DFS goes as deep as possible before going back.

What is a Graph?

A graph is just a collection of nodes (also called vertices) and connections between them (called edges). Example:

Graphs can represent:

• Maps
• Networks
• Friendships (like Facebook friends graph)
• Game paths
• And more!

🧠 So What is DFS?

DFS (Depth-First Search) is a way to explore a graph by going as deep as possible down one path before backtracking.

Think of it like exploring a maze:

1. Choose a direction.
2. Keep going forward.
3. If you reach a dead-end, go back to the last junction.
4. Try a different path.
5. Repeat until everything is explored.

🎨 Visual Thinking

Imagine each node has neighbors. DFS will:

• Visit a node
• Then visit the first neighbor
• Then the neighbor of that neighbor
• And so on…

It goes deep, not wide.

This is different from BFS (Breadth-First Search), which explores layer by layer.

🏁 When to Use DFS?

Use DFS when: ✅ You want to explore deep paths first ✅ You need to detect cycles ✅ You need to check if nodes are connected ✅ You’re searching possible solutions (like puzzles)

Code Example

link: https://leetcode.com/problems/keys-and-rooms/

var canVisitAllRooms = function(rooms) {
  const visited = new Set();

  function dfs(room) {
    if (visited.has(room)) return;

    visited.add(room);

    for (const key of rooms[room]) {
      dfs(key);
    }
  }

  dfs(0);

  return visited.size === rooms.length;
};