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Fibonacci Heap

Fibonacci Heaps were introduced in Fibonacci heaps and their uses in improved network optimization algorithms by Fredman and Tarjan in 1987.

This implementation in C++ was guided by the Introduction to Algorithms book by Cormen, Leiserson, Rivest and Stein.

Usage

The Fibonacci Heap is implemented in the FibonacciHeap.hpp header file. It is templated on the type of the elements it stores. The Fibonacci Heap is a min-heap, i.e. the element with the smallest key is always at the top. This implementation supports the following operations:

  • insert(key): Inserts a new element with the given key into the heap.
  • unite(other_heap): Unites the heap with the given heap. The other heap is empty afterwards.
  • getMin(): Returns the smallest key in the heap.
  • extractMin(): Returns the smallest key in the heap and removes it from the heap.
  • decreaseKey(element, new_key): Decreases the key of the given element to the new key. The new key must be smaller than the old key.
  • deleteElement(element): Deletes the given element from the heap.
  • isEmpty(): Returns whether the heap is empty.

Visualization

The Fibonacci Heap can be visualized using the inherited class implemented in FibonacciHeapViz.hpp. The visualization is done using the GraphViz library in the dot format. The FibonacciHeapViz class has a method that dumps the current state of the heap to the given std::ostream, which can be a file or the standard output:

  • exportDot(ostream): Exports the current state of the heap to the given std::ostream.

Example

Refer to the main.cpp file for an example on how to use the Fibonacci Heap with the following final result visualized using GraphViz:

Example Visualization

References

Michael L. Fredman and Robert Endre Tarjan. 1987. Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34, 3 (July 1987), 596–615. https://doi.org/10.1145/28869.28874

Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. 2009. Introduction to Algorithms, Third Edition (3rd. ed.). The MIT Press.