Unformatted text preview: binary tree,
• nothing else is a complete binary tree. T1 T2 T1 complete binary tree Dept. of Computer Science, University of Toronto, St. George Campus T2 T3 complete ternary tree
Page 1 of 2 CSC 236 H1S Homework Assignment # 1 Winter 2012 Similarly, we can deﬁne complete ternary tree s:
• a single node is a complete ternary tree, • if T1 , T2 , and T3 are complete ternary trees with the same height, then the tree constructed
by placing T1 , T2 , and T3 under a new root node (as illustrated above on the right) is also
a complete ternary tree,
• nothing else is a complete ternary tree.
A coloured complete ternary tree is a complete ternary tree in which every leaf node has been assigned one
of two colours (red or blue). Only the leaves are coloured — internal nodes are colourless.
A subtree of a tree T is a subset of T ’s leaves along with all of the leave’s ancestors (and the edges connecting
them). Every complete ternary tree contains many complete binary subtrees — simply pick two children to
keep and one to remove for every internal node.
A monochromatic complete binary subtree of a coloured complete ternary tree is...
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 Winter '09
 Logic, Mathematical Induction, Recursion, complete ternary tree

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