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

Print a Matrix in Spiral Order Optimal Algorithm with Example

Problem Statement

Given a 2D matrix, your task is to print all its elements in a spiral order starting from the top-left corner and moving clockwise layer by layer.

In spiral order, you start by printing the top row, then the rightmost column, then the bottom row in reverse, and finally the leftmost column from bottom to top. This process is repeated for the inner layers until all elements are printed.

If the matrix is empty or has no elements, the output should be an empty list.

Examples

Input Matrix Spiral Output Description
[[1, 2, 3], [4, 5, 6], [7, 8, 9]]
[1, 2, 3, 6, 9, 8, 7, 4, 5]
3x3 square matrix, classic spiral flow
[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
[1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7]
3x4 rectangular matrix (more columns)
[[1], [2], [3], [4]]
[1, 2, 3, 4]
Single column matrix (4x1)
[[1, 2, 3, 4]]
[1, 2, 3, 4]
Single row matrix (1x4)
[[5]] [5] Single element matrix
[] [] Empty matrix, no elements to print

Visualization Player

Solution

Understanding the Problem

We are given a 2D matrix and asked to print its elements in a spiral order. That means starting from the top-left corner, we go right along the top row, then down the rightmost column, then left along the bottom row, then up the leftmost column—repeating this process inward like peeling layers of an onion until all elements are visited.

For a beginner, think of walking around the boundary of the matrix, one layer at a time, and collecting the numbers in the order you walk.

Step-by-Step Solution with Example

step 1: Initialize boundaries

We define four variables to represent the current unvisited part of the matrix:

  • top – the index of the first row not yet printed
  • bottom – the index of the last row not yet printed
  • left – the index of the first column not yet printed
  • right – the index of the last column not yet printed

step 2: Traverse in spiral order

We use a loop and at each iteration, follow this order:

  1. Go left to right across the top row
  2. Go top to bottom along the rightmost column
  3. If rows remain, go right to left along the bottom row
  4. If columns remain, go bottom to top along the leftmost column

After completing a side, update the boundary variables to move inward (e.g., top++, right--, etc.).

step 3: Continue until all elements are visited

The loop continues as long as top ≤ bottom and left ≤ right. This ensures we don't go beyond the unvisited region.

step 4: Example walk-through

Consider this 3x3 matrix:


[ [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9] ]

Spiral order traversal:

  1. Top row: 1, 2, 3
  2. Right column: 6, 9
  3. Bottom row (reversed): 8, 7
  4. Left column (upward): 4
  5. Remaining element: 5

Output: [1, 2, 3, 6, 9, 8, 7, 4, 5]

Edge Cases

  • Empty matrix: No elements to print. Return an empty list.
  • Single element: Just return that one value.
  • Single row: Only traverse left to right.
  • Single column: Only traverse top to bottom.
  • More rows than columns: Spiral will loop deeper vertically.
  • More columns than rows: Spiral will loop wider horizontally.

Finally

This spiral traversal technique ensures we visit each element exactly once. It's intuitive when we think in terms of peeling layers, and it works efficiently in O(m × n) time for an m x n matrix. For beginners, always visualize the movement and update of boundaries, and use dry runs with small matrices to build confidence.

Algorithm Steps

  1. Given a 2D matrix of size m x n.
  2. Initialize four variables: top = 0, bottom = m - 1, left = 0, right = n - 1.
  3. Traverse the matrix in a spiral form while top <= bottom and left <= right:
  4. → Traverse from left to right across the top row and increment top.
  5. → Traverse from top to bottom along the right column and decrement right.
  6. → If top <= bottom, traverse from right to left across the bottom row and decrement bottom.
  7. → If left <= right, traverse from bottom to top along the left column and increment left.
  8. Repeat until all elements are printed.

Code

C
C++
Python
Java
JS
Go
Rust
Kotlin
TS
#include <stdio.h>

void spiralOrder(int rows, int cols, int matrix[rows][cols]) {
    int top = 0, bottom = rows - 1;
    int left = 0, right = cols - 1;

    while (top <= bottom && left <= right) {
        for (int i = left; i <= right; i++) printf("%d ", matrix[top][i]);
        top++;

        for (int i = top; i <= bottom; i++) printf("%d ", matrix[i][right]);
        right--;

        if (top <= bottom) {
            for (int i = right; i >= left; i--) printf("%d ", matrix[bottom][i]);
            bottom--;
        }

        if (left <= right) {
            for (int i = bottom; i >= top; i--) printf("%d ", matrix[i][left]);
            left++;
        }
    }
}

int main() {
    int matrix[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
    printf("Spiral Order: ");
    spiralOrder(3, 3, matrix);
    return 0;
}

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