Spiral Matrix

Medium Day 10 • Striver Blind 75

📌 Problem Overview

Given an m x n matrix, return all elements of the matrix in spiral order.

Examples & Constraints

Example 1:

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

Constraints:

1 <= m, n <= 10

💡 Approach & Intuition

4 boundaries (top, bottom, left, right) narrowed after each traversal leg.

🎯 Pattern Recognition

Matrix Boundary Shrinking

📊 Step-by-Step Execution (Mermaid Diagram)

graph TD
    Start["Input Data"] --> Process["Process Element by Element"]
    Process --> Lookup{"Hash Map / Set Lookup"}
    Lookup -- "Match Found" --> Return["Return Indices / Result"]
    Lookup -- "No Match" --> Store["Store in Map / Set"]
    Store --> Process

🐢 Brute Force Solution

Code

function spiralOrder(matrix) {
  const res = [];
  let top = 0, bottom = matrix.length - 1, left = 0, right = matrix[0].length - 1;
  while (top <= bottom && left <= right) {
    for (let c = left; c <= right; c++) res.push(matrix[top][c]); top++;
    for (let r = top; r <= bottom; r++) res.push(matrix[r][right]); right--;
    if (top <= bottom) { for (let c = right; c >= left; c--) res.push(matrix[bottom][c]); bottom--; }
    if (left <= right) { for (let r = bottom; r >= top; r--) res.push(matrix[r][left]); left++; }
  }
  return res;
}

Time Complexity: O(m*n)
Space Complexity: O(1)
Explanation: Boundary contraction.

⚡ Optimized Solution

Code

function spiralOrder(matrix) {
  const res = [];
  let top = 0, bottom = matrix.length - 1, left = 0, right = matrix[0].length - 1;
  while (top <= bottom && left <= right) {
    for (let c = left; c <= right; c++) res.push(matrix[top][c]); top++;
    for (let r = top; r <= bottom; r++) res.push(matrix[r][right]); right--;
    if (top <= bottom) { for (let c = right; c >= left; c--) res.push(matrix[bottom][c]); bottom--; }
    if (left <= right) { for (let r = bottom; r >= top; r--) res.push(matrix[r][left]); left++; }
  }
  return res;
}

Time Complexity: O(m*n)
Space Complexity: O(1)
Explanation: Layer-by-layer boundary shrinking traversal.

🐾 Step-by-Step Walkthrough

Initialize State: Setup necessary pointers, dynamic programming arrays, or hash maps.
Iterate & Evaluate: Process the input according to the boundary conditions.
Update & Return: Compute the optimal answer and return early or at termination.

🎙️ FAANG Interview Pitch

Traverse right, down, left, up while shrinking top/bottom/left/right boundary bounds.

💡 Progressive Hints

Maintain top, bottom, left, right boundaries.

⚡ Interactive Practice

👉 Solve this problem interactively in the DSA Lab