**LeetCode #200 - Number of Islands**\nGiven a 2D grid consisting of '1's (land) and '0's (water), count the number of islands. An island is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You need to implement an algorithm that efficiently counts distinct islands in the grid.\n\n**Function Signature:** `def num_islands(grid: List[List[str]]) -> int:`\n\n**Example 1:**\nInput: `grid = [['1','1','0','0','0'],['1','1','0','0','0'],['0','0','1','0','0'],['0','0','0','1','1']]`\nOutput: `3`\nExplanation: There are 3 islands.\n\n**Example 2:**\nInput: `grid = [['1','1','1'],['0','0','0'],['1','1','1']]`\nOutput: `1`\nExplanation: Only one island exists.\n\n**Constraints:**\n- m == grid.length\n- n == grid[i].length\n- 1 <= m, n <= 300