Selection Trees. What are selection trees? Complete binary tree Each node represents a “match” Winner Trees Loser Trees.

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Presentation transcript:

Selection Trees

What are selection trees? Complete binary tree Each node represents a “match” Winner Trees Loser Trees

Diagram – max winner tree … … … … … … … … 7

Diagram – max loser tree … … … … … … … … 7

Runtimes Complexities Initialize  r = the number of runs = number of leaf nodes  r-1 comparison nodes  O(r) to initialize r-runs Compare  O(1) Remove winner and Replay  O(logr) Total Time for n elements  O(nlogr)

What’s this good for? External Sorting Package Loading Problem

Truck Loading Problem n parcels from r sources each parcel has a weight and a size minimize the number of trucks

First Fit Packing with Max Winner Tree Use a max winner tree in which n parcels are t trucks  One at a time in left to right order  Current item is packed in the left-most into which it fits  If there is no truck into which it fits, start a new truck

Best Fit Object is packed into the bin with the least unused capacity that is at least the size of the object  If conditions are not met, start a new truck