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Graph Search Algorithms

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Dijkstra's Algorithm

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Finds the shortest paths from a single source to all other nodes in a weighted graph with non-negative weights. Time complexity: O(V^2) or O(E+V log V) with a priority queue.

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A* Search Algorithm

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Finds the shortest path in a weighted graph using heuristics to guide its search. Time complexity: O(E), where E is the number of edges, with the proper heuristic.

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Bellman-Ford Algorithm

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Computes shortest paths from a single source vertex to all other vertices in a weighted graph. Capable of handling negative weights. Time complexity: O(VE).

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Prim's Algorithm

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A greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. Time complexity: O(V^2) or O(E+V log V) with a binary heap.

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Breadth-First Search (BFS)

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Explores the neighbor nodes at the present depth prior to moving on to nodes at the next depth level. Time complexity: O(V+E) for both adjacency list and matrix.

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Floyd-Warshall Algorithm

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Finds shortest paths between all pairs of vertices in a weighted graph with positive or negative edge weights (but no negative cycles). Time complexity: O(V^3).

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Kruskal's Algorithm

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A greedy algorithm that finds a minimum spanning tree for a connected weighted graph by adding increasing cost edges at each step. Time complexity: O(E log E) or O(E log V).

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Depth-First Search (DFS)

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Explores as far as possible along each branch before backtracking. Time complexity: O(V+E) for adjacency list, O(V^2) for adjacency matrix.

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