Matrix Cells in Distance Order

Matrix Cells in Distance Order - Problem

Array Math Geometry Sorting Matrix Easy

You are given four integers rows, cols, rCenter, and cCenter. There is a rows x cols matrix and you are on the cell with the coordinates (rCenter, cCenter).

Return the coordinates of all cells in the matrix, sorted by their distance from (rCenter, cCenter) from the smallest distance to the largest distance. You may return the answer in any order that satisfies this condition.

The distance between two cells (r1, c1) and (r2, c2) is |r1 - r2| + |c1 - c2| (Manhattan distance).

Input & Output

Example 1 — Small Matrix

$ Input: rows = 1, cols = 2, rCenter = 0, cCenter = 0

› Output: [[0,0],[0,1]]

💡 Note: Only 2 cells: (0,0) at distance 0 and (0,1) at distance 1. Manhattan distance from (0,0): |0-0|+|0-0|=0 for (0,0), |0-0|+|1-0|=1 for (0,1).

Example 2 — Center Position

$ Input: rows = 2, cols = 2, rCenter = 0, cCenter = 1

› Output: [[0,1],[0,0],[1,1],[1,0]]

💡 Note: Center (0,1): distance 0. Adjacent cells (0,0) and (1,1) at distance 1. Diagonal (1,0) at distance 2. Order: d=0 → d=1 → d=1 → d=2.

Example 3 — Corner Center

$ Input: rows = 2, cols = 3, rCenter = 1, cCenter = 2

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

💡 Note: Center at corner (1,2). Distances: (1,2)=0, (0,2)=1, (1,1)=1, (0,1)=2, (1,0)=2, (0,0)=3. Cells are naturally grouped by distance levels.

Constraints

1 ≤ rows, cols ≤ 100
0 ≤ rCenter < rows
0 ≤ cCenter < cols

Visualization

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Asked in

G Google 45 a Amazon 32 f Facebook 28

The key insight is using Manhattan distance |r1-r2|+|c1-c2| to sort matrix cells. BFS approach is optimal as it naturally discovers cells in distance order without sorting. Time: O(mn), Space: O(mn).

Common Approaches

✓ Optimized

⏱️ Time: N/A Space: N/A

Breadth-First Search (BFS)

⏱️ Time: O(mn) Space: O(mn)

Start from the center and use BFS to explore cells level by level. Each BFS level contains all cells at the same distance, so we naturally get sorted order without explicit sorting.

Brute Force with Sorting

⏱️ Time: O(mn log(mn)) Space: O(mn)

Create all possible matrix coordinates, compute Manhattan distance for each cell, then sort by distance. This is straightforward but requires sorting all cells.

Bucket Sort by Distance

⏱️ Time: O(mn) Space: O(mn + d)

Since maximum Manhattan distance in a matrix is limited, we can use bucket sort. Create buckets for each possible distance and group cells accordingly, then output buckets in distance order.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

⚡ Linearithmic Space

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Medium Frequency

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Smart Actions

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