Number of Islands

Medium

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Given a 2D grid grid where '1' represents land and '0' represents water, count and return the number of islands.

An island is formed by connecting adjacent lands horizontally or vertically and is surrounded by water. You may assume water is surrounding the grid (i.e., all the edges are water).

Example 1:

Input: grid = [
    ["0","1","1","1","0"],
    ["0","1","0","1","0"],
    ["1","1","0","0","0"],
    ["0","0","0","0","0"]
  ]
Output: 1

Example 2:

Input: grid = [
    ["1","1","0","0","1"],
    ["1","1","0","0","1"],
    ["0","0","1","0","0"],
    ["0","0","0","1","1"]
  ]
Output: 4

Constraints:

1 <= grid.length, grid[i].length <= 100
grid[i][j] is '0' or '1'.

Recommended Time & Space Complexity

You should aim for a solution with O(m * n) time and O(m * n) space, where m is the number of rows and n is the number of columns in the grid.

Hint 1

An island is a group of 1's in which every 1 is reachable from any other 1 in that group. Can you think of an algorithm that can find the number of groups by visiting a group only once? Maybe there is a recursive way of doing it.

Hint 2

We can use the Depth First Search (DFS) algorithm to traverse each group independently. We iterate through each cell of the grid. When we encounter a 1, we perform a DFS starting at that cell and recursively visit every other 1 that is reachable. During this process, we mark the visited 1's as 0 to ensure we don't revisit them, as they belong to the same group. The number of groups corresponds to the number of islands.

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