Discuss the time complexity of Dijkstra's algorithm and any potential optimizations to improve its performance.
- O((V + E) * log V) where V is vertices and E is edges
- O(V * E) where V is vertices and E is edges
- O(V log V + E log V) with Fibonacci heap
- O(V^2) with adjacency matrix, O(E + V log V) with heap
Dijkstra's algorithm has a time complexity of O((V + E) * log V) using a binary heap. Various optimizations can be applied, such as using a Fibonacci heap to achieve a time complexity of O(V log V + E log V). These optimizations aim to reduce the overall complexity, making Dijkstra's algorithm more efficient for large graphs.
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