Graph Cost

🔥 minimum spanning tree → MST is defined by minimizing the total edge weights; its greedy algorithms (Kruskal, Prim) and correctness proofs rely on cost orderings and cut/cycle comparisons derived from the graph's weight model.

🔥 shortest path → Shortest path algorithms minimize cumulative edge weights; the cost model defines path weight and dictates algorithm choice (e.g., non-negative costs -> Dijkstra, negative edges -> Bellman-Ford).

🔥 maximum spanning tree → A maximum spanning tree is defined by maximizing the sum of edge costs; it requires a well-defined edge-weight (cost) function and comparisons over those costs. Algorithm choices (e.g., Kruskal/Prim variants) operate by ordering edges by cost and rely on properties of the cost model (ties, negative weights, density).

🌟 greedy algorithm →

🌟 single-pair shortest path →

🌟 all-pairs shortest path →

🌟 single-source shortest path →

⭐️ prim algorithm →

⭐️ kruskal algorithm →

⭐️ dijkstra algorithm →

⚡️ network flow →

⚡️ max flow →

⚡️ min cut →