How do you solve Spiral Matrix III on LeetCode?

Spiral Matrix III (LeetCode #885) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: The spiral movement can be visualized as a series of layers expanding outward.

What is the brute force solution for Spiral Matrix III?

The brute force approach for Spiral Matrix III is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach simulates the movement in a spiral pattern, checking each direction and moving step by step. It continues until all cells in the grid are visited, regardless of whether they are within the grid's boundaries. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Spiral Matrix III?

Spiral Matrix III uses the following concepts: Array, Matrix, Simulation. The recommended patterns to study are: Simulation, Array.

What are the interview tips for Spiral Matrix III?

Explain your thought process clearly as you implement the solution. Consider edge cases, such as minimum grid sizes or starting positions on the grid's edge. Practice simulating the movement on paper to visualize the spiral pattern.

What are common mistakes when solving Spiral Matrix III?

Not handling the boundary conditions correctly, leading to index errors. Failing to adjust the number of steps after horizontal movements.

#885

Spiral Matrix III

Medium

ArrayMatrixSimulationSimulationArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses a systematic approach to determine the next position based on the current direction and the number of steps taken. It efficiently tracks the boundaries and adjusts the direction accordingly without unnecessary checks.

⚙️

Algorithm

3 steps

1Step 1: Initialize an empty list for coordinates and set the current position and direction.
2Step 2: Use a loop that continues until all cells are visited, adjusting the direction and steps as needed.
3Step 3: Append valid coordinates to the result list while moving in the current direction.

solution.py16 lines

1def spiralMatrixIII(rows, cols, rStart, cStart):
2    result = []
3    directions = [(0, 1), (1, 0), (0, -1), (-1, 0)]
4    x, y = rStart, cStart
5    steps = 1
6    while len(result) < rows * cols:
7        for direction in directions:
8            for _ in range(steps):
9                if 0 <= x < rows and 0 <= y < cols:
10                    result.append([x, y])
11                x += direction[0]
12                y += direction[1]
13            if direction in [(0, 1), (0, -1)]:
14                steps += 1
15    return result
16

ℹ

Complexity note: The optimal solution efficiently traverses through the grid, visiting each cell exactly once, leading to linear time complexity relative to the number of cells.

1The spiral movement can be visualized as a series of layers expanding outward.
2Boundary conditions are crucial to ensure valid cell visits.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.