Added documentation for Prims algorithm
Added documentation for Prims algorithm as well as links to all different Implementation.pull/1151/head
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# Prim's Algorithm Documentation
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Prim's algorithm is a greedy algorithm used for finding the minimum spanning tree (MST) of a weighted graph. It starts with an arbitrary vertex and grows the tree by adding the minimum weight edge that connects a vertex in the tree to a vertex outside of the tree. The algorithm continues until all vertices are included in the tree.
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## Key Features of Prim's Algorithm
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- Greedy approach: Prim's algorithm follows a greedy approach by always selecting the edge with the minimum weight that connects a vertex in the tree to a vertex outside of the tree.
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- Minimum spanning tree: Prim's algorithm produces a minimum spanning tree, which is a tree that spans all vertices in the graph and has the minimum total edge weight among all such trees.
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## Algorithm Steps
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1. Start with an arbitrary vertex as the root of the tree.
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2. Maintain a set of vertices in the tree and a set of vertices outside of the tree.
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3. Find the minimum weight edge that connects a vertex in the tree to a vertex outside of the tree, and add the edge and the new vertex to the tree.
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4. Repeat step 3 until all vertices are included in the tree.
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## Time and Space Complexity
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The time complexity of Prim's algorithm is O(E log V), where E is the number of edges and V is the number of vertices. The space complexity is O(V), as the algorithm only needs to store the vertices that are in the tree and outside of the tree.
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## Implementation
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- [C](../../../algorithms/C/Graphs/Prim's-algorithm.c)
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- [C++](../../../algorithms/CPlusPlus/Graphs/prim's_algorithm.cpp)
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- [Java](../../../algorithms/Java/graphs/Prims.java)
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## Video URL
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[Youtube Video about Prims Algorithm ](https://www.youtube.com/watch?v=ZtZaR7EcI5Y)
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## Others
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[Wikipedia](https://en.wikipedia.org/wiki/Prim%27s_algorithm)
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