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PWorst Space ability [Remarks I fom) Constant [Stable ‘| « iStable Constant |Stable In the best case (already sorted), every insert requires constant time Constant Stable ullling the arvay prior to sorting) car help aveid — y sorted array Randomly picking, a pivel value (or ‘worst cage scenarios such as 2 Time | erage (Best Worst Priority Queue ae Unsorted array Sorted array Binary heap insertion __0(1) | __ insertion O(n) insertion O(log n) Remove min O(n) | Remove min O(1) Remove min O(log n) initialize initialize O(n*log n) peeking ot1) | | | e Heapsort if the priority queue is implemented with a heap. ¢ Selection sort if the priority queue is implemented with an unordered array. ¢ Insertion sort if the priority queuc is implemented with an ordered array. Dijkstra's original algorithm does not use a min-priority queue and runs in O(|V]*). The common implementation based on a min-priority queue implemented by a Fibonacci heap and running in O(|E| + |V| log | V|) is due to (Fredman & Tarjan 1984). This is asymptotically the fastest known single- source shortest-path algorithm for arbitrary directed graphs with unbounded nonnegative weights. Fibonacci heap and adjacency list O(E + V log V) Using a more sophisticated Fibonacci heap, this can be brought down to O(£ + V log V), which is asymptoticaily faster when the graph is dense enough that E is Q(V). 
