(18) Heaps

# (18) Heaps - Reading CMSC 132 Object-Oriented Programming...

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CMSC 132: Object-Oriented Programming II Department of Computer Science University of Maryland, College Park 1 Reading Read Section 8.5 in the Koffman text (Section 6.5 in the second edition) Complete binary trees A complete binary tree of height h is a tree where It's a perfect tree to level h-1 The leaves at level h are as far left as possible h = 2 h = 3 h = 1 3 Complete binary trees not allowed basic complete tree shape 4

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Heaps A heap is a binary tree with two key properties: It's complete The value in every node is less than or equal to the values in its subtrees A small example heap: X Y X Z Y X Z 5 Examples 6 2 22 8 45 25 6 2 22 8 45 25 5 6 22 25 5 5 45 8 6 45 5 6 45 2 22 8 6 25 Heap properties Heaps are balanced trees Height = log 2 (n) = O (log(n)) The smallest element of a heap can always be found easily A heap could be organized to easily be able to find the maximum value instead by ensuring that the value at every node is larger than the values in its subtrees
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(18) Heaps - Reading CMSC 132 Object-Oriented Programming...

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