July 04, 2019
revaI implemented the following priority-queue/heap with an update-key operation. the update key uses the map from stl, which still requires lg(n) time for lookup. however, replacing it with an unordered_map would require the client program to write hash and equal operations for each class, which is a problem in my case.. In computer science, a heap is a specialized tree-based data structure which is essentially an almost complete tree that satisfies the heap property: if p is a parent node of c, then the key (the value) of p is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of c. the node at the "top" of the. At the moment stl heap does not support decrease key, however one can just change the value on the vector directly and call make_heap again which is o(n) time. however that's not as efficient as a binary heap decrease key which would take o(logn) time..
Hence updates only change the key in one direction. the problem in the implementation of decreasekey is not that it is only decreasing (rather than updating the value). for a binary heap there are quite efficient methods both for increasing and decreasing.. Loop invariant proof at the start of each iteration of the for loop of lines 2{ 3, each node i+1;i+2;:::;n is the root of a max-heap. we need to show that this invariant is true prior to the rst loop itera-. Given a starting key, and an ending key estimate the number of rows that will exist between the two. max_key may be empty which in case determine if start_key matches any rows. used by optimizer to calculate cost of using a particular index..