Graphs mind map
Traverse, color, order, and search weighted graphs.
Core idea: Name the nodes and edges; then ask reachability, order, connectivity, or cheapest path.
Mnemonic: Model → mark → traverse · Cost: O(V + E) traversal
Reach: BFS layers
Signal: Edges are unweighted and the nearest state or fewest moves wins.
Move: Mark on enqueue, process one distance layer at a time, and stop at the first target.
Examples: Word Ladder, Shortest Grid Path, Open the Lock
Explore: DFS structure
Signal: You need components, cycles, coloring, or exhaustive reachability.
Move: Mark each node once; track parent, recursion state, or color when the property needs it.
Examples: Number of Islands, Clone Graph, Bipartite Graph
Organize: Dependencies & connectivity
Signal: Edges mean prerequisite order or undirected membership.
Move: Use indegrees for a topological order; union roots for evolving components.
Examples: Course Schedule, Alien Dictionary, Redundant Connection
Weigh: Cheapest frontier
Signal: Edges carry cost and the answer is a minimum route or spanning connection.
Move: Pop the cheapest unsettled frontier; relax neighbors, or join the cheapest safe component edge.
Examples: Network Delay, Cheapest Flights, Minimum Spanning Tree