

Your goal is to return the sorted array after all necessary passes are completed.

Examples❯

Input Array Sorted Output Description
[5, 1, 4, 2, 8] [1, 2, 4, 5, 8] Multiple elements in random order; standard caseVisualization
[3, 2, 1] [1, 2, 3] Completely reverse sorted; maximum swaps neededVisualization
[1, 2, 3] [1, 2, 3] Already sorted; best case (0 swaps)Visualization
[7] [7] Single-element array is always sortedVisualization
[] [] Empty array; nothing to sort
[4, 2, 2, 8, 4] [2, 2, 4, 4, 8] Array with duplicate valuesVisualization
[5, -1, 0, -3] [-3, -1, 0, 5] Array with negative numbersVisualization

Visualization Player

Solution❯

Bubble Sort works by repeatedly swapping adjacent elements that are in the wrong order, causing larger values to 'bubble up' to the end of the array after each pass.

Understanding the Behavior with Different Cases

Let’s walk through how Bubble Sort behaves in different scenarios so you can understand what to expect:

  • Normal case: For an array like [5, 1, 4, 8, 2], Bubble Sort will make several passes, each time pushing the largest remaining unsorted element to its correct position. After the first pass, the largest value (8) moves to the end. The next pass focuses only on the unsorted portion [1, 4, 5, 2], and so on until the array is fully sorted.
  • Reverse sorted case: For an input like [3, 2, 1], the algorithm performs the maximum number of swaps. Each element has to move all the way to its correct position, making this the worst-case scenario for Bubble Sort in terms of efficiency.
  • Already sorted case: If the array is already in order, like [1, 2, 3], Bubble Sort can detect this and finish early without doing any swaps—especially when optimized. This is its best-case scenario and shows the value of checking if any swaps occurred during a pass.
  • Duplicates and repeated values: Bubble Sort handles duplicates naturally. For example, [4, 2, 2, 8, 4] gets sorted to [2, 2, 4, 4, 8] just like any other array. Duplicate values are compared and only moved when necessary.
  • Negative numbers: The algorithm works the same with negative numbers. For example, [5, -1, 0, -3] becomes [-3, -1, 0, 5] after sorting.
  • Single-element array: An array like [7] is already sorted. No swaps or comparisons are needed, so the algorithm exits immediately.
  • Empty array: If the input is an empty array [], there's nothing to sort, and the output is also []. Bubble Sort simply doesn’t enter the loop.

Algorithm Steps❯

  1. Start from the first element in the array.
  2. Compare the current element with the next element.
  3. If the current element is greater than the next element, swap them.
  4. Move to the next element and repeat steps 2 and 3 for the entire array.
  5. After one complete pass, the largest element will be at the end.
  6. Repeat the process for the remaining unsorted elements (excluding the last sorted ones).
  7. Continue until the array is completely sorted.

Code

Python
Java
JavaScript
C
C++
C#
Go
def bubble_sort(arr):
    n = len(arr)
    # Traverse through all array elements
    for i in range(n):
        # Last i elements are already in place
        for j in range(0, n - i - 1):
            # Swap if the element found is greater than the next element
            if arr[j] > arr[j + 1]:
                arr[j], arr[j + 1] = arr[j + 1], arr[j]
if __name__ == '__main__':
    arr = [6, 3, 8, 2, 7, 4]
    bubble_sort(arr)
    print("Sorted array is:", arr)

Time Complexity❯

CaseTime ComplexityExplanation
Best CaseO(n)In the best case, the array is already sorted. Bubble Sort makes one pass through the array without any swaps, and with an optimized version that checks for swaps, it terminates early. Hence, the time complexity is linear.
Average CaseO(n^2)On average, Bubble Sort compares and possibly swaps each pair of elements in a nested loop. This results in roughly n*(n-1)/2 operations, leading to quadratic time complexity.
Worst CaseO(n^2)In the worst case (when the array is sorted in reverse order), Bubble Sort performs the maximum number of comparisons and swaps, resulting in n*(n-1)/2 operations — hence, O(n^2).

Space Complexity❯

O(1)

Explanation: Bubble Sort is an in-place sorting algorithm. It requires only a constant amount of extra space for swapping elements — typically a temporary variable and loop counters.

Detailed Step by Step Example❯

Let us take the followign array, and apply Bubble Sort algorithm to sort the array.

{ "array": [6,3,8,2,7,4], "showIndices": false, "specialIndices": [] }

Pass 1

➜ Comparing 6 and 3

{ "array": [6,3,8,2,7,4], "showIndices": false, "highlightIndices": [0,1], "highlightIndicesGreen": [], "specialIndices": [] }

6 > 3.
Swap 6 and 3.
We need to arrange them in ascending order.

{ "array": [3,6,8,2,7,4], "showIndices": false, "highlightIndicesBlue": [0,1], "highlightIndicesGreen": [], "specialIndices": [] }

➜ Comparing 6 and 8

{ "array": [3,6,8,2,7,4], "showIndices": false, "highlightIndices": [1,2], "highlightIndicesGreen": [], "specialIndices": [] }

6 <= 8.
No swap needed.
They are already in ascending order.

➜ Comparing 8 and 2

{ "array": [3,6,8,2,7,4], "showIndices": false, "highlightIndices": [2,3], "highlightIndicesGreen": [], "specialIndices": [] }

8 > 2.
Swap 8 and 2.
We need to arrange them in ascending order.

