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

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.