Find Each Island's Maximum Height

# Find Each Island's Maximum Height A rectangular grid uses 0 for water and a positive integer for each land cell's height. Land cells connect only through shared edges. Find the maximum height in every island. ### Function Signature ```text island_max_heights(grid: list[list[int]]) -> list[int] ``` ### Valid Input Domain The grid is rectangular and may be empty. Values are nonnegative integers; zero is water and any positive value is land. ### Exact Output Semantics Discover islands by scanning cells in row-major order. Return one maximum per island in that discovery order, where an island's discovery key is its first row-major land cell. This ordering makes the result canonical. ### Constraints - 0 <= rows, columns <= 1,000. - rows * columns <= 1,000,000. - 1 <= land height <= 10^9. ### Public Examples #### Example 1 Input: grid = [[1, 0, 4], [2, 0, 3]] Output: [2, 4] The left island has maximum 2, and the right island has maximum 4; the left one is discovered first. #### Example 2 Input: grid = [[0, 0], [0, 0]] Output: [] There are no land cells and therefore no islands. ### Hints - Extend the ordinary island traversal with a running maximum for the current component. - The outer row-major scan determines output order; neighbor visitation order does not.