Number of Islands
mediumTime: O(m * n)Space: O(m * n)
Signals to notice
count connected regionsgrid of 1s and 0sflood fill
Brute force first
No simpler alternative — graph traversal is the natural approach. That direct path helps you understand the question, but it tends to treat every possibility as brand new instead of learning from earlier steps.
The key insight
DFS/BFS from each unvisited '1', mark all connected land. The goal is not to be clever for its own sake, but to remember the one relationship that keeps the solution grounded as you move forward.
What must stay true
Each DFS/BFS call discovers one complete island and marks it as visited. If that remains true after every update, the rest of the reasoning has a stable place to stand.
Easy way to go wrong
Not marking cells as visited — causes infinite loops or double counting. The fix is usually to return to the meaning of each move, not just the steps themselves.