Considering $n$ number of pieces of data, what would Dijkstra's shortest path algorithm time complexity be if it was stored using a data structure with following properties?
• delete the record with the minimum value of the key (complexity $O(log n)$);
• decrease the key of some record (complexity $O(1)$);
• find the record with the minimum value of the key (complexity $O(1)$);
• insert a new record (complexity $O(1)$).
I think it would be $O(nlogn)$, but am having trouble proving it. Does anyone have suggestions? Thanks!
