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

Rotate a Matrix by 90 Degrees Clockwise Optimal In-place Algorithm

Problem Statement

Given a square matrix of size n x n, rotate the entire matrix by 90 degrees in the clockwise direction. The rotation should be done in-place, meaning no extra matrix should be used for the transformation.

  • Each element of the matrix should be repositioned so that after rotation, the first row becomes the last column, the second row becomes the second-last column, and so on.
  • If the matrix is empty or has only one element, return it as is.

Examples

Input Matrix Output Matrix Description
[[1,2],[3,4]] [[3,1],[4,2]] 2x2 matrix rotated 90° clockwise
[[1,2,3],[4,5,6],[7,8,9]] [[7,4,1],[8,5,2],[9,6,3]] Standard 3x3 matrix rotation
[[1]] [[1]] Single element matrix remains unchanged
[] [] Empty matrix has no elements to rotate
[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]] [[13,9,5,1],[14,10,6,2],[15,11,7,3],[16,12,8,4]] 4x4 matrix rotated in-place

Visualization Player

Solution

To rotate a square matrix by 90 degrees clockwise without using extra space, we need to reposition the elements in-place. Instead of rotating each layer individually (which is another method), this optimal approach uses two simple steps:

Step 1: Transpose the Matrix

Transposing a matrix means converting rows into columns. We swap every element matrix[i][j] with matrix[j][i] for all i < j. After this step, the matrix is flipped along its diagonal.

Step 2: Reverse Each Row

Now, we reverse each row in the transposed matrix. This aligns all the elements to their new 90-degree rotated positions.

Why This Works

When we transpose the matrix, the top row becomes the left column. But to fully rotate it clockwise, we still need to move the last column to the top, which is achieved by reversing each row after transposition.

Let’s Discuss Different Scenarios

  • Normal Square Matrix: For matrices like 2x2, 3x3, or 4x4, the algorithm works seamlessly and efficiently, with no extra space used.
  • Matrix with One Element: Rotating a 1x1 matrix has no visible effect. The matrix stays the same.
  • Empty Matrix: There's nothing to rotate. The function should simply return an empty list or matrix.
  • Non-Square Matrix: This approach only works on square matrices (equal number of rows and columns). If the matrix is not square, this logic should not be applied as it would produce incorrect results.

Because we don’t use any extra space, this is an in-place O(1) space and O(n²) time solution, where n is the number of rows (or columns).

Algorithm Steps

  1. Given an n x n square matrix.
  2. Step 1: Transpose the matrix: swap matrix[i][j] with matrix[j][i] for all i < j.
  3. Step 2: Reverse each row of the matrix.
  4. The matrix is now rotated 90 degrees clockwise.

Code

Python
JavaScript
Java
C++
C
def rotate_matrix(matrix):
    n = len(matrix)
    # Transpose the matrix
    for i in range(n):
        for j in range(i + 1, n):
            matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]

    # Reverse each row
    for row in matrix:
        row.reverse()

    return matrix

# Sample Input
mat = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]
rotated = rotate_matrix(mat)
for row in rotated:
    print(row)