Topic: graph-theory-problem / Level: advanced

• 2000. Implement the Bellman-Ford algorithm to detect negative weight cycles in a directed graph.
• 2001. Write a program to find the maximum flow in a network using the Dinics algorithm.
• 2002. Implement an algorithm to find the minimum cost flow in a flow network.
• 2003. Write a program to solve the "Chinese Postman Problem" for a directed graph.
• 2004. Implement Tarjans algorithm to find the strongly connected components of a directed graph.
• 2005. Write a program to compute the minimum cut in a flow network using the Stoer-Wagner algorithm.
• 2006. Implement an algorithm to find the maximum bipartite matching in a weighted bipartite graph.
• 2007. Write a program to solve the "Traveling Salesman Problem" using dynamic programming.
• 2008. Implement an algorithm to find the longest path in a directed acyclic graph (DAG).
• 2009. Write a program to check if a directed graph is strongly connected using Kosarajus algorithm.
• 2010. Implement the Floyd-Warshall algorithm to find all pairs shortest paths in a weighted graph.
• 2011. Write a program to compute the minimum spanning tree using Prims algorithm with a Fibonacci heap.
• 2012. Implement an algorithm to check if a graph is planar using Kuratowskis theorem.
• 2013. Write a program to find the maximum flow in a bipartite graph using the Hopcroft-Karp algorithm.
• 2014. Implement an algorithm to compute the diameter of a graph using two BFS/DFS traversals.
• 2015. Write a program to solve the "Steiner Tree Problem" in a weighted graph.
• 2016. Implement the Kahns algorithm for topological sorting in a directed graph.
• 2017. Write a program to find all articulation points and bridges in a graph using DFS.
• 2018. Implement an algorithm to calculate the chromatic number of a graph using graph coloring.
• 2019. Write a program to find all simple cycles in a directed graph using Johnsons algorithm.
• 2020. Implement an algorithm to find the maximum flow in a directed graph using the Edmonds-Karp method.
• 2021. Write a program to determine if a graph is a tree using its properties.
• 2022. Implement an algorithm to find the longest common subsequence using graph techniques.
• 2023. Write a program to find the minimum spanning tree using Boruvkas algorithm.
• 2024. Implement an algorithm to find the maximum weight independent set in a general graph.
• 2025. Write a program to calculate the number of Hamiltonian cycles in a directed graph.
• 2026. Implement an algorithm to find the minimum number of edges to remove to make a graph acyclic.
• 2027. Write a program to find all paths between two vertices in a directed graph.
• 2028. Implement an algorithm to check if a graph is bipartite using DFS and BFS.
• 2029. Write a program to compute the transitive closure of a directed graph using Warshalls algorithm.
• 2030. Implement an algorithm to find the longest path in a weighted graph using dynamic programming.
• 2031. Write a program to find the number of edge-disjoint paths in a directed graph.
• 2032. Implement an algorithm to calculate the maximum matching in a general graph using augmenting paths.
• 2033. Write a program to find the longest increasing path in a matrix represented as a graph.
• 2034. Implement an algorithm to find the shortest path using the A* search algorithm in a graph.
• 2035. Write a program to determine if a graph contains a Hamiltonian cycle using dynamic programming.
• 2036. Implement an algorithm to calculate the number of spanning trees in a directed graph.
• 2037. Write a program to find the minimum cut in a bipartite graph using the Max-Flow Min-Cut theorem.
• 2038. Implement an algorithm to solve the "Max-Cut Problem" in a graph.
• 2039. Write a program to find the longest simple cycle in a directed graph using backtracking.
• 2040. Implement an algorithm to check if two graphs are isomorphic using the degree sequence.
• 2041. Write a program to find all maximal cliques in a graph using the Bron-Kerbosch algorithm.
• 2042. Implement an algorithm to solve the "Feedback Vertex Set Problem" in a directed graph.
• 2043. Write a program to calculate the distance between any two pairs of vertices in a graph.
• 2044. Implement an algorithm to find the longest path that visits every edge in a weighted graph.
• 2045. Write a program to compute the average path length in a graph.
• 2046. Implement an algorithm to find the shortest path in a directed graph with negative edges.
• 2047. Write a program to determine if a directed graph can be 3-colored.
• 2048. Implement an algorithm to find the maximum weight matching in a bipartite graph using the Hungarian method.
• 2049. Write a program to find the longest path in a weighted directed acyclic graph using dynamic programming.

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