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How do you count the number of islands in a grid?

Q: How do you count the number of islands in a grid?

**Intuition.** Each "island" is a connected blob of land cells (1s) surrounded by water (0s). Scan the grid; every time you hit an *unvisited* land cell, you've found a new island — then **flood-fill** all its connected land (DFS or BFS) so you don't count it again. flood-fill each new land cell; count the launches 1 <text x="174" y="53" fi

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DFS flood fill

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def num_islands(grid):
    if not grid: return 0
    rows, cols = len(grid), len(grid[0])

    def dfs(r, c):
        if r < 0 or c < 0 or r >= rows or c >= cols or grid[r][c] != '1':
            return
        grid[r][c] = '0'                  # mark visited
        dfs(r+1, c); dfs(r-1, c); dfs(r, c+1); dfs(r, c-1)

    count = 0
    for r in range(rows):
        for c in range(cols):
            if grid[r][c] == '1':
                count += 1
                dfs(r, c)
    return count


# --- demo ---
grid = [
    ["1", "1", "0", "1"],
    ["1", "0", "0", "0"],
    ["0", "0", "1", "1"],
]
print(num_islands(grid))   # 3

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