Selection Trees What are selection trees Complete Each

Selection Trees

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

Diagram – max winner tree 9 9 8 9 5 8 7 9 4 3 7 5 8 8 5 5 8 4 1 8 5 5 2 4 6 5 6 3 4 8 1 0 9 2 7 0 1 3 3 … … … …

Diagram – max loser tree 4 5 5 7 9 7 9 4 5 4 8 5 5 8 4 5 8 5 5 8 4 6 2 7 3 4 3 3 0 3 1 6 0 1 2 1 … … … …

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