529. Minesweeper - Detailed Explanation

Problem Statement

Description:
You are given a 2D board representing a Minesweeper game. Each cell on the board can be one of the following characters:

'M' – an unrevealed mine,
'E' – an unrevealed empty square,
'B' – a revealed blank square with no adjacent mines,
'1' to '8' – a revealed square indicating the number of adjacent mines,
'X' – a revealed mine (game over).

You are also given a click position (a pair of row and column indices). Based on the click, update the board as follows:

Mine Clicked:
If a mine ('M') is clicked, change it to 'X' to mark that the game is over.
Empty Square Clicked (No Adjacent Mines):
If an empty square ('E') with no adjacent mines is revealed, change it to a blank ('B'). Then, recursively reveal all of its adjacent unrevealed squares.
Empty Square Clicked (With Adjacent Mines):
If an empty square ('E') with one or more adjacent mines is revealed, change it to a digit ('1' to '8') representing the number of adjacent mines.
Stop Condition:
Return the updated board when no more squares can be revealed.

Examples:

Example 1:

Input:

board = [['E', 'E', 'E', 'E', 'E'],
         ['E', 'E', 'M', 'E', 'E'],
         ['E', 'E', 'E', 'E', 'E'],
         ['E', 'E', 'E', 'E', 'E']]
click = [3, 0]

Output:

[['B', '1', 'E', '1', 'B'],
 ['B', '1', 'M', '1', 'B'],
 ['B', '1', '1', '1', 'B'],
 ['B', 'B', 'B', 'B', 'B']]

Explanation:
The click at position [3, 0] (bottom-left corner) reveals an empty square with no adjacent mines. A recursive reveal then occurs to all adjacent squares. For squares adjacent to a mine, the count is shown.

Example 2:

Input:

board = [['B', '1', 'E', '1', 'B'],
         ['B', '1', 'M', '1', 'B'],
         ['B', '1', '1', '1', 'B'],
         ['B', 'B', 'B', 'B', 'B']]
click = [1, 2]

Output:

[['B', '1', 'E', '1', 'B'],
 ['B', '1', 'X', '1', 'B'],
 ['B', '1', '1', '1', 'B'],
 ['B', 'B', 'B', 'B', 'B']]

Explanation:
The click at position [1, 2] hits a mine. The mine is then revealed as 'X', indicating game over.

Constraints:

The board is a 2D array of characters.
The click is a valid coordinate within the board.
Board dimensions and the number of mines/empty squares vary, but you can assume the board is not empty.

Hints Before Diving into the Solution

Hint 1:
Think about how you can explore the board in all 8 directions (up, down, left, right, and the 4 diagonals) from any given cell. This is crucial for counting adjacent mines and for the recursive reveal.
Hint 2:
When revealing cells, consider using either Depth-First Search (DFS) or Breadth-First Search (BFS). What conditions will determine whether you should stop the search in a certain direction?

Approach 1: Depth-First Search (DFS)

Idea:

Click a Mine:
If the clicked cell is 'M', update it to 'X' and return immediately.
Reveal an Empty Cell:
If the clicked cell is 'E', count the number of adjacent mines by exploring all 8 directions.
- No Adjacent Mines:
  If the count is zero, change the cell to 'B' and recursively reveal all adjacent unrevealed cells.
- Adjacent Mines Present:
  If the count is greater than zero, update the cell with the count (as a character) and stop further exploration from that cell.

Visual Walkthrough:

Imagine a cell at position (i, j). For each of the 8 directions (e.g., (i-1, j), (i+1, j), (i, j-1), (i, j+1), and the four diagonals), check if the cell contains a mine ('M').

If zero mines are adjacent, mark it as 'B' and perform DFS on its neighbors.
If there are mines present, update the cell with the number of mines and do not explore its neighbors.

Approach 2: Breadth-First Search (BFS)

Idea:

Use a Queue:
Start by adding the clicked cell to a queue.
Process Each Cell:
While the queue is not empty:
- Remove a cell from the queue.
- If it is an empty cell ('E'), count adjacent mines.
- If the count is zero, mark the cell as 'B' and enqueue all adjacent unrevealed cells.
- Otherwise, update the cell with the count.
Stop When Done:
Continue until there are no cells left to process in the queue.

Comparison:

DFS is naturally recursive and might be easier to implement, but it could run into deep recursion issues on large boards.
BFS uses an iterative approach with a queue, which can help avoid recursion depth problems and might be preferred when the board is large.

Python Code

Python3

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Java Code

Java

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Complexity Analysis

Time Complexity:
In the worst-case scenario, you might end up visiting every cell once. Hence, the time complexity is O(m * n), where m is the number of rows and n is the number of columns.
Space Complexity:
- For DFS, the recursion stack may go as deep as O(m * n) in the worst case.
- For BFS (if implemented), you’d use additional space for the queue but it would also be O(m * n).
- The board itself is modified in place, so extra space is minimal beyond recursion/queue.

Step-by-Step Walkthrough & Visual Example

Consider Example 1:

board = [['E', 'E', 'E', 'E', 'E'],
         ['E', 'E', 'M', 'E', 'E'],
         ['E', 'E', 'E', 'E', 'E'],
         ['E', 'E', 'E', 'E', 'E']]
click = [3, 0]

Click Handling:
The click is on [3, 0], which is 'E'. Since it’s not a mine, we start our DFS.
Counting Adjacent Mines at [3,0]:
Check all 8 directions. If no mines are found, mark [3,0] as 'B' and recursively process its neighbors.
Recursive Reveal:
Continue this process for every cell reached. When a cell has adjacent mines, update that cell with the count (for example, if there is one adjacent mine, it becomes '1') and do not expand further from that cell.
Termination:
The recursion stops when all reachable cells have either been marked as 'B' or updated with a digit. The final board is then returned.

Common Mistakes

Not Checking Boundaries:
When iterating over adjacent cells, always ensure you do not access indices outside the board.
Overlapping Recursion:
Failing to update a cell immediately after processing can lead to repeated DFS calls on the same cell. Make sure to update and then mark cells to avoid cycles.
Incorrect Direction Handling:
It’s important to cover all 8 directions. Omitting one or miscalculating an adjacent index can lead to wrong mine counts.

Edge Cases & Alternative Variations

Edge Case 1:
Clicking on a mine (cell 'M'). The expected behavior is to update that cell to 'X' immediately.
Edge Case 2:
A board where all cells are already revealed or have no unrevealed cells left. Although not common, ensure your solution gracefully handles such cases.
Alternative Variation:
Some variations might require counting adjacent mines differently (for example, considering only four directions instead of eight). Adjust the direction array accordingly.