Topic: Graph-theory-question / Level: Advanced

• 400. Implement an algorithm to find the minimum cut in a flow network using the Max-Flow Min-Cut theorem.
• 401. Write a program to compute the strongly connected components of a directed graph using Kosaraju’s algorithm.
• 402. Create a function to find all articulation points in a graph.
• 403. Write a program to detect cycles in a directed graph using topological sorting.
• 404. Implement a function to find the shortest path in a weighted graph using the Floyd-Warshall algorithm.
• 405. Write a program to calculate the transitive closure of a directed graph using Warshall’s algorithm.
• 406. Create a function to determine if a directed graph is acyclic using Kahn’s algorithm.
• 407. Write a program to find the longest path in a directed acyclic graph (DAG) using dynamic programming.
• 408. Implement a function to find the maximum bipartite matching in a bipartite graph using the Hopcroft-Karp algorithm.
• 409. Write a program to find the maximum flow in a flow network using the Edmonds-Karp algorithm.
• 410. Create a function to determine the minimum spanning tree using Kruskal's algorithm.
• 411. Write a program to compute the chromatic number of a graph using backtracking.
• 412. Implement a function to find the longest common subsequence between two sequences using dynamic programming.
• 413. Write a program to check if a graph is Hamiltonian by finding a Hamiltonian cycle.
• 414. Create a function to find all maximal independent sets in a graph.
• 415. Write a program to compute the centrality of vertices in a graph using various centrality measures.
• 416. Implement an algorithm to solve the Traveling Salesman Problem using dynamic programming.
• 417. Write a program to find the shortest path that visits all nodes in a graph (Chinese Postman Problem).
• 418. Create a function to perform graph coloring using a greedy algorithm.
• 419. Write a program to determine the Eulerian path or circuit in a graph.
• 420. Implement a function to find the smallest dominating set in a graph.
• 421. Write a program to calculate the longest increasing path in a 2D matrix.
• 422. Create a function to find the largest strongly connected component in a directed graph.
• 423. Write a program to compute the minimum spanning tree of a weighted graph using Prim’s algorithm.
• 424. Implement a function to find all topological sorts of a directed acyclic graph (DAG).
• 425. Write a program to compute the maximum clique in an undirected graph using a backtracking approach.
• 426. Create a function to find the shortest path in a grid with obstacles using A* search.
• 427. Write a program to find the min-cost max-flow in a flow network using the Successive Shortest Path algorithm.
• 428. Implement a function to calculate the flow network's capacity for each vertex.
• 429. Write a program to find all pairs shortest paths in a weighted graph using the Floyd-Warshall algorithm.

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