Graph Algorithms • Connected Components

Number of Islands

A fundamental problem in graph theory: identifying isolated regions in a grid. Each island is a maximal connected component of land cells.

Discovery Phase

We iterate through every cell. If we find land ('1') that hasn't been visited, we've found the start of a new island.

Upon finding new land, we use DFS to visit all reachable landmasses, marking them as visited so they aren't counted again.

In this simulation, we consider 4-directional connectivity (up, down, left, right). Diagonals do not connect landmasses.

DFS stops if we hit water ('0'), go out of bounds, or reach a cell that is already part of a discovered island.

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Graph Algorithms • Connected Components

A fundamental problem in graph theory: identifying isolated regions in a grid. Each island is a maximal connected component of land cells.

We iterate through every cell. If we find land ('1') that hasn't been visited, we've found the start of a new island.

Upon finding new land, we use DFS to visit all reachable landmasses, marking them as visited so they aren't counted again.

In this simulation, we consider 4-directional connectivity (up, down, left, right). Diagonals do not connect landmasses.

DFS stops if we hit water ('0'), go out of bounds, or reach a cell that is already part of a discovered island.