Minesweeper Algorithms Explained

Published on January 6, 2026

Interactive Demo

Explore how Minesweeper algorithms work step by step:

Step 1: Building the Grid

The game starts with an empty grid. Each cell is hidden and ready to be filled.

Each gray cell is hidden and waiting to be revealed.

Core Algorithms

Mine Placement

Uses Fisher-Yates shuffle to randomly place mines, excluding the first-clicked cell to ensure the player never loses on their first move.

const placeMines = (grid: Grid, mineCount: number, excludeRow: number, excludeCol: number): Grid => {
  // Collect valid positions (excluding first click area)
  const positions = [];
  for (let row = 0; row < height; row++) {
    for (let col = 0; col < width; col++) {
      if (!(Math.abs(row - excludeRow) <= 1 && Math.abs(col - excludeCol) <= 1)) {
        positions.push({ row, col });
      }
    }
  }

  // Shuffle and place mines at first N positions
  shuffle(positions);
  positions.slice(0, mineCount).forEach(({ row, col }) => {
    grid[row][col].isMine = true;
  });
};

Neighbor Counting

Each cell counts adjacent mines in all 8 directions:

const DIRECTIONS = [[-1,-1], [-1,0], [-1,1], [0,-1], [0,1], [1,-1], [1,0], [1,1]];

const countNeighborMines = (grid: Grid, row: number, col: number): number => {
  return DIRECTIONS.reduce((count, [dr, dc]) => {
      const r = row + dr, c = col + dc;
      return count + (isInBounds(r, c) && grid[r][c].isMine ? 1 : 0);
  }, 0);
};

Flood Fill Reveal

When clicking an empty cell (0 adjacent mines), recursively reveal all connected empty cells:

const reveal = (grid: Grid, row: number, col: number): void => {
  if (!isInBounds(row, col) || grid[row][col].isRevealed) return;

  grid[row][col].isRevealed = true;

  // If empty cell, reveal all neighbors
  if (grid[row][col].neighborMines === 0) {
    DIRECTIONS.forEach(([dr, dc]) => reveal(grid, row + dr, col + dc));
  }
};

This is the heart of Minesweeper - a depth-first search that spreads outward until it hits numbered cells.

Complexity

Algorithm	Time	Space
Mine Placement	O(n)	O(w×h)
Neighbor Count	O(w×h)	O(1)
Flood Fill	O(w×h)	O(w×h)

Try It

Play the game: Minesweeper

References

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