12-Strahler Numbers and Pruning Numbers

# 12-Strahler Numbers and Pruning Numbers - assign to a...

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Strahler Numbers and Pruning Numbers Binary Trees - Strahler Numbers Each node of a binary tree is assigned a Strahler as follows: All leaf nodes are assigned 1. If a node has only one successor, it is assigned the number of its successor otherwise it is assigned the larger of the numbers assigned to its successors if they have different numbers; if they have the same number it is assigned that number plus 1. The Strahler number assigned to the root is the Strahler number of the binary tree. Give some examples! Ordered Forests - Prunning Numbers A filament of a tree is a chain of nodes all of which have only one child except for the last node which is a leaf node and whose first node has at least one sibling or is the root. Give some examples! Pruning a forest means removing all the filaments. The pruning number of a forest is the number of times the forest has to be pruned before the forest is empty. An alternate algorithm for pruning number of a forest: Determine the pruning # of a tree by assigning 1 to each node with no subtrees and then
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Unformatted text preview: assign to a parent the maximum pruning number assigned to its children if only one child has such a maximum, and the maximum plus 1 if more than one child has the maximum. The pruning # of a forest is then the maximum of the pruning numbers of its trees. Give some examples! Assignment 6. Use the program from Assignment 5 (that generates all n node binary trees) to determine the number of n node binary trees with each possible Strahler number and also to determine the number of n node forests with each possible pruning number. These pruning numbers must be determined using the alternate algorithm. In this way, create a table that, for each n from 2 to as close to 20 as you can get (but at least 15), lists the number of n node binary trees with each possible Strahler number and the number of n node forests with each possible pruning number. What do you notice about the two tables?...
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