{ "array": [3,6,2,8,7,4], "showIndices": false, "highlightIndicesBlue": [2,3], "highlightIndicesGreen": [], "specialIndices": [] }

➜ Comparing 8 and 7

{ "array": [3,6,2,8,7,4], "showIndices": false, "highlightIndices": [3,4], "highlightIndicesGreen": [], "specialIndices": [] }

8 > 7.
Swap 8 and 7.
We need to arrange them in ascending order.

{ "array": [3,6,2,7,8,4], "showIndices": false, "highlightIndicesBlue": [3,4], "highlightIndicesGreen": [], "specialIndices": [] }

➜ Comparing 8 and 4

{ "array": [3,6,2,7,8,4], "showIndices": false, "highlightIndices": [4,5], "highlightIndicesGreen": [], "specialIndices": [] }

8 > 4.
Swap 8 and 4.
We need to arrange them in ascending order.

{ "array": [3,6,2,7,4,8], "showIndices": false, "highlightIndicesBlue": [4,5], "highlightIndicesGreen": [], "specialIndices": [] }

8 is now at its correct position.

{ "array": [3,6,2,7,4,8], "showIndices": false, "highlightIndicesGreen": [5], "specialIndices": [] }

Pass 2

➜ Comparing 3 and 6

{ "array": [3,6,2,7,4,8], "showIndices": false, "highlightIndices": [0,1], "highlightIndicesGreen": [5], "specialIndices": [] }

3 <= 6.
No swap needed.
They are already in ascending order.

➜ Comparing 6 and 2

{ "array": [3,6,2,7,4,8], "showIndices": false, "highlightIndices": [1,2], "highlightIndicesGreen": [5], "specialIndices": [] }

6 > 2.
Swap 6 and 2.
We need to arrange them in ascending order.

{ "array": [3,2,6,7,4,8], "showIndices": false, "highlightIndicesBlue": [1,2], "highlightIndicesGreen": [5], "specialIndices": [] }

➜ Comparing 6 and 7

{ "array": [3,2,6,7,4,8], "showIndices": false, "highlightIndices": [2,3], "highlightIndicesGreen": [5], "specialIndices": [] }

6 <= 7.
No swap needed.
They are already in ascending order.

➜ Comparing 7 and 4

{ "array": [3,2,6,7,4,8], "showIndices": false, "highlightIndices": [3,4], "highlightIndicesGreen": [5], "specialIndices": [] }

7 > 4.
Swap 7 and 4.
We need to arrange them in ascending order.

{ "array": [3,2,6,4,7,8], "showIndices": false, "highlightIndicesBlue": [3,4], "highlightIndicesGreen": [5], "specialIndices": [] }

7 is now at its correct position.

{ "array": [3,2,6,4,7,8], "showIndices": false, "highlightIndicesGreen": [4,5], "specialIndices": [] }

Pass 3

➜ Comparing 3 and 2

{ "array": [3,2,6,4,7,8], "showIndices": false, "highlightIndices": [0,1], "highlightIndicesGreen": [4,5], "specialIndices": [] }

3 > 2.
Swap 3 and 2.
We need to arrange them in ascending order.

{ "array": [2,3,6,4,7,8], "showIndices": false, "highlightIndicesBlue": [0,1], "highlightIndicesGreen": [4,5], "specialIndices": [] }

➜ Comparing 3 and 6

{ "array": [2,3,6,4,7,8], "showIndices": false, "highlightIndices": [1,2], "highlightIndicesGreen": [4,5], "specialIndices": [] }

3 <= 6.
No swap needed.
They are already in ascending order.

➜ Comparing 6 and 4

{ "array": [2,3,6,4,7,8], "showIndices": false, "highlightIndices": [2,3], "highlightIndicesGreen": [4,5], "specialIndices": [] }

6 > 4.
Swap 6 and 4.
We need to arrange them in ascending order.

{ "array": [2,3,4,6,7,8], "showIndices": false, "highlightIndicesBlue": [2,3], "highlightIndicesGreen": [4,5], "specialIndices": [] }

6 is now at its correct position.

{ "array": [2,3,4,6,7,8], "showIndices": false, "highlightIndicesGreen": [3,4,5], "specialIndices": [] }

Pass 4

➜ Comparing 2 and 3

{ "array": [2,3,4,6,7,8], "showIndices": false, "highlightIndices": [0,1], "highlightIndicesGreen": [3,4,5], "specialIndices": [] }

2 <= 3.
No swap needed.
They are already in ascending order.

➜ Comparing 3 and 4

{ "array": [2,3,4,6,7,8], "showIndices": false, "highlightIndices": [1,2], "highlightIndicesGreen": [3,4,5], "specialIndices": [] }

3 <= 4.
No swap needed.
They are already in ascending order.

4 is now at its correct position.

{ "array": [2,3,4,6,7,8], "showIndices": false, "highlightIndicesGreen": [2,3,4,5], "specialIndices": [] }

Pass 5

➜ Comparing 2 and 3

{ "array": [2,3,4,6,7,8], "showIndices": false, "highlightIndices": [0,1], "highlightIndicesGreen": [2,3,4,5], "specialIndices": [] }

2 <= 3.
No swap needed.
They are already in ascending order.

3 is now at its correct position.

{ "array": [2,3,4,6,7,8], "showIndices": false, "highlightIndicesGreen": [1,2,3,4,5], "specialIndices": [] }

Pass 6

2 is now at its correct position.

{ "array": [2,3,4,6,7,8], "showIndices": false, "highlightIndicesGreen": [0,1,2,3,4,5], "specialIndices": [] }

Array is fully sorted.


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