Given a grid representing land and water, count the number of distinct islands. An island is formed by connected land cells.

You are given balloons arranged in a line, each with a number. Bursting a balloon yields points based on its value and its neighbors; maximize your total points by strategically choosing the burst order.

Find the length of the longest strictly increasing subsequence within a given array of numbers. A subsequence doesn't need to be contiguous, but the elements must maintain their original order.