#885

Medium

LeetCode Problem Workspace

Spiral Matrix III

Solve the Spiral Matrix III problem by simulating the movement across a matrix with specific constraints on direction and boundaries.

array matrix simulation

Problem Statement

You are given a grid of dimensions rows x cols and a starting point (rStart, cStart). You must simulate a walk starting from this position, moving in a clockwise spiral pattern across the grid. The movement starts facing east and turns right at every boundary or previously visited position.

Whenever you move outside the grid's boundary, the walk continues outside, but you must make sure to return to the boundary and continue the spiral. The task is to return the list of coordinates representing all the positions in the order they are visited.

Examples

Example 1

Input: rows = 1, cols = 4, rStart = 0, cStart = 0

Output: [[0,0],[0,1],[0,2],[0,3]]

Example details omitted.

Example 2

Input: rows = 5, cols = 6, rStart = 1, cStart = 4

Output: [[1,4],[1,5],[2,5],[2,4],[2,3],[1,3],[0,3],[0,4],[0,5],[3,5],[3,4],[3,3],[3,2],[2,2],[1,2],[0,2],[4,5],[4,4],[4,3],[4,2],[4,1],[3,1],[2,1],[1,1],[0,1],[4,0],[3,0],[2,0],[1,0],[0,0]]

Example details omitted.

Constraints

1 <= rows, cols <= 100
0 <= rStart < rows
0 <= cStart < cols

Solution Approach

Simulate the Spiral Walk

Start by simulating the spiral walk. Maintain a direction variable (east, south, west, north) and update it after each boundary hit. Mark the visited positions and store them in an array, ensuring that you only add new positions that are within the bounds of the grid.

Handle Boundary Conditions

Whenever a boundary or already visited cell is encountered, change direction in a clockwise manner. This requires careful handling of grid boundaries to avoid unnecessary moves.

Optimize for Grid Boundaries

Efficiently check if a move is within grid boundaries. When reaching a boundary or previously visited cell, update the position and direction, ensuring that all cells are eventually visited.

Complexity Analysis

Metric	Value
Time	O(\max(\text{rows}, \text{cols})^2)
Space	O(\text{rows} \cdot \text{cols})

The time complexity is O(max(rows, cols)^2) because, in the worst case, we will visit all the cells once. The space complexity is O(rows * cols) since we store each visited coordinate in an array.

What Interviewers Usually Probe

Ensure the candidate handles grid boundaries properly while maintaining an efficient traversal.
Look for the ability to simulate the process step-by-step and adapt to boundary conditions.
Evaluate the candidate's approach to optimizing the space complexity when working with large grids.

Common Pitfalls or Variants

Common pitfalls

Failing to handle the grid boundaries properly, leading to unnecessary moves or invalid coordinates.
Not correctly simulating the clockwise spiral movement, leading to incorrect ordering of visited coordinates.
Mismanaging the direction changes, which might cause infinite loops or missing cells.

Follow-up variants

Handling different grid sizes, including very narrow grids (e.g., 1xN or Nx1).
Optimizing the solution to avoid unnecessary memory usage for very large grids.
Considering cases where the starting point is at the edge or corner of the grid.

FAQ

How do I efficiently simulate the spiral traversal?

To efficiently simulate the traversal, maintain direction changes (right turn) when boundaries or visited cells are encountered. Update position carefully and check grid boundaries to ensure valid moves.

What is the primary pattern behind the Spiral Matrix III problem?

The primary pattern involves simulating an array and matrix traversal by managing direction changes, grid boundaries, and the order in which the cells are visited in a clockwise spiral.

How do I ensure the traversal includes all cells in the grid?

You need to track each visited cell and change direction when boundaries or already visited cells are encountered. Keep moving in a spiral pattern until all cells are visited.

What is the time complexity of Spiral Matrix III?

The time complexity is O(max(rows, cols)^2), as you may have to visit every cell in the grid in the worst case.

How does GhostInterview assist with solving Spiral Matrix III?

GhostInterview helps by providing guided solutions, detecting common pitfalls like boundary mismanagement, and offering insights to optimize space and time complexity during traversal.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def spiralMatrixIII(
        self, rows: int, cols: int, rStart: int, cStart: int
    ) -> List[List[int]]:
        ans = [[rStart, cStart]]
        if rows * cols == 1:
            return ans
        k = 1
        while True:
            for dr, dc, dk in [[0, 1, k], [1, 0, k], [0, -1, k + 1], [-1, 0, k + 1]]:
                for _ in range(dk):
                    rStart += dr
                    cStart += dc
                    if 0 <= rStart < rows and 0 <= cStart < cols:
                        ans.append([rStart, cStart])
                        if len(ans) == rows * cols:
                            return ans
            k += 2

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